CHAPTER 4 EDGE DETECTION TECHNIQUE - Shodhgangashodhganga.inflibnet.ac.in/bitstream/10603/23047/9/09... · 2018. 7. 9. · 4.2.1 The Marr-Hildreth Edge Detector Marr-Hildreth Edge

56

CHAPTER 4

EDGE DETECTION TECHNIQUE

The main and major aim of edge detection is to significantly reduce

the amount of data significantly in an image, while preserving the structural

properties to be used for further image processing. A number of algorithms

already exist. The present chapter focuses on two different methodologies

which already exist, namely Canny Edge Detection and Marr-Hildreth Edge

Detection Techniques. A new edge detection technique is proposed in this

chapter.

4.1 INTRODUCTION

In image processing, the Edge Detection Technique is an important

area. Normally edges define and differentiate between the boundaries of an

image and the background region. It even helps in segmentation and object

recognition. The following are the criteria for a good quality of detecting the

edges,

i. Lighting conditions

ii. The presence of objects of similar intensities

iii. Scene image densities and

iv. Noise

57

Any of the above problems can be handled by adjusting the

threshold values. No good method was proposed to set the threshold values

automatically. The manual change is the only way of changing the values. An

ideal algorithm is needed to make use of the edge detections. In order to

create a good performance, the previous performance must be known

(www.csc.noaa.gov/crs/lca/faq_gen.html#WIRS). In the present research, two

different edge detectors have been tested under a variety of situations and

have been compared with the current system. A new Kodi-Edge Detection

Method is used to analyze the scene sensed by the sensor. The two different

factors considered here are,

i. Intensity

ii. Color composite information.

1) Intensity - It is a measurement of light intruding on a sensor or

photosensitive device. Normally the color specification is done

using three gray levels (Red, Green, and Blue) at each pixel.

One of the useful schemes is called HSI. In this, I stands for

Intensity or brightness. It is measured as the average of the R,

G, and B gray level values (Pratt et al 1991). The overall

brightness of a pixel is specified by the intensity value. It is

done regardless of its color.

The other two parameters are H-Hue and S-Saturation. Hue is

expressed as an angle which will be referred as the spectral wavelength. The

point counted from the origin of the color as radius is the saturation

parameter. Normally, for any arbitrary, hue 0o is red, 120o is green and 240o is

for blue (Castleman et al 2010). The non-spectral colors fall between 240o and

360o. It is in purple color where the eye can perceive.

58

2) Color composite information- From a multi band image9 like

LANDSAT imageries, any three bands are selected to merge to

generate a color image. Additive and subtractive are the two

methods of color composite. The three primary colors of 3 light

sources (RGB) are used for additive color composite. That is

called color graphics display (Castleman et al 2010).

The three pigments of the colors (cyan, magenta and yellow) are

used for subtractive color composite. There are more than 3 spectral bands in

multispectral images. Except the RGB, the human eye cannot detect any

region of electromagnetic spectrum (or color). The visible range of the multi -

spectral image may be 0.4 to 0.7 µm for human eye. The common wavelength

of the electromagnetic spectrum is,

0.4 – 0.446 µm : Violet

0.447 – 0.500 µm : Blue

0.501 – 0.578 µm : Green

0.579 – 0.592 µm : Yellow

0.593 – 0.620 µm : Orange

0.621 – 0.7 µm : Red

The invisible bands can be viewed by combining the colors. When

blue gun of a display device passes blue color and green color from the green

gun and red band from the red gun, the combination is called ‘True’ color

combination [ref.3]. The combinations other than this are called false color

combinations. The change detection is also done with multispectral images.

When a multi spectral image of the 6 bands are used, the number of color

59

composite may be calculated as, 6!/ (6-3)! = 120. A single band is passed

through the blue and green guns to understand the changes between the two

images.

4.2 THE PREVIOUS METHODS – AN OVERVIEW

Edges define the image boundaries which help segmentation and

object recognition. It is the basis of low-level image processing and good

edges (edges without noise) are necessary for higher level processing. There

are only poor behaviors obtained from the general edge detectors where their

behavior may fall within the tolerances in specific situations, but have

difficulty in adapting to different situations. Hence, an edge detector which

has a better performance must have to be developed. It is necessary to first

discuss about the previous edge detectors. In the present research, two

different methodologies are considered.

4.2.1 The Marr-Hildreth Edge Detector

Marr-Hildreth Edge Detector (1979) was very popular before

Canny (1986). It is based on the gradient which uses Laplacian to take the

second derivative of an image (Marr Hildreth 1980). Hence, there are three

steps in Marr-Hildreth edge detector algorithm. They are,

i. Smooth the image using Gaussian, to reduce the error due to

noise.

ii. 2D Laplacian is applied ,

f = + (4.1)

60

iii. Repeat the loop and determine / verify sign change. If there is a

sign change and,

If Slope > threshold, mark the pixel as an edge

Else find another pixel

There is only one Gaussian distribution which optimizes the

relation using equations 4.2 to 4.6 and named as,

G(x) = exp( x /2 ) , with the help of Fourier transform (4.2)

G( ) = exp ) (4.3)

It can be represented in 2D as,

G(r) = exp ( r /2 ) (4.4)

There are two parts in the edge detection analysis in Marr-Hildreth

presentation,

i. The change in intensity values of the natural images are

detected at different scales. Using Gaussian 2nd derivative

filter, some simple conditions are satisfied. The intensity

changes are detected by finding zero values of 2G(x, y) * I

(x, y) for image I where G(x, y) is 2D Gaussian distribution

and 2 is Laplacian. These represented intensity values are

referred as zero-crossing segments and the evidence is given

for this in the Marr-Hildreth theory.

61

ii. Intensity changes arise from surface discontinuities. Owing to

this, the zero-crossing pixels are not independent, and a

description of the image named raw primal sketch is formed

and the rules are deduced. In this, many psychophysical

findings are explained.

4.2.1.1 Detecting Intensity Changes

A change occurs in intensity values, there will be a corresponding

first directional derivative or zero-crossing in the second directional

derivative in intensity values. Hence, the zero-crossing in,

f(x, y) = D2 (G(r) * I (x,y)) (4.5)

In this, I (x, y) is the image and * is the convolution operator.

The derivative rule for convolution is,

f(x,y) = D2 G * I (x,y) (4.6)

Hence, these arguments establish the intensity changes using

Equation (4.6) at one scale.

An image is an array of pixels. These array values may be affected

by noise. Hence, smoothing is done to reduce the noise. The brightness of the

light impinges on the sensor. The direction of edges can be measured by

partial derivatives. The abrupt changes of image brightness will be measured

and it will occur at the curves of the image planes. Thus, blurring of images

are done through smoothening the pixel points and all these operations are

called convolution (Basudeb Bhatta et al 2011). As the edges are abrupt

image intensity changes, the derivation must be started in horizontal direction.

62

The partial derivative D of the continuation function f(x,y) can be

calculated with respect to,

a. x which is called the ‘horizontal variable’

b. Slope of the function

( , ) = ( , ) ( , ) (4.7)

Where,

x is the discrete variable which has a value 1. It may be detected

by,

i. Convolving the image with D2 G and

ii. Looking for zero-crossing in its output.

4.2.1.2 Issues

i. It concerns the orientation associated with D2.

ii. Also, it is not enough to choose zero-crossings of the

second derivative in any direction of the image

representation.

Marr and Ullman presented a theory on edge detection. The

analysis proceeded with 2 parts namely (1) Intensity changes (2) Spatial

localization

63

The intensity values are detected at different scales. The second

derivative Gaussian filter is being adopted at some conditions and thus the

primary filter need not be orientation-dependent. The 2D Gaussian

distribution is considered at a given scale of intensity values. However,

according to Marr, the ‘edge’ concept has a partly visual and partly physical

meaning. The spatial localization is considered the simplification of detection

of intensity changes and the detection process can be based on finding zero-

crossing using second derivative. This representation is complete and

invertible. The physical edges will produce roughly coincident zero-crossings

in channels of nearby sizes. These are sufficient for the real physical edge

existence.

The assurance is not given on the performance of a linear

convolution equivalent to a directional derivative. The symbolic descriptions

provided by zero-crossing segments that need to be matched between images,

not the raw convolution values. The descriptions need to be formed and kept

separate. Hence and Canny (1986) Proposed an Edge Detection Technique.

4.2.2 The Canny Edge Detector

It is possible for Marr-Hildreth to set the slope threshold, sigma of

Gaussian and the size. This edge detector will give connected edges if

hysteresis is used and will not otherwise give for a single threshold. It usually

gets spotty and has thick edges. The Marr-Hildreth (1979) technique does not

use any form of threshold, but an adaptive scheme is used. With Marr-

Hildreth zero-crossings, the edge strength is averaged over its length-part. If

the calculated average is above the threshold, the entire segment is marked

true pixels. If not, no part of the contour appears in the output. However, the

contour is segmented by breaking it at maxima in the curvature.

64

There is a standard edge detector and an algorithm was developed

by John Canny (1986). It is still the main source for detecting the edges of the

images. It outperforms many new algorithms. From this, it is found that there

are two ideas. First, the detection of intensity values can be simplified. This is

done at different resolutions. The detection is then based on finding the

zero-crossing in the second derivative which is called Laplacian. The

representations consist of zero crossing segments and their slopes. The

information from different channels being combined into a single description

is the second main idea. Canny developed the edge detection problem as a

signal processing optimization (Jifen Liu and Maoting Gao 2007).The result

and solution to this was a complex exponential function.

However, in the computational approach algorithm, Canny made no

attempt to pre segment contours. Instead, threshold is done with hysteresis. If

it is high threshold, the points are immediately output. The steps of Canny

Edge Detector are as follows,

i. Smoothing images using Gaussian 2D filter

ii. Finding the gradient which shows the changes in intensity. The

presence of edges indicated using the gradient in X and Y

direction.

iii. Non-maximal suppression, edges are indicated at a maximum

gradient as true edges.

iv. Edge threshold and tracking Hysteresis using high and low

threshold

65

In white Gaussian noise, the determination of edge is started. This

edge is called step-edge. This can be convolved with filter whose impulse

response is illustrated with the first derivative of Gaussian operator. The local

minimum is calculated and the center of an edge is located at this point. The

design problem becomes one of finding the filters. This may be expected to

give better performance. There are three criteria namely,

i. Detection: A low probability of failing to mark the real edge

points may be met. A low probability of marking false edges

and non edge points are also detected. It decreases the signal-to-

noise ratio.

ii. Localization: The edge points that the operator marks the edge

points should be as close as possible to the center of true edge.

iii. There is only one response to a single edge. When there are two

responses to the same edge, one may be false. However, the

multiple responses may not be captured when the mathematical

form is applied as in equation 4.7.

SNR = (G( x)f(x)dx) f (x) dx (4.8)

where n0 is mean-squared noise amplitude per unit length.

f(x) – impulse response of the filter

G(x) – edge

w – finite impulse response limit

66

The first derivative of the response is always zero. So a defined

time period is required to determine the local maxima to mark the true edges.

4.2.2.1 Issues

i. It is expensive.

ii. Gradients can be obtained in the x, y directions.

iii. During the non-maxima suppression, the edges at the high

threshold are only shown.

iv. There is no indication of the false edges.

v. More time is required for calculation.

4.3 PROPOSED KODI-EDGE DETECTION TECHNIQUE

In the present research, the new algorithm is proposed and it is

tested on various images. The following algorithm is illustrated using the

ERDAS implementation.

i. Preprocessing steps

a. Determine AOI (using ERDAS)

b. Conversion of gray scale to obtain the limit for the

computational requirements.

ii. Smoothening images

Blur the image to remove noise. When the remotely sensed image

is taken to obtain the edges, the image is to be blurred to remove the noise.

For such purpose, Gaussian filter is used. The signal to noise ratio is

67

considered for a good detection of false positive edges (Something marked as

edge which is not actually an edge) and false negative edges (Failing to

mask the existing edge). The above mentioned two problems are

monotonically decreasing the functions.

iii. The signal to noise ratio and localization may be defined as

follows,

a. Let f(x) is the impulse response of the Gaussian filter.

b. G(x) is used to denote the edge. There are two gradients

in X and Y direction. Hence, denote the edges at X=0,

where it can be centered. The root mean square (RMS)

response is given by,

(4.9)

Where xi represents the individual noise pixel and n is the number

of noisy pixels in the images and for calculating SNR,

signal represents the desired output and the noise represents

the undesired output (4.9). This quantity is frequently calculated

to assess how well the system works (David Landgrobe 2002, Li Jia-cun et al

2003). That is, how high the desired output is with respect to the undesired

noise level. The higher the SNR, the better is the system performance.

Calculation of SNR requires knowledge of the average values of signal and

noise levels. The SNR is to measure the amount of noise present in any image

acquisition and it takes into account all the different sources of noise present

in an image.

68

= ( )

(4.10)

Where µ is signal mean and is the standard deviation of the noise.

iv. The reciprocal of the root mean square will determine the

Localization to find the true edge.

(4.11)

v. Finding Gradients

Image gradient shows the change of colors. If f(x,y) is a scalar

function and i,j are the unit vectors in x and y directions , the gradient vector

function is given by ,

( , ) = . ( , ) + . ( , ) (4.12)

here is the vector gradient operator.

( , ) - point in upward direction of shape

Magnitude – value of slope

The scalar function may be given like,

| ( , ) = ( , ) + ( , ) (4.13)

69

From this, the steepness of the slope is represented for each point.

But it cannot give the directional information. So the mask of pixels may be

approximately given as (Castleman et al 2010)

| f(x, y) | [max |f(x, y) f(x + 1, y) | , |f(x, y + 1) |f(x + 1, y + 1) | ]

(4.14)

The equation (4.13) will compute the vertical and horizontal pixel

differences (Castleman et al 2010). To enhance the appearance, the filtering

function is used. To obtain a sharp and fine detail in an image, the high pass

edge detection called Kodi method is proposed in the present work. No

division is performed because it is not defined when all input values are found

to be equal, it gives the output value as zero. Hence, smoothening the input

values with low spatial frequency is done. Finally the image mask contains

only edges and zeros as represented in the matrix below,

Kodi =1 2 1

0 0 01 2 1

1 0 12 0 21 0 1

The linear features are highlighted such as roads or residential

boundaries using the 3X3 mask. The magnitude of the gradients should be

large and they are also known as edge strengths which can be determined as a

Euclidean distance measurement. Hence, by using the Pythagoras equation,

the gradient G (Castleman et al 2010) is derived as,

= ( + ) (4.15)

VerticalHorizontal

70

Where,

= ( ) = ( ) , Gx, Gy are the gradients

found in the x,y directions respectively. Normally, as the edges are broad,

they cannot be indicated with their exact location. To determine the direction,

the following expression is used.

= tan (4.16)

vi. Sharpening of edges

Non-maximal suppression is the technique where Canny used to

blur the image edges. Here, in Canny, the eight connected neighborhoods

have been used. The positive and negative strength of the current pixel is

compared and preserved. If not, (i.e., remove) the value is suppressed.

However, in the present research, a new algorithm is proposed for

strengthening the true edges. The algorithm 2D Non-Maxima Suppression

(2D-NMS) for the blocks of images is given below. Normally non-

seperability is the result of this 2D NMS. Hence, an efficient solution is

needed (David Landgrobe 2002). Therefore, the region algorithm is discussed

here.

4.4 REGION ALGORITHM FOR NON MAXIMA

SUPPRESSION

There are two local maxima observed with n +1 pixel. There must

be at least one local maximum in each region. The size can be determined at

(n+1) * (n+1). Hence, this algorithm partitions the entire input image into a

number of regions. Within the partitioned image blocks, it searches for the

71

greatest pixel element, which is known as the maximum candidate

(www.csc.noaa.gov/crs/lca/faq_gen.html#WIRS). With the help of this local

maxima candidate, the full neighborhood is tested. The pseudo code can be,

V i, j belongs to {n, n+1, 2n+1,}

n (0, (worst case x – no. of pixels)) x (0, worst case y – no. of pixels)

Do

(mi, mj) (i,j);

For all (i, j) (i, i+n) x (j, j+n) do

If (img (i2, j2) > img (mi, mj) then

(mi, mj) (i2, j2)

For all (i2, j2) (mi – n, mi+n) x (mj – n, mj + n) – (i, i+n) x (j, j+n) do

If img (i2, j2) > img (mi, mj) then

Goto exit;

Maxat (mi, mj);

Exit: stop

If the blocks candidate is in the local maximum, the worst case

occurs. The algorithm does the testing of neighbors for the pixels in the input

image for (2n+1)2-1 the comparisons per region. Hence, the number of

comparisons will be limited to,

= ( )( )

(4.17)

72

Average analysis will be possible. Hence, the testing starts with

(n+1)2 th neighbor instead of the first one. The average calculation will be ,

Avg Compare =(2n + 1) 1

(2n + 1)1i

( )

( )

( )+ (4.18)

<= 1 + ln 4 (4.19)

This is referred to as straight forward implementation using

Equations 4.9 to 4.12 as the behavior of the pixel is independent of the size of

the neighborhood. Normally, the average comparison calculated using

Equation 4.17, is 1.983 per pixel and in the worst case by 4. Though it is far

from optimal, this algorithm requires no additional memory and there is an

independent process of each region which can improve the straight forward

implementation in the real time scenario of image pre-processing techniques

(Ehsan et al 2008).

4.5 MULTI THRESH-HOLDING AND EDGE TRACKING

The edge pixels which are remaining after the non maxima

suppression can be marked with their strength pixel - by - pixel. Most of them

are true edges. However, sometimes there may be possibilities of bow noises

and color variations, due to the thorough surface of the image. To discern, it

will be better to use a threshold value, so that certain values will be preserved

to strengthen the pixels. The stronger pixels will be marked with

high threshold values, whereas the weaker edge pixels which are lower

73

than the low threshold or suppressed are marked as “weak” (Canny 1986).

A range of 10 to 255 is taken as the thresh hold values and those with weaker

and stronger edges are illustrated in the Figure 4.2.

The interpreted “stronger pixels” are included in the final image.

The weak edges are also included if they are connected to the strong edges.

The logic behind this is that the noise and other variations are unlikely

to result in a strong image with threshold adjustments. Due to the true

edges, only the stronger edges will occur in the original image (John Cipar

and Wood Cooley 2007). The following criteria are considered when the edge

pixels are set.

The weak edges are also connected to the strong edges due to

the true edges.

The high and low threshold values like 255 to 16 ( 28 to 24) are

used .

The edge pixel is set if a pixel has a high threshold value.

If a pixel is found to be the neighbor of an edge pixel and if it

has a low threshold, it is also known as edge pixel (stronger).

If a pixel has a high threshold but it is not the neighbor of an

edge pixel, it is then not set as edge pixel.

If a pixel has a low threshold, it is never set as an edge pixel.

74

Figure 4.1 (a) ,(b) The original images Kodi-Edge Detection Method

(a) (b)

(c)Figure 4.2 The outputs for proposed Kodi Edge Detection technique (a)

Multi thresholding (b) Edge tracking (c) Non maxima

suppression

75

(a) (b) (c ) (d)

Figure 4.3 The canny outputs (a) Double thresholding (b) Edge

tracking (c) Final output (d) Edges after non maxima

suppression

In the specification of edge detection problem, the edges are

marked at local maxima. It is done in response to the linear filter applied to

the image. The detection is done with the discrimination between signal and

noise at the center of an edge. Comparing the figures 4.2 and 4.3, a great

variation is determined when the edge tracking is implemented. Using

ERDAS, the edges are accurately tracked. Hence the maximum pixels were

identified. As in Figure 4.3(d), using canny’s non maxima suppression, the

edges are tracked with very less accuracy since the nearby pixels were unable

to identify.

76

Table 4.1 Comparison of the edge detection techniques

S.No Criteria Marr Canny Ours

1 *false positive High High Reduced

2 **false negative Wrong directionmeasurement

Wrongdirectionmeasurement

Reduced

3 Mean square distance

Spotty and not continuous

Spotty and not continuous

Spotty and not continuous

4 Algorithm tolerance of the corners and functions

Too spotty, noise and wide to identify features

Gives noise outlines, but middle arrangements, featuresdistorted and recovered with condition of colors

Gives good outlines of Land covered features

5. CPU Performance 3.12ms 2.67ms 1.79ms

From the above Table 4.1, the false positive and false negative of

the pixel setting are reduced. The calculation of mean square distance

measured is as in Marr and Canny methods. However, the algorithm tolerance

is very much improved (86%) in the proposed method. In Canny method, the

detected edges are with noise and the features are distorted. In the Marr

algorithm, the image is found with more noise and the features identified are

too spotty. Hence, the proposed method is more accurate and the performance

is tabulated below.

77

Table 4.2 Performance comparison of three methodologies

S.No Criteria Marr Canny Ours

1 *false positive 64% 56% 32%

2 **false negative 73% 61.20% 44.34%

3 Mean square distance 70% 45% 30%

4 Algorithm tolerance of finding pixels 20% 50% 86%

5 CPU Performance 68.1% 76% 84%

From the comparison chart shown below, it is noted that compared

to the Marr-Hildreth and Canny algorithms, obtaining the false positive and

false negative is reduced to32% and 44% respectively. It is done by

identifying the nearest pixel and its boundary.

Table 4.3 Performance comparison of Canny Vs. Kodi Edge detector

S.No Canny Edge detector Kodi Edge detector

1 No analytic solution has been found.

The false positive and false negative edges are found by calculating SNR.

2 Variational approach has been developed.

Finding true-edge method is developed (using equ. 4.3)

3 Localization is less accurate. The true edges are strengthened using region algorithm for sharpening edges.

4 Edge gradients are computed in two orthogonal directions i.e. rows and column vise only

Using local maxima (mi,mj) the neighborhood is tested. (section 4.4)

78

Table 4.3 (Continued)

5 The impulse response of the optimal step edge function was shown with first derivative of a Gaussian.

2nd derivative of Gaussian is used to test the impulse response.

6 Threshold were set according to the amount of noise in the image ( low threshold = 40% of high threshold i.e 1 to 255= 20 to 28)

Using ERDAS 9.3, the blurring of image will remove the noise. ( the threshold was set from 64 to 255)

7 When edge contours are locally straight, canny operator gives better result with maximum of false negative edges.

By setting the threshold values to the maximum of 255, the true edges will be bright and easily measurable. (Using equation 4.4)

8 The unsolved problem in canny is integration of different edge detector outputs into a single description (Figure. 4.2 c,g)

The average pixel comparison for its neighborhood is determined. So that the maximum true edges are the result from kodi. Figure. 4.2(e)

9 The edge and ridge detector outputs were implemented but the results were inconclusive. There is no clear reasons to prefer one edge type over another

Results are conclusive, because of the reduction in false positive edges (Table 4.1)

Reference made from “Edge Detection A computational approach” by Canny(1986)

Reference made from the Implementation using Erdas 9.3

79

Comparison chart

Chart 4.1 Comparison chart of the three different edge detection

methods

4.6 CONCLUSION

Using Marr and Canny, the methods are still produced with single

thick pixels and continuous edges. Finding the optimal way to combine the

three colors may be challenging. In these methods, the fine particle details are

missing. In the present research, the non maximum suppression may help the

granularity of the output for the identified edges. It is also notable that the

average case complexity may be below 1 for small neighborhood pixel sizes.

The column wise maxima are used in the left or right region of the sensed

image. An observation is made during the computation of the CPU

performance where it takes about 5.3 milliseconds only for determining the

Kodi edge detection. The comparison is also listed out in Table 4.1.

0%10%20%30%40%50%60%70%80%90%

100%

*false positive **false negative Mean square distance

Algorithm tolerance of corners and

functions

1 2 3 4

Marr

Canny

Ours