Summer Internship Final Report

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Summer Internship Report

Topic: IMAGE PROCESSING

Operated at:

Department of Electrical & Electronics Engineering

Indian Institute of Technology Guwahati

Submitted by : Aravind N Kumar

BL.EN.U4EEE13006

Amrita School of Engineering Bengaluru

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IMAGE PROCESSING

AN INTERNSHIP REPORT

Submitted by

ARAVIND N KUMAR

BL.EN.U4EEE13006

in partial fulfillment of the award of the degree

of

BACHELOR OF TECHNOLOGY

IN

ELECTRICAL & ELECTRONICS

ENGINEERING

AMRITA SCHOOL OF ENGINEERING, BANGALURU

AMRITA VISHWA VIDYAPEETHAM

BANGALURU-560035

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ACKNOWLEDGEMENT

At first I would like to thank Dr. M.K.Bhuyan Associate Professor Department of EEE IIT

Guwahati for guiding me throughout this project so that the results could be achieved.

I express my sincere regards to the Department of Electrical & Electronics' Indian Institute

of Technology for providing the world class infrastructure and the resources for the internship.

I would take this opportunity to thank Dr. S. Ganguly Coordinator Summer Internship,

Department of EEE, IIT Guwahati for guiding me through the application process of

internship .

I would like to convey my thankfulness to Dr. Rakesh S. G., Associate Dean, Amrita school of

Engineering, Bangalore.

I also take this opportunity to thank Dr. Ravishankar S. Chairman, Electrical and Electronics

Engineering Department, for his motivation and valuable help during the project work. I would

be obliged to the support rendered by two teachers Mrs Sreekala M. Associate Professor & Mrs.

K.Sireesha Associate Professor department of EEE Amrita School of Engineering Bengaluru. I

express my sincere thanks to all the staff of Department of EEE for their kind help and

cooperation.I would also like to thank the Corporate & Industrial Relations (CIR)

department Amrita School of Engineering Bengaluru for providing support and encouragement

to take up this opportunity.

Above all, I thank my parents and the almighty for giving me the strength, courage and blessings

to complete this project.

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Table of Contents

1. Introduction ......................................................................................................................................... 6

1.1Image Processing ............................................................................................................................ 6

1.1.1Image Acquisition & Sampling .................................................................................................... 6

1.1.2 Sources of Image ........................................................................................................................ 6

1.1.3 Images and Digital images .......................................................................................................... 7

1.1.4Aspects of Image Processing ........................................................................................................ 8

1.1.4 Types of Digital Images .............................................................................................................. 9

2.Image Processing Toolbox .................................................................................................................. 10

2.1 Digital Image Representation ....................................................................................................... 10

2.2Coordinate Conventions ................................................................................................................ 10

2.3 Images as Matrices....................................................................................................................... 11

2.4 Reading Images ........................................................................................................................... 11

2.5 Displaying Images ....................................................................................................................... 12

2.6 Compression Ratio ....................................................................................................................... 12

2.7 Data Classes ................................................................................................................................ 13

2.7 Image Types ................................................................................................................................ 14

2.8 Converting between Image Classes and Types ............................................................................. 15

2.9 Array Indexing............................................................................................................................. 16

2.10 Matrix Indexing ......................................................................................................................... 17

2.11Arithmetic Operators .................................................................................................................. 18

2.12 A Model of the Image DegradationIRestoration Process ............................................................. 19

2.13 Adaptive Spatial Filters .............................................................................................................. 20

2.14 Histogram Equalization: ............................................................................................................. 21

2.15 Image Processing Toolbox Standard Spatial Filters .................................................................... 22

2.16 Nonlinear Spatial Filters............................................................................................................. 23

2.17 Lossless and lossy compression .................................................................................................. 24

2.18Discrete Cosine Transform .......................................................................................................... 24

2.18Canny Edge Detection ................................................................................................................ 26

2. Matlab & C Program Implementation ................................................................................................ 28

2.1 Image Arithmetic in MATLAB with example .......................................................................... 28

2.2 To write an m-function that computes the average intensity of an image. ...................................... 32

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2.3 M-function that multiplies two input images and outputs the product of the images, the maximum

and the minimum values of the product are computed and a normalized product image whose values

are in the range [0,1] .......................................................................................................................... 33

2.3 A matlab code to compute the ratio of the bytes in the two images. .............................................. 35

2.4 Write an M-function to compute the implementation of the following two dimensional image

function using for loops and vectorization. ......................................................................................... 37

f(x,y)=asin(u0x+v0y) .......................................................................................................................... 37

for x= 0,1,2,….M-1 and y=0,1,2,….N-1............................................................................................. 37

2.5To corrupt the original lenna image with impulse (Salt & Pepper ) noise of density 0.01.Attempt to

minimize the noise effects by using an appropriate spatial domain filter. ............................................ 39

2.6 To generate a bimodal Gaussian function. .................................................................................... 42

2.7 To extract a rectangular sub image from an image. ....................................................................... 44

2.8 To find the entropy of an image matrix........................................................................................ 45

2.9 To write an m function for Intensity Transformation, Intensity Scaling ......................................... 46

2.10 Program to find the error between two images/matrices. ............................................................. 51

2.11 To perform histogram equilisation. ............................................................................................. 52

2.12 Write a MATLAB code to perform the contrast stretching on the image. Show the original and

stretched image along with their histograms. ...................................................................................... 56

2.13To plot the histogram and bar graph of an image. ........................................................................ 58

2.14Coorrupt the original lenna of the image with a zero mean Gaussian noise,so that the SNR of the

noisy image is 5 dB.Attempt to minimize noise effects by using appropriate filters in spatial domain

and spectral domain. Indicate the cutoff frequency of the spectral domain filter.................................. 63

2.15 To Generate a 3X3 spatial averaging filter and to perform neighborhood averaging.To plot and

observe using fast Fourier transform .................................................................................................. 79

2.16 Read some images and convert them to binary images. Then to show/implement all the binary

image processing technique. .............................................................................................................. 87

2.17 To read an image having some textures and form the co-occurrence matrix. ............................... 89

2.18 (a)-To Load a test image and find the edges by gradient –based and Laplacian-based technique. 91

2.18 (b)-Canny Edge Detection .......................................................................................................... 92

2.19 Lossy Image Compression ....................................................................................................... 104

2.20 Capture a video footage of 1 min duration by a digital camera(Mega Pixels>7.0) and convert it to

frames(25frames/second) and read all the frames one by one .Then detect the edges of the moving

objects in the frame.......................................................................................................................... 116

References ....................................................................................................................................... 121

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Fundamentals Of Image Processing

1. Introduction

1.1Image Processing

Image Processing involves changing the nature of an image in order to either

1. Improve its pictorial information for human interpretation, or

2. Render it more suitable for autonomous machine perception

Digital image Processing involves using a computer to change the nature of the digital image.

The process of image processing in practical scenario include performing operations on image

such as edge detection & sharpening, removing noise from the image, removing motion blur, to

remove unnecessary information and obtain the coarse structure of the image.

1.1.1Image Acquisition & Sampling Sampling: It refers to the process of digitizing a continuous function. Sampling involves three

different types of sampling under sampling, critical sampling & oversampling.

Undersampling:In this condition the image is sampled at such a rate that it is not possible to

reconstruct the original function/image.

To ensure they have enough sampling points, we require that the sampling period is not greater

than one half the finest details in the function this can be explained by use of a criterion known

as the Niquist criterion.

Niqiust criterion can be simply explained as the sampling theorm,which says in effect that a

continuous function can be reconstructed from its samples provided that the sampling frequency

is at least twice the maximum frequency in the function. Here we consider image as our

continuous function of two variables and we wish to sample it to produce a digital image.

The procedure of under sampling often leads to a phenomenon called aliasing, the result is we

loose from useful information from the image and often the final resolution of the image is

affected.

1.1.2 Sources of Image Light is the predominant source of energy for images. Many digital images are captured using

visible light as the energy source this has the advantage of being safe ,cheap, easily detected and

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readily processed with suitable hardware. Two popular methods of producing a digital image are

digital camera and flat bed scanner.

CCD camera stands for “charge-coupled device". This is an array of light sensitive cells called

“photo sites” each of which produces a voltage proportional to the intensity of light falling on

them. Colors are obtained by the use of the red, green and blue filters.CCDs are used in most

digital cameras as they produce good results, can be made high resolution with robust noise. A

complimentary technology is the use of CMOS(Complementary Metal Oxide

Semiconductors),They have advantage of being cheaper to provide and require less power than a

CCD chip, but they are more susceptible to noise.

For a camera attached to a computer it is more efficient and convenient to output to a convenient

storage medium using a card called frame grabbing card. Large number of images are copied to a

permanent storage.

The output image will be an array of values, each representing a sampled point from the original

scene. The elements of this array are called picture elements or simply pixels.

Flat bed scanners work on the principle similar to the CCD camera instead of the entire image

being captured at once the on a large array a single row of photo sites is moved across the image

capturing the entire row as it moves.

Other sources include various components of the electromagnetic spectrum. Visible light is a part

of the electromagnetic spectrum. For microscopy we use x-rays or electron beams. An additional

method of obtaining images is by the use of x-ray tomography, where an object is encircled by

an x-ray beam. The image of the beam is detected such an image is called tomogram. In CAT

scan (computed axial tomography) scan the patient lies within a tube around which the x-ray is

fired. This enables large sections of topographic images in 3D view.

1.1.3 Images and Digital images

If a monochromatic photo is taken the image will have a 2D function where the function velues

give the brightness of the image at any given point. The brightness and darkness values range

between a maxima and a minimal.

**digital image differs from a photo in which all values are discrete.

A digital image can be considered as a large array of sampled points from the continuous image,

each point with a quantized brightness these points are called pixels, which constitute the digital

image. The matrix points around the pixel of consideration form the neighborhood of the pixel.

Applications

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Enormous applications

1. Medicine-Xrays, MRI or CAT scans

2. Analysis of cell image or chromosome karyotypes.

3. Agriculture-Satellite imaging of land, vegetation.

4. Industry-Inspection of item in a production line

5. Law enforcement-Fingerprint analysis, sharpening blurring of speed camera images.

1.1.4Aspects of Image Processing

There are different image processing algorithms such as

IMAGE ENHANCEMENT : Processing an image so that the result is more suitable for a

particular application is called image enhancement.

Sharpening or deblurring an out of focus image

Highlighting edges

Improving images contrast or brightening an image

Removing noise

IMAGE RESTORATION: An image may be restored by the damage done to it by an

unknown cause.

Removing of blur caused by linear motion

Removal of optical distortion

Removal of periodic interference

IMAGE SEGMENTATION: Segmentation involves subdividing an image into constituent

parts or isolating certain aspects of an image including

Finding lines, circles or particular shapes in an image and

Identifying cars,trees,buildings roads in an aerial photograph

Image Processing task

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1 Acquiring the image through a CCD or flat bed scanner.

2 Preprocessing is the task in which it is checked whether the image is compatible for the

processing operations to be performed.

3 Segmentation is performed to check which part of the image has to be extracted.

4 Representation & description the process of extraction allows us to differentiate between

objects.

5 Recognition and Interpretation means to assign labels to objects based on their

description’s and assigning meanings to those labels.

1.1.4 Types of Digital Images

1 Binary:Each pixel is either just black or white.Ther are only two possible values for a pixel

we need only 1 bit per pixel.Such images therefore be very efficient in terms of storage .

Applications: text , fingerprints, architectural plans

2 Greyscale Each pixel is a shade of gray,normally from 0(black) to 255(white).It can be

represented in 8bits.

3 True color or red-blue-green:Here each pixel has a particular color, that being described

by blue,green,red in it.If each of these components range from 0 to 255 this gives a total of

255^3 different possible colors in an image.It is a stack of three matrices red,green and blue.

4 Indexed :Most of color images have only a small subset of the more than16 million possible

colors.For the conveience and storage the image has been associated with color maps or color

palatte which is simply a list of colors in that image,each pixel has a value which doesnot give its

color but the index to the color in the map.

It is possible for an image to have 256 colors or fewer but it will only require 1 byte to

store.Image formats like GIF onl allow 256 or fewer colors in the image.

Image Size

1 kb = 1000 bytes

1 mb = 1 million bytes

Binary images contain only one layer,greyscale contains 2 layers and color images contain 3

layers using the respective pixel resolution multiplied with the no of layesa gives the size.

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2.Image Processing Toolbox

Matlab gives the users the power to compute extensively the Image processing using certain

functions in the Image processing toolbox.The image processing tool box is a collection of

functions which gives MATLAB extended capablity other than the numerical capablity.

2.1 Digital Image Representation

An image may be defined as a two-dimensional function, f (x, y), where x and y are spatial

(plane) coordinates, and the amplitude of f at any pair of coordinates (x, y) is called the intensity

of the image at that point.The term gray level is used often to refer to the intensity of

monochrone images. Color images are formed by a combination of individual 2-D images. For

example, in the RGB color system, a color image consists of three (red, green, and blue)

individual component images. For this reason, many of the techniques developed for

monochrome images can be extended to color images by processing the three component images

individually.The conversion of an image into the digitized form requires sampling along the two

axes ,the digitization along the x axis is called sampling & the digitization along the y axis is

called quantisation.

2.2Coordinate Conventions The result of sampling and quantization is a matrix of real numbers.

Fig2.2.1 :The standard form of representation of images in Image

Processing

Assume that an image f(x, y) is sampled so that the resulting image has M rows and N columns.

We say that the image is of size M x N. The values of the coordinates (x, y) are discrete

quantities.Mostly the matlab IPT tool box refers to this system as pixel distribution but less

frequently, the toolbox also employs another coordinate convention called spatial coordinates,

which uses x to refer to columns and y to refers to rows. This is the opposite of our use of

variables x and y.

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2.3 Images as Matrices

A digital image can be represented naturally as a MATLAB matrix,where each element in the

matrix can be termed as a pixel.

Fig2.3.1: The matrix representation of the image

Matrices in MATLAB are stored in variables with names such as A, a, RGB, real-array, and so

on. Variables must begin with a letter and contain only letters, numerals, and underscores.

2.4 Reading Images

The general syntax for reading images is in the form

f=imread('filename');

Supported file formats are as shown in the table below:

Fig2.3.2: Supported formats in matlab

Function size gives the row and column dimensions of an image:

>> s i z e ( f )

Used in the following form to determine automatically the size of an image:

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>> [M, N ] = s i z e ( f ) ;

This syntax returns the number of rows (M) and columns (N) in the image.

The function whos f gives the additional information about the variable name, type ,size of the

variable etc.

2.5 Displaying Images

Images are displayed on the MATLAB desktop using function imshow, which has the basic

syntax:

To keep the first image and output a second image, we use function figure as follows:

>> figure, imshow(g)

Using the statement

>> imshow(f), figure, imshow(g)

Writing Images

Images are written to disk using function imwrite, which has the following basic syntax:

imwrite(f, 'filename')

In order to get an idea of the compression achieved and to obtain other image file details, we can

use function imf inf o, which has the syntax

imfinfo filename

2.6 Compression Ratio

This compression ratio was achieved while maintaining image quality consistent with the

requirements of the application.In addition to the obvious advantages in storage space, this

reduction allows the transmission of approximately 35 times the amount of uncompressed data

per unit time.

The information fields displayed by i m f i n f o can be captured into a so called structure

variable that can be used for subsequent computations.

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As an illustration, consider the following use of structure variable K to compute

the compression ratio for bubbles25. j pg:

>> K = imfinfo('bubbles25.jpg');

>r image-bytes = K.Width*K.Height*K.BitDepth/8;

>> compressed-bytes = K.FileSize;

>> compression-ratio = image-bytes/compressed_bytes

compression-ratio =

35.1612

More control over export parameters is obtained by using the print command:

print -fno -dfileformat -rresno filename print

where no refers to the figure number in the figure window of interest, fileformat refers to one of

the file formats

2.7 Data Classes

All numeric computations in MATLAB are done using double quantities, so this is also a

frequent data class encountered in image processing applications.The first eight entries in the

table are referred to as numeric data classes.The ninth entry is the char class and, as shown, the

last entry is referred to as the logical data class.

Data class double requires 8 bytes to represent a number, uint8 and i n t a require 1 byte each,

uintl6 and i n t l 6 require 2 bytes, and uint32,int32, and s i n g l e , require 4 bytes each.The char

data class holds characters in Unicode representation. A character string is merely a 1 x n array

of characters.A l o g i c a l array contains only the values 0 and 1, with each element being stored

in memory using one byte per element.

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Fig2.7.1: Different types of data types being used are as in the table above

2.7 Image Types The toolbox supports four types of images:

Intensity images

Binary images

Indexed images

RGB images

Most monochrome image processing operations are carried out using binary or intensity images,

so our initial focus is on these two image types.

Intensity Images

An intensity image is a data matrix whose values have been scaled to represent intensities. When

the elements of an intensity image are of class uint8, or class uint 16, they have integer values in

the range [O, 2551 and [O, 65.5351], respectively. If the image is of class double, the values are

floating-point numbers.

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Binary Images

A binary image is a logical array of 0s and Is. Thus, an array of 0s and Is whose values are of

data class, say, uint8. is not considered a binary image in MATLAB. A numeric array is

converted to binary using function l o g i c a l.

Thus, if A is a array consisting of 0s and Is, we create a logical array B using the statement

To test whether the array given is binary or not

Converting between Data Classes

Converting between data classes is straightforward. The general syntax is

2.8 Converting between Image Classes and Types It is necessary to convert the image datatype from one format to another inorder to compute

operations so to allow this the IPT tool box provides a certain set of fuctions such as

im2double,im2uint8etc.

Fig2.8.1: This table shows the various functions involved in the image data conversion from one

form to another

Converting an arbitrary array of class double to an array of class double scaled to the range [O,

1] can be accomplished by using function mat2gray whose basic syntax is

Function im2double converts an input to class double. If the input is of class uint8, uintl6, or l o

g i c a l , function im2double converts it to class double with values in the range [0, 1].

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We consider conversion between binary and intensity image types. Function im2bw, which has

the syntax

2.9 Array Indexing MATLAB supports a number of powerful indexing schemes that simplify array manipulation

and improve the efficiency of programs. In this section we discuss and illustrate basic indexing

in one and two dimensions (i.e., vectors and matrices).

The elements of such a vector are accessed using one-dimensional indexing.Thus, v (1 ) is the

first element of vector v, v (2) its second element, and soforth. The elements of vectors in

MATLAB are enclosed by square brackets and are separated by spaces or by commas. For

example,

> > v = [ 1 3 5 7 9 ]

v =

1 3 5 7 9

>> v(2)

ans =

.

5

A row vector is converted to a column vector using the transpose operator ( . ' ):

>> w = v.'

W =

1

3

5

7

9

To access blocks of elements, we use MATLAB's colon notation. For example, to access the first

three elements of v we write

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Function linspace, with syntax

generates a row vector x of n elements linearly spaced between and including a and b.

2.10 Matrix Indexing Matrices can be represented conveniently in MATLAB as a sequence of row vectors enclosed by

square brackets and separated by semicolons. For example, typing

>>A=[1 2 3 ; 4 5 6; 7 8 9]

A=

1 2 3

4 5 6

7 8 9

We select elements in a matrix just as we did for vectors, but now we need two indices: one to

establish a row location and the other for the corresponding column.

>> A(2, 3)

ans =

6

The colon operator is used in matrix indexing to select a two-dimensional block of elements out

of a matrix. For example,

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Here, use of the colon by itself is analogous to writing A( 1 : 3 , 3 ) , which simply picks the third

column of the matrix. Similarly, we extract the second row as follows:

2.11Arithmetic Operators

MATLAB has two different types of arithmetic operations. Matrix arithmetic perations are

defined by the rules of linear algebra. Array arithmetic operations are carried out element by

element and can be used with multidimensional arrays. The period (dot) character (.)

distinguishes array operations from matrix operations. For example, A*B indicates matrix

multiplication in the traditional sense, whereas A. *B indicates array multiplication, in the sense

that the result is an array, the same size as A and 6, in which each element 1s the of

corresponding elements of A and B. In other words, if C = A. *B,then C ( I , J ) = A ( I , J ) "6 ( I

, J ) . Because matrix and array operations are the same for addition and subtraction, the

character pairs . + and .- are not used.

Fig:2.11.1 Flow Control

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Fig:2.11.2 Image Restoration

2.12 A Model of the Image DegradationIRestoration Process The degradation process is modeled in this chapter as degradation function that, together with an

additive noise term, operates on an input image f ( x , y ) to produce a degraded image g(x, y):

g(x3y) = H [ f ( x , y ) l + V ( X, Y )

If His a linear, spatially invariant process, it can be shown that the degraded & I image is given

in the spatial domain by

g(x>Y ) = h( x7Y ) * f ( x ,Y ) + V ( X ,Y )

Noise Models

Adding Noise with Function imnoise

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the basic syntax

g = imnoise(f, type, parameters)

2.13 Adaptive Spatial Filters In certain cases adaptive filters are designed which can act based on the behaviour of the filters

at the time of image restoration which include the following types.

zmin = minimum intensity value in S,y, filtering.

zmax = maximum intensity value in Sxy

zmed = median of the intensity values in S,,

zxy = intensity value at coordinates ( x , y)

The syntax is

f = adpmedian(g, Smax)

f , corrupted by salt-and pepper noise, generated using the command

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g=imnoise(f, ' s a l t & pepper', .25);

With the use of the median filter we can filter out the noise which has corrupted the lenna of the

image, the syntax is as follows:

f = medfilt2(g, [7 7], 'symmetric');

Intensity Transformation Functions

The simplest form of the transformation T is when the neighborhood in is of size 1 X 1 (a single

pixel). In this case, the value of g at (x, y) depends only on the intensity o f f at that point, and T

becomes an intensity or gray-level transformation function. These two terms are used

interchangeably, when dealing with monochrome (i.e., gray-scale) images.

Function imadjust

Function imadjust is the basic IPT tool for intensity transformations of grayscale images. It has

the syntax

g = imadjust(f, [low-in high-in], [low-out high-out], gamma)

this function maps the intensity values in image f to new values in g, such that values between

low-in and high-in map to low-in high-in low-in high-in slues between low-out and high-out.

Values below low-in and above high-in are clipped; that is, values below low-in map to low-out,

and thoseabove high-in map to high-out. The input image can be of class uint8,uint16, or double,

and the output image has the same class as the input. All puts to function imad j ust, other than f,

are specified as values between 0 1, regardless of the class of f. If f is of class uint8, imad j ust

multiplies values supplied by 255 to determine the actual values to use; if f is of class uint 1 6,

the values are multiplied by 65535. Using the empty matrix ([ 1) for [low-in high-in] or for [low-

out high-out] results in the default values 0 1 1. If high-out is less than low-out, the output

intensity is reversed.

2.14 Histogram Equalization:

Histogram equalization is used to enhance contrast. It is not necessary that contrast will always

be increase in this. There may be some cases were histogram equalization can be worse. In that

cases the contrast is decreased.Intensity transformation functions based on information extracted

from image intensity histograms play a basic role in image processing, in areas such as

enhancement, compression, segmentation, and description.

The core function in the toolbox for dealing with image histograms is

imhist, which has the following basic syntax:

h = imhist (f , b)

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The f is the input image, h is its histogram, h(rk), and b is the number of bins used in forming the

histogram (if b is not included in the argument, b = 256 is used by default). A bin is simply a

subdivision of the intensity scale.

We obtain the normalized histogram simply by

p = imhist(f, b)/numel(f);

The simplest way to plot its his- EXAMPLE 3.4:

gram is to use imhist with no output specified:

The histogram display default in the tool. However, there are many other ways to plot a

histogram, and we take this oppurtunity to explain some of the plotting options in MATLAB that

are repsentative cof those used in image processing applications.

Histograms often are plotted using bar graphs. For this purpose we can use

bar(horz, v, w i d t h )

Histogram equalization is implemented in the toolbox by function histeq:

which has the syntax

g = histeq(f, nlev)

where f is the input image and nlev is the number of intensity levels specified for the output

image. If nlev is equal to L (the total number of possible levels in the input image), then histeq

implements the transformation function, T(rk), directly. If nlev is less than L, then histeq

attempts to distribute the levels so that they will approximate a flat histogram. Unlike imhist, the

default value in histeq is nlev = 64. For the most part, we use the maximum possible number of

levels (generally 256) for nlev because this produces a true implementation of the histogram-

equalization method just described.

2.15 Image Processing Toolbox Standard Spatial Filters

Linear Spatial Filters

The toolbox supports a number of predefined 2-D linear spatial filters, obtained by using

function f special, which generates a filter mask, w, using the syntax

w = fspecial ( ' typ l, parameters)

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where ' t y p e ' specifies the filter type, and parameters further define the specified filter. The

spatial filters supported by f special are summarized in table , including applicable parameters

for each filter.

Fig:2.12.1 Syntax and parameters of different filters

2.16 Nonlinear Spatial Filters

generates order-statistic filters (also called rank filter).

These are nonlinear spatial filters whose response is based on ordering (ranking) the pixels

contained in an image neighborhood and then replacing th ecall that the median. 5, of a set of

values is such that half the values in the set are less than or equal value of the center pixel in the

neighborhood with the value determined by the ranking result.

Because of its practical importance, the toolbox provides a specialized implementation of the 2-

D median filter:

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g = medf ilt2( f , [m n ] , padopt) k

where the tuple [m n] defines a neighborhood of size m x n over which median is computed, and

padopt specifies one of three possible padding options: ' zeros ' (the default), ' symmetric ' in

which f is extended symmetrically by mirror-reflecting it across its border, and 'indexed '

which f is padded with 1s if it is of class double and with 0s otherwise.The fault form bf this

function is 3

g = m e d f l l t 2 ( f ) i

which uses a 3 X 3 neighborhood to compute the median, and pads the border

of the input with 0s.

2.17 Lossless and lossy compression

Lossless and lossy compression are terms that describe whether or not, in the compression of a

file, all original data can be recovered when the file is uncompressed. With lossless compression,

every single bit of data that was originally in the file remains after the file is uncompressed. All

of the information is completely restored. The Graphics Interchange File (GIF) is an image

format used on the Web that provides lossless compression.

On the other hand, lossy compression reduces a file by permanently eliminating certain

information, especially redundant information. When the file is uncompressed, only a part of the

original information is still there (although the user may not notice it). Lossy compression is

generally used for video and sound, where a certain amount of information loss will not be

detected by most users. The JPEG image file, commonly used for photographs and other

complex still images on the Web, is an image that has lossy compression. Using JPEG

compression, the creator can decide how much loss to introduce and make a trade-off between

file size and image quality.

Image compression systems are composed of two structural blocks an encoder and a

decoder.Image f(x,y) is fed into the encoder,which creates a set of symbols from input data and

uses them to represent the image.If let n1,n2 denote the number of information carrying units in

the original and encoded images respectively,the compression that is achieved can be quantified

numerically via the compression ratio.

Cr=n1/n2

2.18Discrete Cosine Transform

The discrete cosine transform (DCT) represents an image as a sum of sinusoids of varying

magnitudes and frequencies. The dct2 function computes the two-dimensional discrete cosine

transform (DCT) of an image. The DCT has the property that, for a typical image, most of the

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visually significant information about the image is concentrated in just a few coefficients of the

DCT. For this reason, the DCT is often used in image compression applications. For example,

the DCT is at the heart of the international standard lossy image compression algorithm known

as JPEG. (The name comes from the working group that developed the standard: the Joint

Photographic Experts Group.

The two-dimensional DCT of an M-by-N matrix A is defined as follows

The values Bpq are called the DCT coefficients of A.

The DCT is an invertible transform, and its inverse is given by

The inverse DCT equation can be interpreted as meaning that any M-by-N matrix A can be

written as a sum of MN functions of the form

These functions are called the basis functions of the DCT. The DCT coefficients Bpq, then, can

be regarded as the weights applied to each basis function.

In accordance inorder to subdivide an image into blocks we use certain functions in matlab such

as blockproc() the general syntax of this function is as follows:

B = blkproc(A, [M N ] , FUN, PI, P2, . . . )

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B = im2col(A, [ M N ] , ' d i s t i n c t ' )

2.18Canny Edge Detection

The purpose of edge detection in general is to significantly reduce the amount of data in an

image, while preserving the structural properties to be used for further image processing.

The aim of JFC was to develop an algorithm that is optimal with

regards to the following

criteria:

1.Detection:

The probability of detecting real edge points should be maximized while the probability of

falsely detecting non-edge points should be minimized. This corresponds to maximizing the

signal-to-noise ratio.

2. Localization:

The detected edges should be as close as possible to the real edges.

3.Number of responses:

One real edge should not result in more than one detected edge (one can argue that this is

implicitly included in the first requirement). With JFC’s mathematical formulation of these

criteria, Canny’s Edge Detector is optimal for a certain class of edges (known as step edges).

The Canny Edge Detection Algorithm

The algorithm runs in 5 separate steps:

1.Smoothing:

Blurring of the image to remove noise.

2.Finding gradients:

The edges should be marked where the gradients of the image has large magnitudes.

3. Non-maximum suppression:

Only local maxima should be marked as edges.

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4. Double thresholding:

Potential edges are determined by thresholding.

5. Edge tracking by hysteresis:

Final edges are determined by suppressing all edges that are not connected to a very certain

(strong) edge

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2. Matlab & C Program Implementation

2.1 Image Arithmetic in MATLAB with example

Image Arithmetic

An image is represented in a matrix format. To perform image arithmetic the size of the two

matrices should be same. The operation on two images results in a new image. Consider two

images A and B with same size.

Image Addition

In a RGB image, the addition of two images can be done using the ‘+’ operator. C=A+B;

Here, the minimum value of A+B and 255 is taken.

(i.e) C(i,j,1)=min(A(i,j,1)+B(i,j,1),255) where (i,j) represents the pixel position.

Image addition can be used to add the components from one image into other image.

Program Code

B=imread('jerry.png')

C=imread('tom2.png')

D=C+B;

imshow(D)

Input : The image pixel size is 320 X 320

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Output

D(i,j,1)=min(B(i,j,1)+C(i,j,1),255) where (i,j) represents the pixel position.

Image addition can be used to add the components from one image into other image.

Image Multiplication

Image multiplication is used to increase the average gray level of the image by multiplying with

a constant.

It is used for masking operations.

C=A.*B;

Program Code



D=C.*B;

imshow(D)

Output:

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Image Division

Image division can be considered as multiplication of one image and the reciprocal of other

image.

C=A.\B;

Logical Operations:

Logical operations are done on pixel by pixel basis.

The AND and OR operations are used for selecting subimages in an image.

This masking operation is referred as Region of Interest processing.

Logical AND

To isolate the interested region from rest of the image portion logical AND or OR is used.

Consider a mask image L for the image A.

To obtain the interested area, D= and(L,A) ;

We can use L&A also.

The resulting image will be stored in D which contains the isolated image part.

Program Code



D= and(B,C) ;

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%the output is logical array of zeros and ones the input array becomes logical and binary hard to

display in @ 2D

Logical OR

Syntax: D= or(L,A). We can also use L|A

To find the MAXIMUM or MINIMUM values

PROGRAM CODE:



D=C.*B;

>>maxP = max(P(:));

>> E

E =

1

>> F=min(D(:));

>> F

F =

0

Aim

To wirte a program to vertically flip an image.

Code:

>> fp=imread('tom2.png');

>> fc = fp(end: -1 : 1 , : );

>> imshow(fc)

>> figure,imshow(fp)

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Input Output

2.2 To write an m-function that computes the average intensity of an

image.

Code:

>> A=imread('jerry.png');

>> n=numel(A)

n =

307200

>> av=sum(A(:))/numel(A)

av =

38.4374

>>whos A

Name Size Bytes Class Attributes

A 320x320x3 307200 uint8

Script function saved in matlabfile average.m

function av = average(A)

%"AVERAGE Computes the average value of an array.

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% AV = AVERAGE(A) computes the average value of input

% array, A, which must be a I-D o r 2-D array.

% Check the validity of the input . (Keep in mind that

% a I-D array is a special case of a 2-D array.)

if ndims(A) > 2

error ( ' The dimensions of the input cannot exceed 2 . ' )

end % Compute the average

av = sum(A(:))/length( A ( : ) ) ;

The input image

Result

The average intensity of the image was computed and its average intensity was obtained as

38.4374.

2.3 M-function that multiplies two input images and outputs the

product of the images, the maximum and the minimum values of the

product are computed and a normalized product image whose

values are in the range [0,1] Code

A=imread('jerry.png')

B=imread('tom2.png');

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[F,K]=sumprod(A,B)

imshow(F)

imshow(K)

subscript name sumprod.m

function [s,p] = sumprod(f,g)

s=f+g;

p=f.*g;

Output

Product

SUM

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Output

An mfile was written to add and multiply two different images.

Code

A=imread('jerry.png');


C=A.*B;

>> t=max(max(max(C)));

>> t

t =

255

>> t=min(min(min(C)));

>> t

t =

0

Result:The maximum value obtained was 255 and the minimum value obatained was 0

2.3 A matlab code to compute the ratio of the bytes in the two images.

Program Code

function cr = imratio(f1, f2)

%IMRATIO Computes the ratio of the bytes in two images/variables.

% CR = IMRATIO(F1, F2) returns the ratio of the number of bytes in

% variables/files F1 and F2. If F1 and F2 are an original and

% compressed image, respectively, CR is the compression ratio.

error(nargchk(2, 2, nargin)); % Check input arguments

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cr = bytes(f1) / bytes(f2); % Compute the ratio

%-------------------------------------------------------------------%

function b = bytes(f)

% Return the number of bytes in input f. If f is a string, assume

% that it is an image filename; if not, it is an image variable.

if ischar(f)

info = dir(f); b = info.bytes;

elseif isstruct(f)

% MATLAB's whos function reports an extra 124 bytes of memory

% per structure field because of the way MATLAB stores

% structures in memory. Don't count this extra memory; instead,

% add up the memory associated with each field.

b = 0;

fields = fieldnames(f);

for k = 1:length(fields)

b = b + bytes(f.(fields{k}));

end

else

info = whos('f'); b = info.bytes;

end

Execution Sequence in Command window



r = ratio(A,B)

r =

1

Result

The Code to compute the ratio of the bytes in the two images was computed and the result was

obtained.

mfile:ratio.m

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2.4 Write an M-function to compute the implementation of the

following two dimensional image function using for loops and

vectorization.

f(x,y)=asin(u0x+v0y)

for x= 0,1,2,….M-1 and y=0,1,2,….N-1

Code:

>> f=imread('tom2.png');

>> [rt,f,g] = twodsin(1,1/(4*pi),1/(4*pi),512,512);

rt

rt =

1.1353e+003

>> g=mat2gray(g);

imshow(g)

matlab function

m file :twodsin.m

function [rt,f,g] = twodsin(A,uO,vO,M,N)

%TWOCISIN Compares f o r loops vs. v e c t o r i z a t i o n .

% The comparison i s based on implementing the f u n c t i o n

% f ( x , y) = Asin(u0x + vOy) f o r x = 0, 1, 2, ..., M - 1 and

% y = 0, 1, 2, ..., N - 1. The i n p u t s t o t h e f u n c t i o n are

% M and N and the constants i n the f u n c t i o n .

% F i r s t implement using f o r loops.

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tic % S t a r t t i m i n g .

for r = 1:M

uOx = uO*(r - 1 ) ;

for c = 1 : N

vOy = vO*(c - 1 ) ;

f(r,c)= A*sin(uOx+vOy);

end

end

t1= toc; % End t i m i n g .

% Now implement using v e c t o r i z a t i o n . C a l l the image g.

tic % S t a r t timing.

r=0:M-1;

C=0:N - 1;

[C, R] = meshgrid(c, r ) ;

g = A*sin(uO*R + vO*C);

t2 = toc; % End t i m i n g .

% Compute the r a t i o of the two times.

rt = t1/(t2+eps); % Use eps i n case t 2 is close t o 0.

Input Image f becomes

Output

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2.5To corrupt the original lenna image with impulse (Salt & Pepper

) noise of density 0.01.Attempt to minimize the noise effects by using

an appropriate spatial domain filter. Code:

>> B=imread('tom2.png'); % B is an array to read the image tom2.png

>> J = imnoise(B,'salt & pepper',0.01); % adding 0.01 density of noise

>> imshow(J) %display the noise added image

%Now to remove the corrupt image there are linear and nonlinear spatial filters here first I am

using linear filter

>> w=fspecial('laplacian',0)

w =

0 1 0

1 -4 1

0 1 0

>> g1=imfilter(J,w,'replicate');

>> imshow(g1)

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>>g2=im2double(f);

>>g2=imfilter(J,w,'replicate');

>> imshow(g2)

Output

Image before adding Salt & Pepper Image after adding Salt & Pepper noise

After linear filtering the corrupted image g2 image

Program 2

Page 41 of 122

Aim

To corrupt the original lenna image with impulse (Salt & Pepper ) noise of density 0.01.Attempt

to minimize the noise effects by using an appropriate spatial domain filter.

Code

>> B=imread('tom2.png'); % B is an array to read the image tom2.png

>> J = imnoise(B,'salt & pepper',0.01); % adding 0.01 density of noise

>> imshow(J) %display the noise added image

%Now to remove the corrupt image there are linear and nonlinear spatial filters here first I am

using linear filter

>> w4=fspecial('Laplacian',0);

>> w8=[111;1-81;111];

>> J=im2double(J);

>> g4=J-imfilter(J, w4, 'replicate');

>> g8 = J - imfilter(J, w8, 'replicate');

>> imshow(J)

>> figure, imshow(g4)



Output

g1 g2

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g4 g5

Result

The image was rectified using linear spatial filter

2.6 To generate a bimodal Gaussian function. Code:

%M-file:twomodegauss.m

function p = twomodegauss(m1,sig1,m2,sig2,A1,A2,k )

%TWOMODEGAUSS Generates a bimodal Gaussian function.

% P = TWOMODEGAUSS(M1, SIG1, M2, SIG2, Al, A2, K) generates a bimodal,

% Gaussian-like function i n the interval [0, I ] . P is a 256-element

% vector normalized so that SUM(P) equals 1 . The mean and standard

% deviation of the modes are (MI, SIG1) and (M2, SIG2), respectively.

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% A1 and A2 are the amplitude values of the two modes. Since the output is normalized, only

the relative values of A1 and A2 areimportant. K is an offset value that raises the "floor" of the

%function. A good set of values to try is MI = 0.15, SIGI = 0.05,M2 = 0.75, SIG2 = 0.05, A1 =

1, A2 = 0.07, and K - 0.002.

c1=A1*(1/((2*pi)^0.5)*sig1);

k1=2*(sig1^2);

c2=A2*(1/((2*pi)^0.5)*sig2);

k2=2*(sig2^2);

z=linspace(0, 1, 256) ;

p= k+ c1 *exp(-((2 - m1).^2)./k1)+...

+ c2 *exp(-((2 - m2).^2) ./k2);

p=p./sum(p(:));

Command line Code

>>p=twomodegauss(0.15,0.05,0.75,0.05,1,0.07,0.002);

>>plot(p)

>>imhist(p)

>>f=imhist(p);

>> plot(f)

imshow(f)

Output

Page 44 of 122

2.7 To extract a rectangular sub image from an image. Code

mfile:subimage.m

function s = subim(f, m, n, rx, cy)

%SUBIM Extracts a subimage, s , from a given image, f .

% The subimage is of size m-by-n,and the coordinates

% of its top, left corner are(rx,cy).

s=zeros(m, n);

rowhigh= rx+ m - 1;

colhigh = cy + n - 1;

xcount = 0;

for r = rx:rowhigh

xcount = xcount + 1;

ycount = 0;

for c = cy:colhigh

ycount = ycount + 1;

s(xcount,ycount) = f(r,c);

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end

end

Command line execution

s = subimage(A,200,200,10,10);

imshow(s)

OUTPUT

Image before Image after execution

2.8 To find the entropy of an image matrix

Code:

function h = entropy(x,n)

% H = ENTROPY(X, N) returns the first-order estimate of matrix X

% with N symbols(N=256 if omitted)in bitslsymbol. The estimate

% assumes a statistically independent source characterized by t lsl

% relative frequency of occurrence of the elements i n X.

error(nargchk(1, 2, nargin)); % Check input argument

if nargin < 2

n = 256; % Default for n.

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end

x = double(x); % Make input double

xh = hist(x(:),n); % Compute N-bin histogram

xh = xh/sum(xh(:)); % Compute probabilities

% Make mask to eliminate 0's since log2(0) = -inf.

i = find(xh)

h = -sum(xh(i) .* log2(xh(i))); % Compute entropy

Command line code

h = entropy(A,256)

h =

2.7470

>> whos A

Name Size Bytes Class Attributes

A 320x320x3 307200 uint8

Result

The first order entropy of the image was computed as 2.7470

2.9 To write an m function for Intensity Transformation, Intensity

Scaling

Program Code

function g = intrans(f,varargin)

%INTRANS Performs lntenslty (gray-level) transformatlons. a - - -

% G = INTRANS(F, 'neg') computes the negatlve of Input Image F.

Page 47 of 122

%

% G = INTRANS(F, ' l o g ' , C, CLASS) computes C*log(l + F ) and

% multlplles the result by (posltlve) constant C. If the last t w o

% parameters are omltted, C defaults to 1 . Because the l o g 1s used

% frequently to dlsplay Fourler spectra, parameter CLASS offers the

% optlon to speclfy the class of the output as 'ulnt8' or

% 'ulntl6'. If parameter CLASS 1s omltted, the output 1s of the

% same class as the lnput.

%

% G = INTRANS(F, 'gamma', GAM) performs a gamma transformatlon on

% the Input Image uslng parameter GAM ( a requlred ~nput).

%

% G = INTRANS(F, 'stretch', M , E ) computes a contrast-stretching

% transformatlon uslng the expression 1. / ( I + ( M . I ( F +

% eps)). ^ E ) . Parameter M must be l n the range [0, I ] . The default

% value for M IS mean2(lm2double(F)),and the default value for E

% is 4.

%

% For the ' n e g ' , 'gamma', and 'stretch' transformatlons, double

% lnput lmages whose maxlmum value 1s greater than 1 are scaled

% flrst uslng MAT2GRAY. Other lmages are converted to double flrst

% uslng IM2DOUBLE. For the ' l o g ' transformatlon, double lmages are

% transformed wlthout berng scaled; other Images are converted to

% double flrst uslng IM2DOUBLE.

%

% The output 1s of the same class as the ~nput,except ~ . fa

% different class 1s speclfled for the ' l o g ' optlon.

% Verlfy the correct number of lnputs.

error(nargchk(2,4,nargin))

% Store the class of the input for use later

classin =class(f);

% If the input is of class double, and it is outside the range

% [O, 1], and the specified transformation i s not ' l o g ' , convert the

% input to the range (0, 1).

if strcmp(class(f),'double') & max(f(:))> 1 & ...

-strcmp(varargin{l}, 'log' )

f = mat2gray( f );

else % Convert to double, regardless of class(f).

f = im2double ( f );

end

% Determine the type of transformation specified.

method = varargin{1};

% Perform the intensity transformation specified.

switch method

case ' neg '

g = imcomplement( f ) ;

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case ' log '

if length (varargin) == 1

c = 1;

elseif length(varargin) == 2

c = varargin{2};

elseif length(varargin) == 3

c = varargin{2};

classin = varargin{3};

else

error('1ncorrect number of inputs for the log option.')

end

g = c*(log(l + double(f)));

case 'gamma'

if length(varargin) < 2

error('Not enough inputs for the gamma option.')

end

gam = varargin{2};

g = imadjust(f, [ ] , [ ], gam);

case 'stretch'

if length(varargin) == 1

% Use defaults.

m = meanZ(f);

E = 4.0 ;

elseif length (varargin) == 3

m = varargin{2};

E = varargin{3};

else error('1ncorrect number of inputs for the stretch option. ' )

end

g=1/(1+(m./(f+eps)).^E);

otherwise

error( ' U n k n o w n enhancement method. ' )

end

% Convert to the class of the input image.

Command Line Code

g =intrans( f ,'stretch',mean2(im2double(f)),0.9);

>> figure,imshow(g)

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Input Output

Program Code for Intensity Scaling

%Program for Intensity Scaling

function g=gscale(f,method,low,high)

% GSCALE adjusts the scale of an image.

%

% GSCALE returns the input image with the scale adjusted according to the

% input specifications.

%

% USAGE:

% g=gscale(f,'minmax'); adjusts the image to the default min and max of

% class of the input image

%

% g=gscale(f,'full8'); adjusts the image to a 8bit scale

%

% g=gscale(f,'full16'); adjsuts the image to a 16bit scale

%

% INPUTS:

% f: grayscale image (any class)

% method: scaling method

%

% OUTPUTS:

% g: adjusted image

% Modified Donald G. Dansereau 2013, minor fix: replace NaNs resulting from div-by-zero

with zeros

% input error checking

if ~exist('f','var') || isempty(f)

error('Please Input Image');

end

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if ~exist('method','var') || isempty(method)

error('Please Specify Method');

end

if ~exist('low','var') || isempty(low)

low=0;

end

if ~exist('high','var') || isempty(high)

high=1;

end

if numel(low)>1 || numel(high)>1

error('Low and High should be scalars');

end

if low>1 || low<0 || high>1 || high<0

error('Low and High should be between 0 and 1');

end

g=double(f);

low=double(low);

high=double(high);

gmin=min(g(:));

gmax=max(g(:));

%Adjust to [0,1]

g=(g-gmin)./(gmax-gmin);

g(isnan(g)) = 0; % removing NaNs from divide by zero, above

switch method

case 'full8'

g=im2uint8(g);

case 'full16'

g=im2uint16(g);

case 'minmax'

g=g.*(high-low)+low;

switch class(f)

case 'uint8'

g=im2uint8(g);

case 'uint16'

g=im2uint16(g);

case 'double'

g=im2double(g);

otherwise

error('Unsupported Format, Supported Formats: unit8, uint16, double');

end

otherwise

error('Invalid Method');

end

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Command Line Code

>> g=gscale(g,'full8',0,0.5) %There are two methods for intensity scaling either through full8 or

through full16.

>>imshow(g)

Output

The g image obtained after Intensity transformation is being applied through Intensity scaling

function.

2.10 Program to find the error between two images/matrices. Program Code:


B=imread('tom2.png')

C=A-B

imshow(C)

Page 52 of 122

Inputs

Output

Result

The error between the two matrices were found out and resultant image/,matrix was obtained.

2.11 To perform histogram equilisation. Code

>> I=imread('jerry.png');

>> I=rgb2gray(I);

>> Ieq=histeq(I);

>> subplot(2,2,1)

>> imshow(I)

>> title('original image');

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>> subplot(2,2,2)

>> imshow(Ieq)

>> title('Ieq');

>> subplot(2,2,3)

>> imshow(imhist(I))

>> title('histogram of I');

>> subplot(2,2,4)

>> imshow(imhist(Ieq))

>> title('histogram of Ieq');

%plot of images and respective bar graphs

>> subplot(2,2,1)

>> imshow(I)

>> title('original image');

>> subplot(2,2,2)

>> bar(I)

>> title('bar graph of original image');

>> subplot(2,2,3)

>> imshow(Ieq)

>> title('After histogram Equilisation');

>> subplot(2,2,4)

>> bar(Ieq)

>> title('bar graph of histogram equilized plot')

Page 54 of 122

Output:

Program 2

>> I=imread('lesscontrast.jpg');

Page 55 of 122

>> I=rgb2gray(I);

Ieq=histeq(I);

subplot(2,2,1)

imshow(I)

title('original image');

subplot(2,2,2)

imshow(Ieq)

title('Ieq');

subplot(2,2,3)

imshow(imhist(I))

title('histogram of I');

subplot(2,2,4)

imshow(imhist(Ieq))

title('histogram of Ieq');

>> %plot of images and respective bar graphs

subplot(2,2,1)

imshow(I)

title('original image');

subplot(2,2,2)

bar(I)

title('bar graph of original image');

subplot(2,2,3)

imshow(Ieq)

title('After histogram Equilisation');

subplot(2,2,4)

Page 56 of 122

bar(Ieq)

title('bar graph of histogram equilized plot')

OUTPUT

Result

Histogram equlisation of the image was performed.

2.12 Write a MATLAB code to perform the contrast stretching on

the image. Show the original and stretched image along with their

histograms. clear all;

close all;

clc;

%% Reading an image

a=imread('Mario_png.png');

a=double(a);

s=size(a);

%% Defingin points and calculating equation parameters

p1=[0,0];

p2=[150,20];

p3=[200,200];

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p4=[255,255];

m1=(p1(1,2)-p2(1,2))/(p1(1,1)-p2(1,1));

m2=(p2(1,2)-p3(1,2))/(p2(1,1)-p3(1,1));

m3=(p3(1,2)-p4(1,2))/(p3(1,1)-p4(1,1));

c1=p1(1,2)-m1*p1(1,1);

c2=p2(1,2)-m2*p2(1,1);

c3=p3(1,2)-m3*p3(1,1);

%% Transformation function

t=[];

for x=0:255

if(x<=p2(1,1))

t=[t (m1*x+c1)];

end

if(x>p2(1,1) && x<=p3(1,1))

t=[t (m2*x+c2)];

end

if(x>p3(1,1) && x<=p4(1,1))

t=[t (m3*x+c3)];

end

end

%% Getting output image

for n=1:s(1,1)

for m=1:s(1,2)

ot(n,m)=t(a(n,m)+1);

end

end

plot(t)

grid on;

xlabel('Intensity in input image');

ylabel('Intensity in output image')

title('Piece-wise linear transformation : Contrast stretching function')

figure()

subplot(1,2,1)

imshow(a/255)

title('Original image')

subplot(1,2,2)

imshow(ot./255)

title('Contrast stretching')

Page 58 of 122

Output

2.13To plot the histogram and bar graph of an image. To find the bar-graph of the image.

Code:

>> h=imread('tom2.png');

>> h=rgb2gray(h);

Page 59 of 122

>> hl = h(1:10:256);

horz = 1:10:256;

>> subplot(1,2,1)

>> imshow(h)

>> subplot(1,2,2)

>> title('bargraph of the image');

>> bar(h)

>> title('bargraph of the image');

Output of the image

Result:

The bar-graph of the image was plotted.

Code

>> a=imread('tom2.png');

Page 60 of 122

>> b=zeros(1,256);

[row,col]=size(a);

for x=1:1:row

for y=1:1:col

if a(x,y)<1

continue;

else

t=a(x,y);

end

b(t)=b(t)+1;

end

end

subplot(1,2,1);

>> imshow(uint8(a));

>> title('Original Image');

subplot(1,2,2);

bar(b);

title('Histogarm of image');

>>

Page 61 of 122

Output

Alternate method using imhist( ) function which only uses 2D array

>> I=rgb2gray(I);

BW = edge(I);

>> imhist(I)

>> I=imread('tom2.png');

>> I=rgb2gray(I);

>> imhist(I)

>> imshow(I)

>> subplot(1,2,1);

>> imshow(uint8(I));

Page 62 of 122

>> title('Original Image');

>> subplot(1,2,2);

>> imhist(I)

>> imhist(I);

>> title('histogram of image');

Output

Page 63 of 122

2.14Coorrupt the original lenna of the image with a zero mean

Gaussian noise,so that the SNR of the noisy image is 5 dB.Attempt

to minimize noise effects by using appropriate filters in spatial

domain and spectral domain. Indicate the cutoff frequency of the

spectral domain filter.

Spectral Domain filter

Low pass filter

Code

>> SNR = 5;

footBall=imread('football.jpg');

footBall=im2double(footBall);

vm = var(footBall(:)) / 10^(SNR/10);

>> footBall= imnoise(footBall, 'gaussian', 0, vm);

>> imshow(footBall);

%Convert to grayscale

footBall=rgb2gray(footBall);

imshow(footBall)

%Determine good padding for Fourier transform

PQ = paddedsize(size(footBall));

%Create a Gaussian Lowpass filter 5% the width of the Fourier transform

D0 = 0.05*PQ(1);

H = lpfilter('gaussian', PQ(1), PQ(2), D0);

% Calculate the discrete Fourier transform of the image

F=fft2(double(footBall),size(H,1),size(H,2));

% Apply the highpass filter to the Fourier spectrum of the image

LPFS_football = H.*F;

Page 64 of 122

% convert the result to the spacial domain.

LPF_football=real(ifft2(LPFS_football));

% Crop the image to undo padding

LPF_football=LPF_football(1:size(footBall,1), 1:size(footBall,2));

%Display the blurred image

figure, imshow(LPF_football, [])

% Display the Fourier Spectrum

% Move the origin of the transform to the center of the frequency rectangle.

Fc=fftshift(F);

Fcf=fftshift(LPFS_football);

% use abs to compute the magnitude and use log to brighten display

S1=log(1+abs(Fc));

S2=log(1+abs(Fcf));

figure, imshow(S1,[])


Output

Original Image Fourier

For applying a high pass filter

Page 65 of 122

M-files (paddedsize.m, dftuv.m, and hpfilter.m)

function PQ = paddedsize(AB, CD, PARAM)

%PADDEDSIZE Computes padded sizes useful for FFT-based filtering.

% PQ = PADDEDSIZE(AB), where AB is a two-element size vector,

% computes the two-element size vector PQ = 2*AB.

%

% PQ = PADDEDSIZE(AB, 'PWR2') computes the vector PQ such that

% PQ(1) = PQ(2) = 2^nextpow2(2*m), where m is MAX(AB).

%

% PQ = PADDEDSIZE(AB, CD), where AB and CD are two-element size

% vectors, computes the two-element size vector PQ. The elements

% of PQ are the smallest even integers greater than or equal to

% AB + CD -1.

%

% PQ = PADDEDSIZE(AB, CD, 'PWR2') computes the vector PQ such that

% PQ(1) = PQ(2) = 2^nextpow2(2*m), where m is MAX([AB CD]).

if nargin == 1

PQ = 2*AB;

elseif nargin == 2 & ~ischar(CD)

PQ = AB + CD - 1;

PQ = 2 * ceil(PQ / 2);

elseif nargin == 2

m = max(AB); % Maximum dimension.

% Find power-of-2 at least twice m.

P = 2^nextpow2(2*m);

PQ = [P, P];

elseif nargin == 3

m = max([AB CD]); %Maximum dimension.


PQ = [P, P];

else

error('Wrong number of inputs.')

end

function [U, V] = dftuv(M, N)

%DFTUV Computes meshgrid frequency matrices.

% [U, V] = DFTUV(M, N) computes meshgrid frequency matrices U and

% V. U and V are useful for computing frequency-domain filter

% functions that can be used with DFTFILT. U and V are both M-by-N.

% Set up range of variables.

u = 0:(M-1);

http://www.cs.uregina.ca/Links/class-info/425/Lab5/M-Functions/paddedsize.m

http://www.cs.uregina.ca/Links/class-info/425/Lab5/M-Functions/dftuv.m

http://www.cs.uregina.ca/Links/class-info/425/Lab5/M-Functions/hpfilter.m

Page 66 of 122

v = 0:(N-1);

% Compute the indices for use in meshgrid

idx = find(u > M/2);

u(idx) = u(idx) - M;

idy = find(v > N/2);

v(idy) = v(idy) - N;

% Compute the meshgrid arrays

[V, U] = meshgrid(v, u);

function H = hpfilter(type, M, N, D0, n)

%HPFILTER Computes frequency domain highpass filters

% H = HPFILTER(TYPE, M, N, D0, n) creates the transfer function of

% a highpass filter, H, of the specified TYPE and size (M-by-N).

% Valid values for TYPE, D0, and n are:

%

% 'ideal' Ideal highpass filter with cutoff frequency D0. n

% need not be supplied. D0 must be positive

%

% 'btw' Butterworth highpass filter of order n, and cutoff D0.

% The default value for n is 1.0. D0 must be positive.

%

% 'gaussian' Gaussian highpass filter with cutoff (standard deviation)

% D0. n need not be supplied. D0 must be positive.

%

% The transfer function Hhp of a highpass filter is 1 - Hlp,

% where Hlp is the transfer function of the corresponding lowpass

% filter. Thus, we can use function lpfilter to generate highpass

% filters.

if nargin == 4

n = 1; % Default value of n.

end

% Generate highpass filter.

Hlp = lpfilter(type, M, N, D0, n);

H = 1 - Hlp;

Code

>> SNR = 5;


Page 67 of 122



footBall= imnoise(footBall, 'gaussian', 0, vm);

imshow(footBall);



imshow(footBall)



%Create a Gaussian Highpass filter 5% the width of the Fourier transform

D0 = 0.05*PQ(1);

H = hpfilter('gaussian', PQ(1), PQ(2), D0);




HPFS_football = H.*F;


HPF_football=real(ifft2(HPFS_football));


HPF_football=HPF_football(1:size(footBall,1), 1:size(footBall,2));

%Display the "Sharpened" image

figure, imshow(HPF_football, [])



Fc=fftshift(F);

Page 68 of 122

Fcf=fftshift(HPFS_football);


S1=log(1+abs(Fc));

S2=log(1+abs(Fcf));



>>

Ouput

Original Image

Image found after adding zero mean Gaussian noise and SNR of 5 db

Page 69 of 122

Fourier Spectrum of image

Fourier with high pass filter

Spectrum of image with high pass filter

>> SNR = 5;




Page 70 of 122


imshow(footBall);

>> footBall=rgb2gray(footBall);


>> footBall= medfilt2(footBall);

imshow(footBall);

Image when the original lenna is corupted with zero-mean Gaussian noise, so that the SNR of the

noisy image is 5 dB.

The noise of the image is being reduced by using median filter

To find the spectral domain filtering of an image.

Mfunctions required paddedsize.m, lpfilter.m and dftuv.m

http://www.cs.uregina.ca/Links/class-info/425/Lab5/M-Functions/paddedsize.m

http://www.cs.uregina.ca/Links/class-info/425/Lab5/M-Functions/lpfilter.m

http://www.cs.uregina.ca/Links/class-info/425/Lab5/M-Functions/dftuv.m

Page 71 of 122

function PQ = paddedsize(AB, CD, PARAM)

%PADDEDSIZE Computes padded sizes useful for FFT-based filtering.

% PQ = PADDEDSIZE(AB), where AB is a two-element size vector,

% computes the two-element size vector PQ = 2*AB.

%

% PQ = PADDEDSIZE(AB, 'PWR2') computes the vector PQ such that

% PQ(1) = PQ(2) = 2^nextpow2(2*m), where m is MAX(AB).

%

% PQ = PADDEDSIZE(AB, CD), where AB and CD are two-element size

% vectors, computes the two-element size vector PQ. The elements

% of PQ are the smallest even integers greater than or equal to

% AB + CD -1.

%

% PQ = PADDEDSIZE(AB, CD, 'PWR2') computes the vector PQ such that

% PQ(1) = PQ(2) = 2^nextpow2(2*m), where m is MAX([AB CD]).

if nargin == 1

PQ = 2*AB;

elseif nargin == 2 & ~ischar(CD)

PQ = AB + CD - 1;

PQ = 2 * ceil(PQ / 2);

elseif nargin == 2

m = max(AB); % Maximum dimension.

% Find power-of-2 at least twice m.


PQ = [P, P];

elseif nargin == 3

m = max([AB CD]); %Maximum dimension.


PQ = [P, P];

else

error('Wrong number of inputs.')

end

function H = lpfilter(type, M, N, D0, n)

%LPFILTER Computes frequency domain lowpass filters

% H = LPFILTER(TYPE, M, N, D0, n) creates the transfer function of

% a lowpass filter, H, of the specified TYPE and size (M-by-N). To

% view the filter as an image or mesh plot, it should be centered

% using H = fftshift(H).

%

% Valid values for TYPE, D0, and n are:

%

Page 72 of 122

% 'ideal' Ideal lowpass filter with cutoff frequency D0. n need

% not be supplied. D0 must be positive

%

% 'btw' Butterworth lowpass filter of order n, and cutoff D0.

% The default value for n is 1.0. D0 must be positive.

%

% 'gaussian' Gaussian lowpass filter with cutoff (standard deviation)

% D0. n need not be supplied. D0 must be positive.

% Use function dftuv to set up the meshgrid arrays needed for

% computing the required distances.

[U, V] = dftuv(M, N);

% Compute the distances D(U, V).

D = sqrt(U.^2 + V.^2);

% Begin fiter computations.

switch type

case 'ideal'

H = double(D <=D0);

case 'btw'

if nargin == 4

n = 1;

end

H = 1./(1 + (D./D0).^(2*n));

case 'gaussian'

H = exp(-(D.^2)./(2*(D0^2)));

otherwise

error('Unknown filter type.')

end

function [U, V] = dftuv(M, N)

%DFTUV Computes meshgrid frequency matrices.

% [U, V] = DFTUV(M, N) computes meshgrid frequency matrices U and

% V. U and V are useful for computing frequency-domain filter

% functions that can be used with DFTFILT. U and V are both M-by-N.

% Set up range of variables.

u = 0:(M-1);

v = 0:(N-1);

% Compute the indices for use in meshgrid

idx = find(u > M/2);

u(idx) = u(idx) - M;

idy = find(v > N/2);

v(idy) = v(idy) - N;

Page 73 of 122

% Compute the meshgrid arrays

[V, U] = meshgrid(v, u);

Code

>> SNR = 5;




>> footBall= imnoise(footBall, 'gaussian', 0, vm);




imshow(footBall)



%Create a Gaussian Lowpass filter 5% the width of the Fourier transform

D0 = 0.05*PQ(1);

H = lpfilter('gaussian', PQ(1), PQ(2), D0);




LPFS_football = H.*F;


LPF_football=real(ifft2(LPFS_football));


LPF_football=LPF_football(1:size(footBall,1), 1:size(footBall,2));

%Display the blurred image

figure, imshow(LPF_football, [])

Page 74 of 122



Fc=fftshift(F);

Fcf=fftshift(LPFS_football);


S1=log(1+abs(Fc));

S2=log(1+abs(Fcf));



Orignal Image


Page 75 of 122


Fourier with gaussian lowpass filter

Spectrum of image with Gaussian Lowpass filter

Page 76 of 122

Aim

Spectral Filtering using notch filter.

Code

>> SNR = 5;





imshow(footBall);



imshow(footBall)



>> %Create a Gaussian Highpass filter 5% the width of the Fourier transform

D0 = 0.05*PQ(1);

H = hpfilter('gaussian', PQ(1), PQ(2), D0);




HPFS_football = H.*F;

>> % convert the result to the spacial domain.

HPF_football=real(ifft2(HPFS_football));


HPF_football=HPF_football(1:size(footBall,1), 1:size(footBall,2));

Page 77 of 122

%Display the "Sharpened" image

figure, imshow(HPF_football, [])



Fc=fftshift(F);

Fcf=fftshift(HPFS_football);

% use abs to compute the magnitude and use log to brighten di

>> S1=log(1+abs(Fc));

S2=log(1+abs(Fcf));



Output


Page 78 of 122


Fourier with high pass filter

Spectrum of image with high pass filter

Page 79 of 122

2.15 To Generate a 3X3 spatial averaging filter and to perform

neighborhood averaging.To plot and observe using fast Fourier

transform Aim:

To Generate a 3X3 spatial averaging filter and to perform neighborhood averaging

Code

>> h = fspecial('average');

>> h

h =

0.1111 0.1111 0.1111

0.1111 0.1111 0.1111

0.1111 0.1111 0.1111

>> I = im2double(imread('tire.tif'));

>> f = @(h) sqrt(min(h(:)));

>> I2 = nlfilter(I,[3 3],f);

>>imshow(I);

>>figure, imshow(I2);

Output

Before applying 3X3 neighborhood averaging filter

Page 80 of 122

After applying a 3X3 neighborhood filter h

Code: To find the Fourier Transform of the images

>> F = fftshift(I);

>> % Center FFT

>>F = abs(F); % Get the magnitude

>> F = log(F+1); % Use log, for perceptual scaling, and +1 since log(0) is undefined

>>F = mat2gray(F); % Use mat2gray to scale the image between 0 and 1

>>imshow(F,[]); % Display the result

The Fourier Transform of the original Image

Page 81 of 122

The Fourier Transform of the image I2 on which neighborhood averaging is being performed

Aim

To plot and observe using fast Fourier transform

Code

>> h = fspecial('average');

>> h

h =

0.1111 0.1111 0.1111

0.1111 0.1111 0.1111

Page 82 of 122

0.1111 0.1111 0.1111

>> I = im2double(imread('tire.tif'));

>> f = @(h) sqrt(min(h(:)));

>> I2 = nlfilter(I,[3 3],f);

imshow(I)

figure, imshow(I2)

imageA =I;

imageB = I2;

%Perform 2D FFTs

fftA = fft2(double(imageA));

fftB = fft2(double(imageB));

%Display magnitude and phase of 2D FFTs

figure, imshow(abs(fftshift(fftA)),[24 100000]), colormap gray

title('Image A FFT2 Magnitude')

figure, imshow(angle(fftshift(fftA)),[-pi pi]), colormap gray

title('Image A FFT2 Phase')

figure, imshow(abs(fftshift(fftB)),[24 100000]), colormap gray

title('Image B FFT2 Magnitude')

figure, imshow(angle(fftshift(fftB)),[-pi pi]), colormap gray

title('Image B FFT2 Phase')

%Switch magnitude and phase of 2D FFTs

Page 83 of 122

fftC = abs(fftA).*exp(i*angle(fftB));

fftD = abs(fftB).*exp(i*angle(fftA));

%Perform inverse 2D FFTs on switched images

imageC = ifft2(fftC);

imageD = ifft2(fftD);

%Calculate limits for plotting

cmin = min(min(abs(imageC)));

cmax = max(max(abs(imageC)));

dmin = min(min(abs(imageD)));

dmax = max(max(abs(imageD)));

%Display switched images

figure, imshow(abs(imageC), [cmin cmax]), colormap gray

title('Image C Magnitude')

figure, imshow(abs(imageD), [dmin dmax]), colormap gray

title('Image D Magnitude')

%Save images

Page 84 of 122

saveas(1,'imageA.png')

saveas(2,'imageB.png')

saveas(3,'imageAfftmag.png')

saveas(4,'imageAfftpha.png')

saveas(5,'imageBfftmag.png')

saveas(6,'imageBfftpha.png')

saveas(7,'imageC.png')

saveas(8,'imageD.png')

The Output after performing fast fourier transform is as follows.

Figure 1

Figure 2

Page 85 of 122

Image A FFT2 magnitude

Image A FFT2 Phase

Image B FFT2 Magnitude

Page 86 of 122

Image B FFT2 phase

Image C Magnitude

Image D magnitude

Page 87 of 122

2.16 Read some images and convert them to binary images. Then to

show/implement all the binary image processing technique. Code:

>> I=imread('Mario_png.png');

>> BW = im2bw(I,0.5);%converts the intensity image I to black and white.

>> imshow(BW)

Input

Output

Alternate methods:

>> BW = im2bw(I,winter,0.4);

>> imshow(BW)

Output:

Page 88 of 122

>> BW = im2bw(I,summer,0.4);

>> imshow(BW)

Alternate


>> I=im2double(I);

>> BW = im2bw(I,0.5);

>> imshow(BW)

Output

Page 89 of 122

Result:

Three various methods of binary image conversion was performed using

BW = im2bw(I,level) %converts the intensity image I to black and white.

BW = im2bw(X,map,level)% converts the indexed image X with colormap map to black and

white.

BW = im2bw(RGB,level) %converts the RGB image RGB to black and white.

2.17 To read an image having some textures and form the co-

occurrence matrix. Code:

>> I = imread('pikachu.png');

>> I=rgb2gray(I);%to convert the image to a 2d array

BW = edge(I);

imshow(BW)

>> glcm = graycomatrix(I,'Offset',[2 0])

Page 90 of 122

Input Image

Output after Conversion to grayscale and then to double

Result

An image with texture was uploaded and a co-occurrence matrix was obtained.

Page 91 of 122

2.18 (a)-To Load a test image and find the edges by gradient –based

and Laplacian-based technique. Aim

To Load a test image and find the edges by gradient –based and Laplacian-based technique.

Code:


>> I=rgb2gray(I);

>> BW = edge(I,'log');

>> imshow(BW)

%Alternate code

BW = edge(I,'log',[],2);

imshow(BW)

Output

Original Image

Image after edge detection

Page 92 of 122

2.18 (b)-Canny Edge Detection Code:


I=rgb2gray(I);

>> h = fspecial('gaussian');

>> h

h =

0.0113 0.0838 0.0113

0.0838 0.6193 0.0838

0.0113 0.0838 0.0113

>> C = conv2(h,I);

>> imshow(I)

>> imshow(C)

>> h2 = fspecial('sobel');

Page 93 of 122

>> h2

h2 =

1 2 1

0 0 0

-1 -2 -1

>> C2 = conv2(h2,C);

>> imshow(C2)

>> canny_edges(1, 0.04,1.2,C2);

adjust =

5

mfile used canny_edges.m

function canny_edges(max_hysteresis_thresh, min_hysteresis_thresh,sigma,I);

ORIGINAL_IMAGE=I;

%%Save height and width

[H,W]=size(ORIGINAL_IMAGE);

%%Derivatives in x and y

derivative_x=zeros(H,W);

derivative_y=zeros(H,W);

%%Gaussian kernel

size_of_kernel = 6*sigma+1;

adjust= ceil(size_of_kernel/2)

Page 94 of 122

Y_GAUSSIAN=zeros(size_of_kernel,size_of_kernel);

X_GAUSSIAN=zeros(size_of_kernel,size_of_kernel);

%%Create gaussian kernels for both x and y directions based on the sigma

%%that was given.

for i=1:size_of_kernel

for iiii=1:size_of_kernel

Y_GAUSSIAN(i,iiii) = -( (i-((size_of_kernel-1)/2)-1)/( 2* pi * sigma^3 ) ) * exp ( - ( (i-

((size_of_kernel-1)/2)-1)^2 + (iiii-((size_of_kernel-1)/2)-1)^2 )/ (2*sigma^2) );

end

end

for i=1:size_of_kernel

for iiii=1:size_of_kernel

X_GAUSSIAN(i,iiii) = -( (iiii-((size_of_kernel-1)/2)-1)/( 2* pi * sigma^3 ) ) * exp ( - ( (i-

((size_of_kernel-1)/2)-1)^2 + (iiii-((size_of_kernel-1)/2)-1)^2 )/ (2*sigma^2) );

end

end

GRADIENT = zeros(H,W);

non_max = zeros(H,W);

post_hysteresis = zeros(H,W);

Page 95 of 122

%%Image Derivatives:

for r=1+ceil(size_of_kernel/2):H-ceil(size_of_kernel/2)

for c=1+ceil(size_of_kernel/2):W-ceil(size_of_kernel/2)

reference_row= r-ceil(size_of_kernel/2);

reference_colum= c-ceil(size_of_kernel/2);

for yyy=1:size_of_kernel

for yyy_col=1:size_of_kernel

derivative_x(r,c) = derivative_x(r,c) + ORIGINAL_IMAGE(reference_row+yyy-1,

reference_colum+yyy_col-1)*X_GAUSSIAN(yyy,yyy_col);

end

end

end

end



reference_row= r-ceil(size_of_kernel/2);

reference_colum= c-ceil(size_of_kernel/2);

for yyy=1:size_of_kernel

for yyy_col=1:size_of_kernel

derivative_y(r,c) = derivative_y(r,c) + ORIGINAL_IMAGE(reference_row+yyy-1,

reference_colum+yyy_col-1)*Y_GAUSSIAN(yyy,yyy_col);

end

end

Page 96 of 122

end

end

%%Compute the gradient magnitufde based on derivatives in x and y:



GRADIENT(r,c) = sqrt (derivative_x(r,c)^2 + derivative_y(r,c)^2 );

end

end

%%Perform Non maximum suppression:

non_max = GRADIENT;



%%quantize:

if (derivative_x(r,c) == 0) tangent = 5;

else tangent = (derivative_y(r,c)/derivative_x(r,c));

end

if (-0.4142<tangent & tangent<=0.4142)

if(GRADIENT(r,c)<GRADIENT(r,c+1) | GRADIENT(r,c)<GRADIENT(r,c-1))

non_max(r,c)=0;

Page 97 of 122

end

end

if (0.4142<tangent & tangent<=2.4142)

if(GRADIENT(r,c)<GRADIENT(r-1,c+1) | GRADIENT(r,c)<GRADIENT(r+1,c-1))

non_max(r,c)=0;

end

end

if ( abs(tangent) >2.4142)

if(GRADIENT(r,c)<GRADIENT(r-1,c) | GRADIENT(r,c)<GRADIENT(r+1,c))

non_max(r,c)=0;

end

end

if (-2.4142<tangent & tangent<= -0.4142)

if(GRADIENT(r,c)<GRADIENT(r-1,c-1) | GRADIENT(r,c)<GRADIENT(r+1,c+1))

non_max(r,c)=0;

end

end

end

end

post_hysteresis = non_max;



Page 98 of 122

if(post_hysteresis(r,c)>=max_hysteresis_thresh) post_hysteresis(r,c)=1;

end

if(post_hysteresis(r,c)<max_hysteresis_thresh &

post_hysteresis(r,c)>=min_hysteresis_thresh) post_hysteresis(r,c)=2;

end

if(post_hysteresis(r,c)<min_hysteresis_thresh) post_hysteresis(r,c)=0;

end

end

end

vvvv = 1;

while (vvvv == 1)

vvvv = 0;



if (post_hysteresis(r,c)>0)

if(post_hysteresis(r,c)==2)

if( post_hysteresis(r-1,c-1)==1 | post_hysteresis(r-1,c)==1 | post_hysteresis(r-

1,c+1)==1 | post_hysteresis(r,c-1)==1 | post_hysteresis(r,c+1)==1 | post_hysteresis(r+1,c-1)==1

| post_hysteresis(r+1,c)==1 | post_hysteresis(r+1,c+1)==1 ) post_hysteresis(r,c)=1;

vvvv == 1;

end

Page 99 of 122

end

end

end

end

end



if(post_hysteresis(r,c)==2)

post_hysteresis(r,c)==0;

end

end

end

imwrite(ORIGINAL_IMAGE,'D:\addition\original_image.bmp');

imwrite(derivative_x,'D:\addition\derivative_x.bmp');

imwrite(derivative_y,'D:\addition\derivative_y.bmp');

imwrite(GRADIENT,'D:\addition\gradient.bmp');

imwrite(non_max,'D:\addition\non_max_supr.bmp');

imwrite(post_hysteresis,'D:\addition\original_image.bmp');

Output

For maxthresh=1,minthresh=0.04,sigma=1.2,image=C2

Page 100 of 122

Original Image

Derivative x

Derivative y

Page 101 of 122

gradient

Non Maximum Suppressed Image

Aim

To convolve gradient at each pixel by convolving it with 2 D gaussian and then by sobel

operators


I=rgb2gray(I);

>> h = fspecial('gaussian');

>> h

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h =

0.0113 0.0838 0.0113

0.0838 0.6193 0.0838

0.0113 0.0838 0.0113

>> C = conv2(h,I);

>> imshow(I)

>> imshow(C)

>> h2 = fspecial('sobel');

>> h2

h2 =

1 2 1

0 0 0

-1 -2 -1

>> C2 = conv2(h2,C);

>> imshow(C2)

Mfile to be used is NonMaximalSupp.m

function H = nonMaximalSupp(dx, dy, magGrad, lowThresh, highThresh)

% Perform Non-Maximum Suppression Thining and Hysteresis Thresholding of Edge

% Strength

% H = nonMaximalSupp(dx, dy, magGrad, lowThresh, highThresh)

% H is suppressed image

% dx and dy are the gradients

% magGrad is the magnitude of gradient

Page 103 of 122

% lowThresh and highThresh are the thresholds

magmax = max(magGrad(:));

if magmax > 0

magGrad = magGrad / magmax;

end

[row, col] = size(magGrad);

E = false(row, col);

idxStrong = [];

for dir = 1:4

idxLocalMax = cannyFindLocalMaxima(dir,dx,dy,magGrad);

idxWeak = idxLocalMax(magGrad(idxLocalMax) > lowThresh);

E(idxWeak)=1;

idxStrong = [idxStrong; idxWeak(magGrad(idxWeak) > highThresh)]; %#ok<AGROW>

end

[m,n] = size(E);

if ~isempty(idxStrong) % result is all zeros if idxStrong is empty

rstrong = rem(idxStrong-1, m)+1;

cstrong = floor((idxStrong-1)/m)+1;

H = bwselect(E, cstrong, rstrong, 8);

else

H = zeros(m, n);

end

Output

Original Image

Page 104 of 122

Image after convolution of I with gaussian operator

Image C2 after circular convolution with the sobel operator

2.19 Lossy Image Compression

Code:

>> RGB = imread('autumn.tif');

I = rgb2gray(RGB);

J = dct2(I);

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imshow(log(abs(J)),[]), colormap(jet(64)), colorbar

>> J(abs(J) <64) = 0;

>> K = idct2(J);

imshow(I)

figure, imshow(K,[0 255])

>> err = immse(I,K);

>> err

err =

1.8432e+04

Output

Original Image

Image restored after compression

Page 106 of 122

>> I = imread('cameraman.tif');

>> T = dctmtx(8);

dct = @(block_struct) T * block_struct.data * T';

B = blockproc(I,[8 8],dct);

mask = [1 1 1 1 0 0 0 0

1 1 1 0 0 0 0 0

1 1 0 0 0 0 0 0

1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0];

B2 = blockproc(B,[8 8],@(block_struct) mask .* block_struct.data);

invdct = @(block_struct) T' * block_struct.data * T;

I2 = blockproc(B2,[8 8],invdct);

imshow(I)

figure

imshow(I2)

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InputImage=I;

ReconstructedImage=I2;

n=size(InputImage);

Code:

>> I = imread('cameraman.tif');

>> f = @(x) uint8(round(mean2(x)*ones(size(x))));

I2 = blkproc(I,[2 2],f);

imshow(I)

figure, imshow(I2);

>> err = immse(I,I2);

>> B=size(I2);

err=

183.8470

OUTPUT

Original Image

Page 108 of 122

After 2X2 subdivision

Code for 8X8 subdivision

I = imread('cameraman.tif');

f = @(x) uint8(round(mean2(x)*ones(size(x))));

>> I2 = blkproc(I,[8 8],f);

>> imshow(I)

figure, imshow(I2);

>> C=size(I2);


err =

733.2871

Output

Page 109 of 122

Code for 16 X 16


>> I2 = blkproc(I,[16 16],f);

>> imshow(I)

figure, imshow(I2);

>> D=size(I2);


err =

1.0829e+03

Output:

Page 110 of 122

Code for 64X64



>> I2 = blkproc(I,[64 64],f);

>> imshow(I)

figure, imshow(I2);


>> E=size(I2);

>> err =

2.2994e+03

Output



>> I2 = blkproc(I,[128 128],f);

>> imshow(I)

figure, imshow(I2);

>> F=size(I2);


>> err =

Page 111 of 122

3.1064e+03

Output

Code:



>> I2 = blkproc(I,[256 256],f);

>> imshow(I)

figure, imshow(I2);

>> G=size(I2);


>> err

err =

3.8865e+03

Page 112 of 122

Aim:

To subdivide an image of 256 X 256 into 8 X8 subimages.

>> I=imread('super-paper-mario.png');

>> %# desird number of horizontal/vertical tiles to divide the image into

>>numBlkH =8;

>> numBlkW = 8;

>> %# compute size of each tile in pixels

>>[imgH,imgW] = size(I);

>>szBlkH = [repmat(fix(imgH/numBlkH),1,numBlkH-1) imgH-

fix(imgH/numBlkH)*(numBlkH-1)];

>>szBlkW = [repmat(fix(imgW/numBlkW),1,numBlkW-1) imgW-

fix(imgW/numBlkW)*(numBlkW-1)];

%# divide into tiles, and linearize using a row-major order

C = mat2cell(I, szBlkH, szBlkW)';

C = C(:);

%# display tiles i subplots

figure, imshow(I)

Page 113 of 122

figure

for i=1:numBlkH*numBlkW

subplot(numBlkH,numBlkW,i), imshow( C{i} )

end

Output:

OriginalImage

Image divided into 8X8 sub images

Code:

>> T = dctmtx(8);

dct = @(block_struct) T * block_struct.data * T';

B = blockproc(I,[8 8],dct);

>> mask = [1 1 1 1 0 0 0 0

Page 114 of 122

1 1 1 0 0 0 0 0

1 1 0 0 0 0 0 0

1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0];

>> B2 = blockproc(B,[8 8],@(block_struct) mask .* block_struct.data);

>> invdct = @(block_struct) T' * block_struct.data * T;

I2 = blockproc(B2,[8 8],invdct);

>> imshow(I)

figure

imshow(I2)

>> InputImage=I;

>> ReconstructedImage=I2;

>> n=size(InputImage);

M=n(1);

N=n(2);

MSE = sum(sum((InputImage-ReconstructedImage).^2))/(M*N)

MSE =

0.0029

Page 115 of 122

Output

Original Image

The image reconstructed after DCT compression

Page 116 of 122

2.20 Capture a video footage of 1 min duration by a digital

camera(Mega Pixels>7.0) and convert it to frames(25frames/second)

and read all the frames one by one .Then detect the edges of the

moving objects in the frame.

Code:

clc;

close all;

clear all;

%nframes = length(video);

nframes=video.NumberOfFrames;

for i=1:nframes

mov(i).cdata=read(video,i)

%creating '.cdata' field to avoid much changes to previous code

end

temp = zeros(size(mov(1).cdata));

[M,N] = size(temp(:,:,1));

for i = 1:10

temp = double(mov(i).cdata) + temp;

end

imbkg = temp/10;centroidx = zeros(nframes,1);

centroidy = zeros(nframes,1);

Page 117 of 122

predicted = zeros(nframes,4);

actual = zeros(nframes,4);

R=[[0.2845,0.0045]',[0.0045,0.0455]'];

H=[[1,0]',[0,1]',[0,0]',[0,0]'];

Q=0.01*eye(4);

P = 100*eye(4);

dt=1;

A=[[1,0,0,0]',[0,1,0,0]',[dt,0,1,0]',[0,dt,0,1]'];

kfinit = 0;

th = 38;

for i=1:nframes

imshow(mov(i).cdata);

hold on

imcurrent = double(mov(i).cdata);

diffimg = zeros(M,N);

diffimg = (abs(imcurrent(:,:,1)-imbkg(:,:,1))>th) ...

| (abs(imcurrent(:,:,2)-imbkg(:,:,2))>th) ...

| (abs(imcurrent(:,:,3)-imbkg(:,:,3))>th);

labelimg = bwlabel(diffimg,4);

markimg = regionprops(labelimg,['basic']);

[MM,NN] = size(markimg);

for nn = 1:MM

if markimg(nn).Area > markimg(1).Area

tmp = markimg(1);

markimg(1)= markimg(nn);

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markimg(nn)= tmp;

end

end

bb = markimg(1).BoundingBox;

xcorner = bb(1);

ycorner = bb(2);

xwidth = bb(3);

ywidth = bb(4);

cc = markimg(1).Centroid;

centroidx(i)= cc(1);

centroidy(i)= cc(2);

hold on

rectangle('Position',[xcorner ycorner xwidth ywidth],'EdgeColor','b');

hold on

plot(centroidx(i),centroidy(i), 'bx');

kalmanx = centroidx(i)- xcorner;

kalmany = centroidy(i)- ycorner;

if kfinit == 0

predicted =[centroidx(i),centroidy(i),0,0]' ;

else

predicted = A*actual(i-1,:)';

end

kfinit = 1;

Ppre = A*P*A' + Q;

K = Ppre*H'/(H*Ppre*H'+R);

Page 119 of 122

actual(i,:) = (predicted + K*([centroidx(i),centroidy(i)]' - H*predicted))';

P = (eye(4)-K*H)*Ppre;

hold on

rectangle('Position',[(actual(i,1)-kalmanx)...

(actual(i,2)-kalmany) xwidth ywidth],'EdgeColor','r','LineWidth',1.5);

hold on

plot(actual(i,1),actual(i,2), 'rx','LineWidth',1.5);

drawnow;

end

OUTPUT:

Page 120 of 122

Page 121 of 122

Broad Conclusions and Discussions

References

[1] 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins Digital Image Processing Using

MATLAB, Prentice-Hall, 2004

[2] http://in.mathworks.com/help/images/ref/imnoise.html

[3] http://learnprotech.blogspot.in/2014/02/write-matlab-code-to-perform-contrast.html

[4] http://what-when-how.com/embedded-image-processing-on-the-tms320c6000-dsp/contrast-

stretching-image-processing/

[5]http://www.rocktheit.com/2012/09/matlab-program-to-plot-histogram.html

[6] http://in.mathworks.com/help/images/ref/imhist.html

[7] http://in.mathworks.com/help/matlab/ref/bar.html

[8] http://www.cs.uregina.ca/Links/class-info/425/Lab5/

[9] http://matlabgeeks.com/tips-tutorials/how-to-do-a-2-d-fourier-transform-in-matlab/

[10] http://www-rohan.sdsu.edu/doc/matlab/toolbox/images/im2bw.html

[11] http://in.mathworks.com/help/images/ref/im2bw.html

[12] http://in.mathworks.com/matlabcentral/answers/21527-edge-function-error

[13] http://in.mathworks.com/help/images/ref/graycomatrix.html

[14]Fundamentals of Digital Image Processing -A Practical Approach

with Examples in Matlab- Chris Solomon, Toby Breckon

[15]Fundamentals of Digital Signal Processing by Anil K Jain.

http://in.mathworks.com/help/images/ref/imnoise.html

http://learnprotech.blogspot.in/2014/02/write-matlab-code-to-perform-contrast.html

http://what-when-how.com/embedded-image-processing-on-the-tms320c6000-dsp/contrast-%20%20%20%20%20%20stretching-image-processing/

http://what-when-how.com/embedded-image-processing-on-the-tms320c6000-dsp/contrast-%20%20%20%20%20%20stretching-image-processing/

http://www.rocktheit.com/2012/09/matlab-program-to-plot-histogram.html

http://in.mathworks.com/help/images/ref/imhist.html

http://in.mathworks.com/help/matlab/ref/bar.html

http://www.cs.uregina.ca/Links/class-info/425/Lab5/

http://matlabgeeks.com/tips-tutorials/how-to-do-a-2-d-fourier-transform-in-matlab/

http://www-rohan.sdsu.edu/doc/matlab/toolbox/images/im2bw.html

http://in.mathworks.com/help/images/ref/im2bw.html

http://in.mathworks.com/matlabcentral/answers/21527-edge-function-error

http://in.mathworks.com/help/images/ref/graycomatrix.html

Page 122 of 122

Summer Internship Final Report

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