Linear and Nonlinear Image Processing Filter · LINEAR AND NONLINEAR IMAGE PROCESSING FILTER 1 1. INTRODUCTION 1.1 PROBLEM SCOPE In the modern world, digital images are necessary

LINEAR AND NONLINEAR FILTER FOR

IMAGE PROCESSING USING

MATLAB’S IMAGE PROCESSING

TOOLBOX

This report is submitted to the School of Engineering and Information

Technology, Murdoch University as a partial fulfilment of the requirement for

the Bachelor of Engineering (Honours)

FATIHAH MOHD PADZIL

PROJECT SUPERVISOR:

DR. GREGORY CREBBIN

JANUARY, 2016

LINEAR AND NONLINEAR IMAGE PROCESSING FILTER

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ACKNOWLEDGEMENT

Firstly, I would like to take this opportunity to express my sincere gratitude to my supervisor,

Dr. Gregory Crebbin, who was always there to listen and give advice with patience and a

smile on his face, despite his busy schedule. His valuable comments, guidance and constant

encouragement gave me motivation to finish this project. Also, I cannot forget to thank Dr.

Linh Vu, as my second supervisor, and the School of Engineering and Information

Technology for their support throughout this project.

Finally, to all my family and friends, I would like to send my deep appreciation and respect

for their continuous support and encouragement throughout my thesis and entire degree.


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ABSTRACT

The proposal of the thesis is basically to study techniques in digital image processing. This

thesis will cover two image processing areas, which are image restoration and image

enhancement. More specifically, image restoration will involve the removal of noise and

image enhancement will look into technique for edge enhancement.

In this project, two classes of filter will be introduced, which are linear and nonlinear filters.

Two type of noise source will be used which are Gaussian noise and salt and pepper noise.

For noise removal, the mean filter is used as example of a linear filter and the median filter is

used as an example of a nonlinear filter. For edge enhancement, only a linear filter is used,

which is the unsharp mask filter.

The simulation programs are written using the Image Processing Toolbox in MATLAB

(MATrix LABoratory). Test images that corrupted by noise will be used in investigations to

assess the strength and weakness for each type of filter.


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TABLE OF CONTENTS

ACKNOWLEDGEMENT ...............................................................................................................................

ABSTRACT ................................................................................................................................................ ii

TABLE OF CONTENTS .............................................................................................................................. iii

1. Introduction .................................................................................................................................... 1

1.1 Problem scope ........................................................................................................................ 1

1.2 Thesis Objective ...................................................................................................................... 3

1.3 Report Outline......................................................................................................................... 4

2 Technical Review of Image Processing ........................................................................................... 5

2.1 Overview of Digital Image Processing ..................................................................................... 5

2.2 Image Processing System ........................................................................................................ 6

2.3 Digital Image Representation ................................................................................................. 7

2.4 Image Processing Operations ................................................................................................. 8

2.4.1 Noise ............................................................................................................................... 8

2.4.2 Neighborhood Operations ............................................................................................ 11

2.5 Image Restoration ................................................................................................................. 13

2.5.1 Linear Filter ................................................................................................................... 13

2.5.2 Nonlinear Filter ............................................................................................................. 15

2.6 Image Enhancement ............................................................................................................. 17

2.6.1 2.6.1 Unsharp mask filter .............................................................................................. 19

2.7 MATLAB ................................................................................................................................. 21

2.7.1 Image Processing Toolbox ............................................................................................. 21

3 Methodology ................................................................................................................................. 23

3.1 Image Input ........................................................................................................................... 23

3.2 Noise Removal ...................................................................................................................... 24

3.2.1 3.2.1 Process plan ......................................................................................................... 24

3.2.2 Mean Filter .................................................................................................................... 26

3.2.3 Median Filter ................................................................................................................. 27

3.3 Edge Enhancement ............................................................................................................... 29

3.3.1 Process Plan .................................................................................................................. 29

4 Results ........................................................................................................................................... 32

4.1 Mathematical rules ............................................................................................................... 32


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4.2 Mean Filter Result ................................................................................................................. 33

4.2.1 Result of 3 by 3 filtered image ...................................................................................... 33


4.3 Median Filter Result .............................................................................................................. 37



4.4 Result of 11-by-11 window filter .......................................................................................... 41

4.5 Unsharp Mask Filter Result ................................................................................................... 41

4.6 Result Summary .................................................................................................................... 44

5 Problem Encountered and Countermeasures .............................................................................. 45

6 Conclusion and Recommendations............................................................................................... 46

6.1 Conclusion ............................................................................................................................. 46

6.2 Recommendations ................................................................................................................ 47

7 References .................................................................................................................................... 48

8 Appendix ....................................................................................................................................... 49

8.1 Appendix A ............................................................................................................................ 49

Result for a 11 by 11 mean filter ................................................................................................... 49

Result for a 11 by 11 median filter. ............................................................................................... 51

8.2 Appendix B ............................................................................................................................ 53

8.3 Appendix C ............................................................................................................................ 55

8.4 Appendix D ............................................................................................................................ 57

8.5 Appendix E ............................................................................................................................ 58


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LIST OF FIGURES

Figure 1: Typical overall image processing system ................................................................................. 6

Figure 2: An image and the conversion used to represent rows (m) and columns (n) of the image. .... 7

Figure 3: Different type of noise ........................................................................................................... 10

Figure 4: A 3x3 window that centered over the picture element ........................................................ 11

Figure 5: Illustration of Median filter operates. ................................................................................... 16

Figure 6: Different between ideal edges and ramp edge ..................................................................... 17

Figure 7: Illustartion of Unsharp mask filter operates .......................................................................... 20

Figure 8: 8-bit image ............................................................................................................................. 23

Figure 9: Program simulation process for noise removal ..................................................................... 24

Figure 10: Pixel value before filter take place ...................................................................................... 26

Figure 11: Pixel value after filter take place ......................................................................................... 26

Figure 12: original pixel value ............................................................................................................... 27

Figure 13: After median filtering ........................................................................................................... 28

Figure 14: Process flow of image sharpening by unsharp mask filter .................................................. 30

Figure 15: 3-by-3 Mean filter with salt and pepper noise .................................................................... 33

Figure 16: 3-by-3 Mean Filter with Gaussian Noise .............................................................................. 34

Figure 17: 5-by-5 mean filter with salt and pepper noise..................................................................... 35

Figure 18: 5-by-5 mean filter wit Gaussian noise ................................................................................. 35

Figure 19: 3-by-3 median filtered image with salt & pepper noise ...................................................... 37

Figure 20: 3-by-3 median filtered image with Gaussian noise ............................................................. 38

Figure 21: 5-by-5 median filtered image with salt & pepper noise ...................................................... 39

Figure 22: 5-by-5 median filtered image with Gaussian noise ............................................................. 39

Figure 23: Result of blurring with mean filter ....................................................................................... 42

Figure 24: The edge image .................................................................................................................... 42

Figure 25: Image edge enhancement with different scaling constant k .............................................. 43

LIST OF TABLES

Table 1: Image file formats ................................................................................................................... 22

Table 2: MSE value for mean filter ........................................................................................................ 34

Table 3: MSE value for 5-by-5 mean filter ............................................................................................ 36

Table 4: MSE value for median filter ..................................................................................................... 38

Table 5: MSE value for 5 by 5 median filter .......................................................................................... 40


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1. INTRODUCTION

1.1 PROBLEM SCOPE

In the modern world, digital images are necessary for a broad field of human

activities. Image processing is rapidly evolving field with growing application in science and

engineering. An image is a visual representation of an object or a scene produced by an

optical device such as mirror or lens (Marques 2011). Digital images are pictures that have

been transformed into a computer readable binary format consisting of logical 0s and 1s.

They are widely used in medical applications such as digital radiography and MRI (Magnetic

Resonance Imaging), in industrial applications such as safety system and quality control in

manufacturing process, and in law enforcement and security system applications such as

biometric techniques used in face, hand and fingerprint recognition (Solomon 2010)

(Marques 2011).

Image processing begins with the capture of an analog image by suitable devices,

which is then converted to digital image before the image is processed by computer for better

visual appearance to a human viewer (Marques 2011). Image processing covers a wide range

of techniques and algorithms. Digital image processing can be separated into four categories,

which are restoration, enhancement, coding and understanding (Lim 1990).

In image restoration, the objective is to reduce or remove the noise in an image. Two

type of filter will be designed, which are the mean filter, which is an example of a linear

filter, and the median filter, which is an example of a nonlinear filter (Lim 1990). Two type

of noise source are added to the image before filtering by both types of filter.


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In image enhancement, the objective is to improve the pictorial appearance for human

viewers and to prepare an image for storage and representation for machine perception. An

unsharp mask filter is an example of an edge enhancement filter (Solomon 2010).


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1.2 THESIS OBJECTIVE

The aim of the project is designing the two classes of filter in image processing for noise

removal and edge enhancement. The investigations that will be carried out in this project are

motivated by the following scenario:

An image is read using a special Matlab toolbox. For noise removal, noise is added to the

image. After that, different filters will be applied to the noisy image. The strengths and

weaknesses of each class of filter will be investigated and compared. For edge enhancement,

different scale degree of enhancement are used to the one type of blurred picture.

The main technical objectives of the thesis are:

To identify the requirements of filters for specified image processing applications.

These applications will include the removal of unwanted artefacts, such as noise, and

the enhancement of critical features, such as the edges of objects.

To develop a simulation program in Matlab, using the image processing toolbox.

To design both linear and nonlinear filters for specific image processing tasks, and to

compare the results of these two classes of filter.

To design and implement image filters using MATLAB.

To brief an introduction to the vast field of image processing.

The main personal development objectives of the thesis are:

To apply the theoretical and practical knowledge gained from 3 years of study at

Murdoch University.

To develop skills in programming, troubleshooting and system design.

To develop project and time management skills.


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1.3 REPORT OUTLINE

The remaining chapters of this thesis will describe to the works undertaken in the project. The

thesis is outlined as follows:

Chapter 2: Will present a literature review and provide a background of image

processing that covers the overview, techniques, and operations including edge

enhancement.

Chapter 3: Will describe the methodology and implementation of the simulation

program. The linear and nonlinear filters for noise removal and image edge

enhancement will be described. A process flow of the simulation program for both

types of noise removal filter and edge enhancement filter will be described clearly.

Chapter 4: Will investigate the findings of each type of image filtering technique.

The strengths and weaknesses of each filter will be discuss in this chapter.

Chapter 5: Will describe the problems that were encountered and the

countermeasures that were taken to finish the thesis project.

Chapter 6: Will conclude of the thesis report. This will also include recommendation

for future research based on the findings of this thesis.


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2 TECHNICAL REVIEW OF IMAGE PROCESSING

The aim of this chapter is to conduct a literature review on digital image processing.

This will include the basics of two image processing methods, which are image filtering and

image edge enhancement. It will end by introducing MATLAB functions for reading, writing,

querying, converting and displaying images. To conduct the review, books, journals, websites

and the online resources were consulted so that more could be learnt about image processing.

2.1 OVERVIEW OF DIGITAL IMAGE PROCESSING

The field of digital imaging has grown rapidly in recent years. Humans are exposed

to the images on a daily basis in print, photographs and computer displays, where the images

are still pictures that do not change with time. An image is a representation of an object or a

view that is produced by an optical device such as camera or mirrors. A digital image

represents an image by a two dimensional array of numbers, where each element of the array

is a sampled value of the original image within a small square segment of space. These

picture elements are called “pixels”. Each pixels is addressed by its rows and columns

position in the array (Marques 2011).

Digital image processing refers to the processing of a digital image by digital

computers. The processing serves two main purposes, which are to improve the pictorial

appearance of the original image for human viewers (Lim 1990) and to prepare the image for

storage, transmission and representation for autonomous machine perception (Lim 1990)

(Russ 2007). Digital image processing is widely used in various fields of application such as


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industrial inspection, meteorology, astronomy, ultrasonic imaging, radiology, satellite

imaging, remote sensing, and law enforcement (Bovik 2009).

Digital image processing can be divided into three levels of processing which are low,

mid and high. Low level processes involve basic operations such as noise reduction, contrast

enhancement and image sharpening. The input and output at this level are both images. Mid-

level processes result in attributes being extracted from an image, such as edges, contours,

and the identity of individual objects. Lastly, higher level processes involves the analysis of

images and interpretation of the contents of a scene (Marques 2011).

2.2 IMAGE PROCESSING SYSTEM

A typical image processing system is built around a computer that performs digital

signal processing, as shown in Figure 1 (Marques 2011). The input source is usually an object

or a natural scene which is digitized and stored as a matrix of binary digits inside the

computer. The digitized image is then processed using either a general purpose computer, a

microprocessor or special purpose hardware. The result of processing is then displayed for

human viewing or is used as an input to another system. The display could be a monitor, a

photograph or it could be just a printer (Lim 1990).

Figure 1: Typical overall image processing system

object (input)

imaging system

(observer)

sample and

quantitize (digitize)

digital storage (store)

digital computer (process)

display (output)


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2.3 DIGITAL IMAGE REPRESENTATION

A digital image, I (m, n) is a representation of an image as a two-dimensional array of

picture elements or pixels where the indicator m is represent the row of image and the

indicator n represents the column of the image. The number of column times the number of

rows gives the total number of pixels in the image. Figure 2 shows an image and the

conversion used to represent rows, m and column, n of an image. Each pixel is represents an

as intensity value of the image, with intensity values typically ranging from 0 to 255. For

grayscale images, a pixel is usually encoded as a value between 0 and 255, where “black”

corresponds to pixel value 0 and “white” corresponds to pixel value 255. Intermediate values

represent the various “shades of grey” (Marques 2011). For color images, each pixel is

encoded with red, green, and blue (RGB) components, where each component value usually

encoded in 8-bits, so that the combination these three elements is 24 bits in total (Tan 2007).

Figure 2: An image and the conversion used to represent rows (m) and columns (n) of the image.

The size of an image is a measure of its resolution. The resolution is related to image quality.

Most image are not square but also in rectangular form with a width up to 4000pixels. In

image processing the standard image sizes are used 256 x 256, 512 x 512 and 1024 x 1024

(Lim 1990).


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2.4 IMAGE PROCESSING OPERATIONS

In this section, several fundamental techniques that are commonly used in image

processing will be discussed. Digital image processing can be divided to four common

application areas which are image enhancement, restoration, coding and understanding. This

thesis will focus on image restoration (noise removal) and enhancement (edge enhancement).

The usual objective of these techniques is to make the processed image look better than the

unprocessed image (Lim 1990).

2.4.1 Noise

An important problem for image processing is noise removal. Noise is unwanted

contamination of an image. In digital images, noise can come from a variety of sources

including noise of capture noise that results of variations of lighting i.e. too much or too little

light, and processing noise that results from limitations in numerical precision, and

mathematical approximations (e.g. 𝜋 = 3.142. . ). A digital image is a representation of an

original scene but it is not always perfect because of limitations of resolution by sampling

and noise contamination (Solomon 2010).

Noise in images can be characterized in many ways. In image processing, two main

type of noise are often used, which are salt and pepper noise and Gaussian noise (Ajay 2015).

Salt-and-pepper noise, also known as an impulsive noise, is caused by the random

introduction of pure white or pure black pixels into image. This noise is commonly caused by

camera sensor faults. Meanwhile, Gaussian noise, is also known as additive noise is noise

with random intensity levels that have a Gaussian or normal probability density function.

Usually it is caused by random processes in electronic equipment. Gaussian noise is the most


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commonly used noise model in image processing (Solomon 2010). Figure 3 shows an

example of different types of noise at an image.

(a): Original Image

(b): Image with salt-and-

pepper noise


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(b): Image with Gaussian noise

Figure 3: Different type of noise


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2.4.2 Neighborhood Operations

Usually, in image processing it is impractical to work on the whole image at once.

When processing an image, usually the only a reference pixel and nearby pixels are used. To

apply this principle, a neighborhood technique (also known as windowing technique) is used.

A window in image processing is usually a small square array centered on the reference pixel.

The operation on a given pixel is called a neighborhood operation because it used only the

original pixel value at the given point and the pixel values in a neighborhood around that

point (Marques 2011). For example, a 3x3 window that is centered over the picture at

location (i, j) is shown in Figure 4.

Figure 4: A 3x3 window that centered over the picture element

A windowing function starts by defining a reference point in the input array, and then

it performs an operation that involves only pixels in the neighborhood surrounding that

reference point. It could be any shape or size of window but usually it is a square array

centered on the input pixel (e.g. 3 x 3 or 5 x 5 windows centered at the given input pixel)

(Marques 2011).


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The result of the operation becomes the pixel value at the same location in the output

image. For the edge pixels, it also use same window size, but the pixels value for outside an

image is set at 0. The process is repeated for every pixel in the input image. For example, the

function that is applied might be an averaging operation; it will sum the values of the

neighborhood pixel then divide the result by the number of pixels in the neighborhood,

thereby replacing the centre pixel by the “average” values of pixels in the neighborhood

(Jaehne 2005).


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2.5 IMAGE RESTORATION

Image restoration is used to carry out several useful tasks in image processing. One of

the primary tasks is noise removal. A filter is used to reduce the amount of unwanted noise in

the particular image. As mentioned early, a filter usually operates on a neighborhood of

pixels in an image. In the spatial domain, image filtering is done by convolving the input with

the filter function to obtain the filtered image, (Abdul Rasak Zubair 2014) where the

convolution takes place over the neighborhood of each input pixel.

A mean filter and a median filter are both types of filter that can be used for noise

removal. Whereas the mean filter is an example of a linear filter, the median filter is an

example of a nonlinear filter (Lim 1990) (Solomon 2010). The next section will discuss in

more detail both types of filter.

2.5.1 Linear Filter

Linear filtering is carried out by convolving the input with a filter function to obtain

the filtered image. A linear filter can be written as follows (Marques 2011):

𝑓(𝑥, 𝑦) = ∑ 𝐼 (𝑚, 𝑛) ∙ 𝑤(𝑥 − 𝑚, 𝑦 − 𝑛)

𝑚,𝑛

Here, I is represents the original image, f is represents the filtered pixels value, and w

is represents the filter coefficients.


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The mean filter, also known as an averaging filter, is an example of a simple linear

filter. It operates by assigning the average value of all pixels in the neighborhood of the input

pixels to the corresponding pixel in the output image. The principle of this filter matches

perfectly with it name, as each pixel in the targeted image is replaced with the mean value of

pixels surrounding it. The mathematical formulation for the mean filter (Marques 2011) is

given as follows:

𝑓(𝑥, 𝑦) =1

𝑚𝑛 ∑ 𝐼(𝑚, 𝑛)(𝑚,𝑛)∈𝑊

Where: I = the noisy image, f = the restored image and (m, n) = the row and column

coordinate respectively, within a window W of size m x n where the operation take places

centered on input pixels at (x, y) (Marques 2011).

For example, if a 3 x 3 window is used, the averaging operation uses the following

3x3 mask, which is placed over at the input pixel and its eight neighborhoods:

1

9 [

1 1 11 1 11 1 1

]

Averaging has the effect of smoothing the noise, as along as the noise is addictive and

not impulsive. This filter is effective in removing the noise, but at the same time it blurs the

image. Despite this drawback, it is still a useful filtering technique.


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2.5.2 Nonlinear Filter

One type of nonlinear filter operates by ranking the pixels in the specified

neighborhood. It replaces the target pixel by a value corresponding to the chosen rank. The

rank could be maximum value, minimum value or middle value in the neighborhoods pixels

(Marques 2011) (Solomon 2010). In this project, the median filter will be used as an example

of nonlinear filter. It used the middle value in the neighborhood of the target pixel.

The median filter is a popular example of a nonlinear filter that is used in image

processing. The median filter overcomes one of the limitations of the mean filter, which is its

inability to reduce impulsive noise. The median filters are also useful in preserving edges of

an image while reducing the image noise (Marques 2011).

The median filter operates by sorting the pixel values within a neighborhood, then

finding the median value from that ordered list and the replacing the original pixel by this

median value in output image (Marques 2011). The mathematical formulation for median

filter is given as follows:

𝑓(𝑥, 𝑦) = 𝑚𝑒𝑑𝑖𝑎𝑛 {𝐼 (𝑚, 𝑛)|(𝑚, 𝑛) ∈ 𝑊}

Where, I = the noisy image, f = the restored image and (m, n) = the row and column

coordinate respectively, within a window W of size m x n where the operation take places

(Marques 2011).


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For example, the pixel values within a window are 9, 12, 0, 5, 5, 9, 8, 10 and 7, and

they are processed and ranked in order to give 0, 5, 5, 7, 8, 9, 9, 10 and 12. The median

values is 8, which is then used as the output pixel value (Marques 2011). Figure 5 shows an

illustration of how the median filter works.

Figure 5: Illustration of Median filter operates.

Compared to the mean filtering technique, the median filter simply replaces each

pixel with the middle value in the neighborhood of the pixel, instead of using an averaging

operation. As the median is one of the pixel values in the input image, the median filter does

not create a new pixel value. This helps in preserving edges and shows why these filters can

be useful for image processing (Solomon 2010).


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2.6 IMAGE ENHANCEMENT

Instead of image smoothing for image restoration, there are techniques for image

enhancement that are called edge enhancement or image sharpening. If noise removal is an

application of low pass filtering, then the image sharpening is an example of high pass

filtering. Image sharpening refers to any enhancement technique that highlights edges and

fine details in an image. Because edges contain the high frequency components of an image,

high pass filters are used to sharpen the images and increase the contrast. Image sharpening is

widely used in printing and photography (Bovik 2009).

An edge represents a discontinuity or change of intensity (e.g. brightness, contrast) or

color (e.g. luminance, chrominance) in an image. Edges in grayscale images appear at

transitions between dark and bright areas in an image such as the boundaries that separate

foreground objects and background scene. Figure 6 illustrates the difference between an ideal

edge which is a sharp transition, and a ramp edge, which is a gradual transition between dark

and bright areas in an image (Marques 2011) (Abdul Rasak Zubair 2014).

a) Ideal edge

b) Ramp edge

Figure 6: Different between ideal edges and ramp edge


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Edge detection is the extraction of edges of significant objects in an image. It is

basically a method of segmenting an image into regions based on discontinuities between

their regions. Detection of edges is very useful in many applications such as pattern

recognition and fingerprint and iris biometric identification, space science and robot vision

(Abdul Rasak Zubair 2014).

Image edge enhancement enhances the edges, such that an image with highlighted

edges is more attractive than the original image. The objective of image edge enhancement is

to improve visual appeal of the processed image compared to the unprocessed image. An

alternative to an image sharpening filter is the unsharp mask filter (Marques 2011).


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2.6.1 2.6.1 Unsharp mask filter

Unsharp mask filtering is method that boosts the high frequency edge information in

images (Lim 1990). An unsharp mask filter operates by subtracting a blurred version of the

image from the original image in order to highlight the edges in the image. An unsharp

masking filter is described by the equations (Solomon 2010):

𝐼𝑒𝑑𝑔𝑒(𝑚, 𝑛) = 𝐼𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙(𝑚, 𝑛) − 𝐼𝑠𝑚𝑜𝑜𝑡ℎ𝑒𝑑(𝑚, 𝑛)

𝐼(𝑠ℎ𝑎𝑟𝑝)(𝑚, 𝑛) = 𝐼𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙(𝑚, 𝑛) + 𝑘 [𝐼𝑒𝑑𝑔𝑒(𝑚, 𝑛)]

where k is a scaling constant.

To use this approach, first the edge image, 𝐼𝑒𝑑𝑔𝑒 must be produced by subtracting the

smoothed image, 𝐼𝑠𝑚𝑜𝑜𝑡ℎ𝑒𝑑 from the original image, 𝐼𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 , where the smoothed image,

𝐼𝑠𝑚𝑜𝑜𝑡ℎ𝑒𝑑 is often obtained by filtering the original image with a low pass filter, of which

mean filter is the simplest example. (Solomon 2010).

Using a specified scaling constant 𝑘, the edge image is then added to the original

image to obtain the sharpened image. As the scaling constant k is increased from 0 to 𝑘𝑙𝑖𝑚𝑖𝑡 ,

the degree of enhancement is increased. Generally, values for k is between 0.2 and 0.7 are

acceptable, depending on level of enhancement required (Solomon 2010) (Bovik 2009).

Figure 7 illustrate the idea of unsharp mask filter works.


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Figure 7: Illustartion of Unsharp mask filter operates


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2.7 MATLAB

MATLAB (MATrix LABoratory) is a high-level text language and interactive

environment used for numeric computation and data analysis (The MathWorks Inc 2016).

MATLAB is the software that is used to illustrate signal processing concepts in this project. It

consists of a main engine to perform computations and also several toolboxes for special

purpose applications. Some special code will clarify why these are used instead of the other

code. MATLAB is an essential of learning for Industrial Computer Systems Engineering

(ICSE) and Instrumentation & Control Engineering (ICE) students as it can be used to

simulate process systems and analyze process data. This section will describe the Image

Processing Toolbox (IPT) in MATLAB that is used in developing the simulation programs

for this thesis.

2.7.1 Image Processing Toolbox

The image processing toolbox is distributed by MathWorks is contains a collection of

functions for performing different operations specifically for signal and image processing.

The operations available in this toolbox are: image analysis, segmentation, morphology,

image enhancement, noise removal, blurring, geometric transformation, image registration

and others. Each of these operations is performed by using their own in-built functions and

can operate on diverse image types and on different features of the images (MathWorks

2016).


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In MATLAB’s IPT, there are two basic built-in functions, imread and imshow, that

are used to read and display the image respectively. The imread function allows users to read

image files in any type of image format. While imshow is used to display an image and

includes a number of optimization parameters for setting properties associated with image

display. These functions support all prevalent image formats and create the image array for

use by other MATLAB functions. A various type of image format can be used inside the

MATLAB toolbox. Table 1 simplify the image formats that are supported by MATLAB

(Solomon 2010). For this project, the TIFF format was chosen because it comes with

compressed and uncompressed formats.

Table 1: Image file formats


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3 METHODOLOGY

This section will discuss the approach that is used to develop the simulation program.

Both of the core image processing operations, which are noise removal and edge

enhancement, will be discussed here.

3.1 IMAGE INPUT

The original images that is used in this thesis come from the Signal and Image

Processing Institute (SIPI) at University of Southern California (USC). These images can be

accessed in their webpage (SIPI 2015). The images in the USC-SIPI image database are

provided for research purposes. SIPI provide image of various sizes in their database, the

images are stored in TIFF format.

Figure 8: 8-bit image

Figure 8 show the original image clock is used throughout project. This grayscale image is

256 width x 256 height. This is an uncompressed version of the original image.


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3.2 NOISE REMOVAL

The purpose of this section is to describe the methods that are used to complete the

simulation program to filter images for noise removal. As discussed in Section 2.5, two types

of filter are used for noise removal: mean filter and median filter.

3.2.1 3.2.1 Process plan

In this thesis project, the image database was simulated in MATLAB’s IPT by following the

flow diagram given in Figure 9.

Figure 9: Program simulation process for noise removal

Read

•Input image

Convert

•Indexed image

•Double precision classes

Add

•Salt and Pepper Noise

•Gaussian Noise

Choose

•Window size for mean Filter and median Filter

Display

•Original image

•Noisy Image

•Filtered image

Compare

•Mean- square value


25

First, when the simulation program is run the image input is read using imread

function. The input image is a grayscale image with 256 x 256 pixels with 1 byte per pixel

that stored an intensity value from 0 to 255. This image is indexed image in uint8 (unsigned

8-bit integer) data classes. To make the input image suitable for image processing that

performs a numbers of an arithmetic operations, the image input is changed from uint8 to

double (double precision floating point) class to allow for more precision. This class

increases storage from 1 byte per pixel to 8 bytes per pixel, with pixels value that range from

0.0 to 1.0, with no negative numbers. This format is more useful when arithmetic operations

are performed.

Next is where the noise is added to the input image. Two types of noise were

introduced in Chapter 2 Section 2.4.1 which were salt and pepper noise and Gaussian noise.

The imnoise function in IPT can set the type of noise along with intensity parameter value

ranging from 0 to 1. The noise is added to the image. For salt and pepper noise, the noise

density, which has a default value of 0.5 is the additional parameter. While, for Gaussian

noise, mean and variance of Gaussian noise is needed in, this has default values of zero mean

with 0.01 variance.

Then the window operation size is chosen. In the simulation program the window size

can be added manually. This makes it easier to change the size when the visual appearance of

image is compared for different window sizes. Lastly, after filtering the original image, the

noisy image and the filtered image are displayed. There will be two windows that will pop up

for image display, where the “Figure 1” window displays the original image and the “Figure

2” window display the noise added image and the filtered image.


26

When the image displays, the image processing results can be see subjectively. But to

confirm that a filter is good at reducing noise, the mean-square error between original and

processed images is calculated. The smaller the error, the better the filtering performance.

3.2.2 Mean Filter

The mean filter operates by replaces each pixel by the average value of the

neighborhood. In this simulation a by 3 x 3 mean window filter is used. The method of mean

filter works is illustrated in Figures 10 and 11:

Figure 10: Pixel value before filter take place

Figure 11: Pixel value after filter take place


27

Consider the pixels at the coordinate (2, 3), which has an original value of is 0.7216

as shown in Figure 10. The nine neighboring pixels value are summed and then divided by 9

to give the average value;

1

9(0.7412 + 0.7176 + 1.0 + 0.7490 + 0.7216 + 0.7176 + 1.0 + 0.7296 + 0.7176)

= 𝟎. 𝟕𝟖𝟖𝟐

The output value is shown in Figure 11. The process is repeated at the next pixel until

all pixels are processed. The same method could be apply to 5 x 5 mean filter but, this time a

25 neighborhood of pixels would be used in the averaging.

3.2.3 Median Filter

The median filter operates by sorting the pixel values within the neighborhood, where

the median value within the window replaces the original value. The simulation using a 3 by

3 median filter is shown in Figures 12 and 13.

Figure 12: original pixel value


28

Figure 13: After median filtering

Again, the pixels at coordinate (2, 3) with original pixel values of is 0.7216, is shown in

Figure 12. The nine neighboring pixels is arranged in ascending order as follows:

0.7176, 0.7176, 0.7176, 0.7216, 0.7255, 0.7296, 0.7412, 0.7412, 0.7490

The median value of 0.7255 replaces the original value, as shown in Figure 13. The process is

repeated at the next pixel until all pixels are processed. The same method could be applied to

a 5 x5 median filter but this time 25 neighborhood pixels would be sorted.


29

3.3 EDGE ENHANCEMENT

The purpose of this section is to describe a method of operation that is used to complete

the simulation program for image sharpening by using an unsharp mask filter. As discussed

in Section 2.6.1, the unsharp mask filter is a technique that is used to increases the sharpness

of the image by using a blurred image of the original input image.

3.3.1 Process Plan

In this section, the image sharpening was simulated by following the flow diagram shown in

Figure 14.


30

Figure 14: Process flow of image sharpening by unsharp mask filter

Read

• Input image

Convert

• Double precision

Blur

• Using mean filter 3 by 3 window

Subtract

• Original image with filtered image

Choose

• Scaling constant, k

Add

• Original image with blurry image

Display

• Original image and sharpening image


31

The simulation for edge enhancement is based on the unsharp masking theory

(Solomon 2010) (Marques 2011). Firstly, the image was read by using the imread function.

The image input values that range from 0 to 255 in the uint8 data class are converted to the

double precision data class with values that range from 0.0 to 1.0. This allows for more

precise calculation when the arithmetic operations of addition, and subtraction are done.

Next, the input image is filtered with a 3 x 3 mean filter to obtain the blurred image

from an original image. The blurred image is now subtracted from the original image to get

an edge image. The edge detect image will be displayed together with the final result.

Then, the scaling constant k is chosen. It can be varied manually in this simulation

program. After the scaling constant k is chosen, each pixel in the edge images is scaled by k

and then is added back into the original image to obtain the edge sharpened image. The image

edge enhancement was tested using three different values of scaling constant.

Lastly, the blurred image, the edge image and the enhanced image are displayed

together in the “Figure 1” window.


32

4 RESULTS

In this section the results from this project are presented. The results are in the form of

filtered images and mean square error measurements. For noise removal technique, two types

of noise are added to the input image. The filtered image is then compared to the original

noise-free image and noisy image. The results will show how effective the filters are at

removing the different kinds of noise in the image. For edge enhancement, three different

scaling factors are compared to find scaling factor that gives the best enhancement of the

edges in the image.

4.1 MATHEMATICAL RULES

The mean square error (MSE) is chosen as an objective metric for deciding which

type of filter is best at removing the different types of noise. MSE is widely used in image

processing (Kaiwen Zhang 2002). It measures overall gray-value difference between pixels of

the reference image and the filtered image for the entire image without considering

correlation between the neighborhood pixels. The MSE is defined as:

𝑀𝑆𝐸 =1

𝑚𝑛 ∑ ∑(𝑥𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙(𝑚, 𝑛) −

𝑛

𝑥𝑓𝑖𝑙𝑡𝑒𝑟𝑒𝑑(𝑚, 𝑛))2

𝑚

Pixels are treated individually so all pixels in the image are equally important. As a

human observer, some pixels errors may cause more significant visual effects than other

pixels errors, but MSE would assign the same error value to both pixels. The greatest quality

is when the MSE equal to zero. The smaller MSE, the better the filter for filtering that type of

noise.


33

4.2 MEAN FILTER RESULT

4.2.1 Result of 3 by 3 filtered image

The first result that is presented are for the 3-by-3 mean filter applied to images with

both type of noise. From Figure 15 and Figure 16, the filtered image give evidence of less

noise than the unfiltered noisy image. The noise tends to be removed but some details such as

edges, becomes blurred so, while the mean filter can remove the noise, it tends to blur the

image.

Figure 15: 3-by-3 Mean filter with salt and pepper noise


34

Figure 16: 3-by-3 Mean Filter with Gaussian Noise

The Gaussian noise is removed more effectively with the mean filter compared to salt

and pepper noise. The salt and pepper noise becomes blurred but is not removed. The mean-

square-errors support these observations. The MSE value is calculated for, the original to the

noise added image, and the original image to the filtered image. The values are recorded in

Table 2.

Table 2: MSE value for mean filter

Gaussian Salt and pepper

Original image and noise added image 0.01617 0.01753

Original image and filtered image 0.00425 0.0464

From the table, the filtered Gaussian noise image has the smallest MSE value, which

shows that the mean filter removes Gaussian noise better than it removes salt and pepper

noise.


35


This is result that is presented are for the 5-by-5 mean filter applied to images with

both type of noise. Figure 17 shows the 5 by 5 mean filter with salt and pepper noise and

Figure 18 shows the 5-by-5 mean filter with Gaussian noise. From the image review, the both

image became more blurred because the mean filter tends to blur the noise instead of reduce

it. It shows that window 5-by-5 mean filter not really suitable to uses when to reduce the

noise.

Figure 17: 5-by-5 mean filter with salt and pepper noise

Figure 18: 5-by-5 mean filter wit Gaussian noise


36

Table 3: MSE value for 5-by-5 mean filter




The MSE value for 5-by-5 mean filter is recorded in Table 3. From the table, with the

almost same noise- added to the image, the Gaussian noise is seen to be more reduce from the

image but the both image filtered look more blurred.


37

4.3 MEDIAN FILTER RESULT


The median filter has uses in image processing because it is the simplest nonlinear

filter that can produce interesting results. Figure 19 shows an image with salt and pepper

noise that is filtered by 3 x 3 median filter, while Figure 20 shows Gaussian noise that is

filtered by the same median filter.

Both types of noise are reduced in the image, but by looking at Figure 19, it is clear

that salt and pepper noise has being removed more effectively than the Gaussian noise. From

these images, the median filter is not only good at removing the noise but also at preserving

the edges of the image. It is clear that the median filter works better when removing the salt

and pepper noise compared to removing Gaussian noise.

Figure 19: 3-by-3 median filtered image with salt & pepper noise


38

Figure 20: 3-by-3 median filtered image with Gaussian noise

The MSE value for the median filter is calculated between the original and the noise-

added image, and between the original image and the filtered image. The MSE for both types

of noise are recorded in Table 4. From the table, the filtered salt and pepper noise image has

the smallest MSE value, which is near to zero. By comparing Table 2 and Table 4, the

median filter is considerably more effective than mean filter in removing salt and pepper

noise.

Table 4: MSE value for median filter





39


This is result that is presented are for the 5-by-5 median filter applied to images with

both type of noise. Figure 21 shows the 5-by-5 median filter with salt and pepper noise and

Figure 22 shows the 5-by-5 median filter with Gaussian noise.

Figure 21: 5-by-5 median filtered image with salt & pepper noise

Figure 22: 5-by-5 median filtered image with Gaussian noise


40

From the image review, for salt and pepper noise clearly can see the noise is remove

from the image and still have some edge is preserved. For Gaussian noise, the image become

a bit blurred but still good when compare to the 5-by-5 mean filter.

The mean-square-errors support these observations. The MSE value is calculated for,

the original to the noise added image, and the original image to the filtered image. The values

are recorded in Table 5.

Table 5: MSE value for 5 by 5 median filter




From the table, the salt and pepper noise is seen to work better than the Gaussian noise

when to remove the noise using median filter. By comparing to window of median filter, 3-

by-3 window is work better than the 5-by-5 window filter.


41

4.4 RESULT OF 11-BY-11 WINDOW FILTER

The uses of larger windows for mean and median filter were also studied. A window

of size 11-by-11 was chosen. The result are not included here because the larger windows

caused the image to become more blurring, especially when using mean filter on salt and

pepper noise which is not effective at all. The results for 11-by11 mean filter and 11-by-

11median filter are included in Appendix A of this thesis.

4.5 UNSHARP MASK FILTER RESULT

The unsharp masking filter is one technique for edge enhancement. Figure 19 shows

the blurred image resulting from the application of a 3 by 3 mean filter to the input image.

The blurred image is then subtracted from the original image to obtain the edge difference

image, as shown in Figure 23. The final enhancement images based on using different scaling

constants is shown in Figure 24.


42

Figure 23: Result of blurring with mean filter

Figure 24: The edge image


43

k= 0.2

MSE = 0.00009

k= 0.5

MSE =0.00056

K= 0.7

MSE = 0.00110

k= 0.8

MSE =0.00143

k=7

MSE = 0.109

K=11

MSE= 0.27126

Figure 25: Image edge enhancement with different scaling constant k

The results in Figure 25 show that by increasing the parameter k, the degree of

enhancement increases but the noise within the image becomes more apparent. The different

values of k that were used are 0.2, 0.5, 0.7, 0.8, 1.0 and 11. A value of 0.8 is upper value for

k, beyond which the noise effects become more severe.


44

4.6 RESULT SUMMARY

In this section the findings of this project are summarized here. For noise removal

technique, two type of noise is added which is salt-and-pepper and Gaussian noise and two

type of filter is apply to remove this noise.

For linear filter example is mean filter, works better when removing the Gaussian noise

compared to removing the salt and pepper noise. For nonlinear filter example is median filter.

Median filter are introduced to overcome the limitation of mean filter so it works better when

removing the salt and pepper noise comparing to removing Gaussian noise. But median filter

not only remove the noise but also preserve the edges of image. For noise removal, only

small size of window is consider to use for removing noise. This can see when the bigger size

of window is applied the image tends to become more blurred when filtering job is done.

For edge enhancement, three different scaling factors are compared to find scaling

factor that gives the best enhancement of the edges in the image. The k value is measured

from k = 0.2 to 11. Results from Figure 25 shows that the degree of enhancement, 0.8 is

chosen because the edge is enhance nicely without amplify the false edge (noise). The false

edge is amplify can clearly see on when k = 11 compared to the original image.


45

5 PROBLEM ENCOUNTERED AND COUNTERMEASURES

During the progress plan stage of this project a few of problem were encountered.

Corrective action was taken to ensure this project and thesis could be completed according to

the plan and design.

The first problem that was identified was that Murdoch University only has one

license for the MATLAB Image Processing Toolbox. This license only could be accessed

from a special server which is ENGEN2 and only one person can accessed the toolbox at the

time. To solve this problem, a request was sent to the technician, Will Stirling, to open this

server.

The second problem was the limited resources in the library. There were only a

limited number of book for image processing. A few useful books could not be found either

in hardcopy or e-book format from library resources. There are also a lot of journal articles

available but the books have more detail explanation about MATLAB code. The

countermeasure for this problem was to borrow a book from the supervisor.


46

6 CONCLUSION AND RECOMMENDATIONS

6.1 CONCLUSION

In conclusion, different filters have different strengths and weaknesses. So different

types of filter are needed when solving image processing problems. Sometimes a nonlinear

filter may work better than a linear filter. In image restoration, the nonlinear filter can do a

better job that the linear filter. As seen in the results, while the linear filter can remove the

noise, the nonlinear filter not only removes the noise but also can preserve edges. This is

why, not just a single filter is needed to remove noise, but a range of filters are needed,

depending on the situation encountered.

In summary, this project had archieved its main objective to develop a simulation

program in MATLAB using the Image Processing Toolbox. Basic knowledge about image

processing was introduced in the literature review chapter. Both linear and nonlinear filters

for specific image processing tasks were designed: the mean filter as a linear filter type and

the median filter as a nonlinear filter type. The requirements of the filters to remove

unwanted artefacts (noise) and to enhance edges were identified.

Lastly, with this thesis, the main achievement when developing these programs, was

that the theoretical and practical knowledge gained from three years study at Murdoch could

be applied to a new problem. This is a significant achievement because it helped develop the

skills in programming, troubleshooting and system design.


47

6.2 RECOMMENDATIONS

Due to the time limitation, there is still a lot of works that could be done in this area.

Following the investigations described in this thesis, a number of more advanced image

processing tasks could be investigated:

- The simulation programs were limited to basic applications of image processing;

the existing program could be extended to other application such as object

identification and image coding.

- The simulations used only a gray-level image. The next step would be to upgrade

to using color images.

- Other enhancement methods can be applied to enhance the edges of images such

as the Laplacian-based method (Solomon 2010).

- The simulation program was built by using the MATLAB Image Processing

Toolbox. It is possible to build simulators using other toolbox such as signal and

processing toolbox and computer vision toolboxes.


48

7 REFERENCES

Abdul Rasak Zubair, Olasebikan Alade Fakolujo. "International Journal of Computer and Information

Technology." Image Edge Detection and Image Edge Enhancement: Numerical experiment on

High Pass Spatial Filtering, 2014: 772-781.

Ajay Kumar Boyat, Brijendra Kumar Joshi. "A Review Paper." Noise Models in Digital Image

Processing, April 2015.

Bovik, Alan C. The Essential Guide to Image Processing 2nd Edition. London, UK: Academic Press,

2009.

Jae S. Lim. Two- Dimensional Signal and Image Processing. Englewoods Cliff, NJ: Prentice Hall, 1990.

Jaehne, Bernd. Digital Image Processing. Heidelberg, Germany: Springer-Verlag Berlin, 2005.

Kaiwen Zhang, Shouzhong Wang, Xiepen Zhang. A New Metric for Quality Assesment of Digital Image

Based on Weighed-Mean Square Error, 2002.

Marques, Oge. Practical Image and Video Processing Using Matlab. Somerset, NJ , USA: John Wiley &

Son, 2011.

Russ, John C. The Image Processing Handbook 5th Edition. Raleigh, North Carolina: Taylor & Francis

Group, 2007.

SIPI. Signal and Image Processing Institute, University of Southern California. 2015.

http://sipi.usc.edu/database/ (accessed September 2015, 1).

Solomon Chris, Toby Brecken. In Fundamental of Digital Image Processing: A Practical Approach with

Example in Matlab. Hoboken, NJ: John Wiley & Son, 2010.

Tan, Li. Digital Signal Processing : Fundamentals and Applications. Burlington, MA, USA: Academic

Press, 2007.

The MathWorks Inc. 2016. http://au.mathworks.com/help/images/product-description.html

(accessed December 2015).

Zubair, Abdul Rasak. "International Journal of Research in Commence, IT & Management."

Comparison of Image Enhancement Techniques, 2012.


49

8 APPENDIX

8.1 APPENDIX A

Result for a 11 by 11 mean filter


50


51

Result for a 11 by 11 median filter.


52


53

8.2 APPENDIX B

Appendix B shows the Matlab code for noise removal by a mean filter.

clc; clear;

% Read image. I = imread('C:\Users\32112635\Documents\MATLAB\Thesis Ariesa\clock.tiff');

[r c]=size(I)

%convert image to double precesion Id = im2double (I);

% Apply salt and pepper noise to image using |imnoise| . Isp = imnoise(Id,'salt & pepper',0.05);

% Apply gaussian noise to image using |imnoise| . Ig = imnoise(Id,'gaussian',0,0.02);

%predefined filter NxN window (mean filter) n = input ('enter the window size of MEAN Filter, (n for NxN matrix):');

%specify window size mean = ones (n,n)/(n*n)

%imfilter=computes each element of the output,using double-precision

floating point. %for salt and pepper noise Ispf = imfilter (Isp,mean);

%for gaussian noise Igf = imfilter (Ig,mean);

% Display original image and noise image for comparison. figure (1) subplot (1,2,1), imshow(Isp) title ('Image with Noise (Salt&Pepper)') subplot (1,2,2), imshow(Ispf) title ('Filtered Image Using Mean Filter')

% Display original image and noise image for comparison. figure (2) subplot (1,2,1), imshow(Ig) title ('Image with Noise (Gaussian)') subplot (1,2,2), imshow(Igf) title ('Filtered Image Using Mean Filter')


54

%-------------------MSE-------------------- % 1st try % ORIGINAL - FILTERED IMAGE diffg = ( Id -Ispf).^2; MSE1= sum(sum(diffg))/ (r*c); fprintf('\n\nORIGINAL IMAGE AND FILTERED IMAGE') fprintf('\nThe Mse value for Salt and pepper noise is: %.5f', MSE1);

diffg = ( Id -Igf).^2; MSE2= sum(sum(diffg))/ (r*c); fprintf('\nThe Mse value for Gaussian noise is: %.5f', MSE2);

%-------------------MSE-------------------- % 2nd try % OORIGINAl - NOISY IMAGE

diffg = ( Id -Isp).^2; MSe1= sum(sum(diffg))/ (r*c); fprintf('\n\nORIGINAL IMAGE AND NOISE ADDED IMAGE'); fprintf('\nThe Mse value for salt and pepper noise is: %.5f', MSe1);

diffg = ( Id -Ig).^2; MSe2= sum(sum(diffg))/ (r*c); fprintf('\nThe Mse value for Gaussian noise is: %.5f', MSe2);


55

8.3 APPENDIX C

Appendix C shows the Matlab code for noise removal by a median filter.

clc; clear;

% Read image. I = imread('C:\Users\32112635\Documents\MATLAB\Thesis Ariesa\clock.tiff');

%convert image to double precesion Id = im2double (I); [r c] = size (I) % Apply salt and pepper noise to image using |imnoise| . Isp = imnoise(Id,'salt & pepper',0.05);

% Apply gaussian noise to image using |imnoise| . Ig = imnoise(Id,'gaussian',0,0.02);

%predefined filter NxN window (mean filter) n = input ('enter the window size of MEDIAN Filter, (n for NxN matrix):');

%specify window size

%B = medfilt2(A, [m n]) performs median filtering, where each output pixel % contains the median value in the m-by-n

% neighborhood around the corresponding pixel in the

% input image.

%median = medfilt2 ((image_noise,[n n]); %median filter with NxN window

% %for salt and pepper noise Ispf = medfilt2 (Isp,[n n]);

%for gaussian noise Igf = medfilt2 (Ig, [n n]);

% Display original image and noise image for comparison. figure (1) subplot (1,2,1), imshow(Isp) title ('Image with Noise (Salt&Pepper)') subplot (1,2,2), imshow(Ispf) title ('Filtered Image Using Median Filter')

% Display original image and noise image for comparison. figure (2) subplot (1,2,1), imshow(Ig) title ('Image with Noise (Gaussian)') subplot (1,2,2), imshow(Igf) title ('Filtered Image Using Median Filter')

%------------------Mean Square Error--------------- %--- calculates the MSE. % calculates the "square error" image. % change to double so that we can get negative differences. %--------------------------------------------------------\


56

%-------------------MSE-------------------- % 1st try % ORIGINAL - FILTERED IMAGE diffg = ( Id -Ispf).^2; MSE1= sum(sum(diffg))/ (r*c); fprintf('\n\nORIGINAL IMAGE AND FILTERED IMAGE') fprintf('\nThe Mse value for Salt and pepper noise is: %.5f', MSE1);

diffg = ( Id -Igf).^2; MSE2= sum(sum(diffg))/ (r*c); fprintf('\nThe Mse value for Gaussian noise is: %.5f', MSE2);

%-------------------MSE-------------------- % 2nd try % OORIGINAl - NOISY IMAGE

diffg = ( Id -Isp).^2; MSe1= sum(sum(diffg))/ (r*c); fprintf('\n\nORIGINAL IMAGE AND NOISE ADDED IMAGE'); fprintf('\nThe Mse value for salt and pepper noise is: %.5f', MSe1);

diffg = ( Id -Ig).^2; MSe2= sum(sum(diffg))/ (r*c); fprintf('\nThe Mse value for Gaussian noise is: %.5f\n\n', MSe2);


57

8.4 APPENDIX D

Appendix C shows the Matlab code for an unsharp mask filter.

clc; clear;

% Read image.

I = imread('C:\Users\32112635\Documents\MATLAB\Thesis Ariesa\clock.tiff');

[r c] = size (I)

%convert image to double precesion Id = im2double (I);

%--------smoothes by 3x3 mean filter mean = ones (3,3)/(3*3) smooth = imfilter (Id,mean);

edge= Id- smooth;

k = input ('enter the scaling constant,k:'); sharp1 = Id + k*(edge);

figure(1) imshow(smooth); title ('Blurred Image');

figure (2) subplot(1,2,1); imshow(edge); title('Edge Detection'); subplot (1,2,2) imshow(sharp1); title('Sharpened Image')

%-------------------MSE-------------------- % 1nd try % noisy image - filterd image % salt and pepper image

diffs1 = ( Id- sharp1).^2; mse1= sum(sum(diffs1))/ (r*c); fprintf('\n\nSharpened Image without noise'); fprintf('\nThe Mse value is: %.5f', mse1);


58

8.5 APPENDIX E

Result for an unsharp mask filter.


59