20th Iranian Conference on Electrical Engineering, (ICEE2012), May 15-17,2012, Tehran, Iran

An Efficient Edge Detection Model Based on Multi-Scale and Multi­Directional Analysis in the Human Visual System

Reza Ramazanzadeh*, Naser Mehrshad**, Mahdie Saboori *** * Faculty of Electrical Engineering, Birjand University. Iran, r.ramazanzadeh@yahoo.com **Faculty of Electrical Engineering, Birjand University. Iran, nmehrshad@birjand.ac.ir

***Faculty of Electrical Engineering, Birjand University. Iran, m.saboori24@yahoo.com

Abstract: Edge detection is one of the most commonly used operations in image analysis and machine vision. This means that if the edges in an image can be identified accurately and localized properly, all of the objects and elements can be located and basic properties such as area, perimeter, and shape can be measured. One new trend in edge detection starts from knowledge about the Human Visual System (HVS) in order to mimic some of its properties. In this paper we propose a biologically inspired model for efficient edge detection. Our model combines the Gabor filters and the traditional Canny operator . The model consists of applying Multi-Scale and Multi­Directional(MSMD) Gabor filter to the input image, which mimics the processing by simple cells in the primary visual cortex (VI ),and can be used to model receptive fields in the retina and primary visual cortex to peiform edge detection in computer vision. The proposed method is in good agreement with some classical results in human vision, such as Weber's law and Ricco's law.

Keywords: Edge detection, Multi-scale and Multi­Directional, Model, Human Visual System, Canny operator.

1. Introduction

Edge detection is a very important area in the low-level image processing and good edges are necessary for higher level processing [1]. This is because edges contain the most important information regarding the characterization of the objects contained within the image [2]. An accurate edge detection technique is important for many imaging systems. For example, edge detection has played a great role in medical imaging, several machine vision and military applications [3]. Edges define the boundaries between regions and indicate the boundary between overlapping objects in an image, which work by means of segmentation and object recognition. An edge is a luminance transition from a light to dark area (or vice versa) in the image. Despite considerable work and progress made on this subject, edge detection is still a challenging research problem due to the lack of a robust and efficient general algorithm. Any edge detector should tackle with the trade-off between good localization property forcing the location of the detected edges to be close as much as possible to the real edges and good noise rejection property forcing the intensity surface to be

smooth [4]. Edge detection methods are mainly as follows:

1) Edge detection based on the gradient operator: The classical gradient operators are Sobel operator[5], Prewitt operator[6], Roberts operator, Laplacian operator. These operators are very simple to be understood, can easily be implemented, and are largely based on convolution operations. The weakness of the aforementioned approaches is that the optimal result may not be obtained using a fixed operator.

2) Edge detection based on the optimum operator: such as Marr-Hildreth operator [7], Canny operator [8,9].

3) Multi-scale edge detection: A general trend in many of the multi-scale methods is combining single scale edge detector outputs at multiple scales and generating a synthesis of these edges. Wavelet transform is particularly suitable for signal mutation detection and edge detection [10,11,12].

4) Some other methods : for example, methods based on integral transform and based on tensor or the adaptive smooth filter method. However, no single edge-detection algorithm, at present, has been devised which be able to successfully determine every different type of edge [13].

The human visual system can be viewed as being composed of a filter bank. The responses of the respective-fields can be modeled using Gabor functions with different scales and orientations. Image processing in the visual system is carried out in multiple scales. The image is broken into various representations at multiple scales starting with the neural processing at the retina. At the output of the retinal ganglion cells, the image is represented by isotropic bandpass-filtered versions at different scales [14]. At higher cortical levels, the representation is multi-scale bandpass-filtered, but is also orientation selective [15], [16]. We will in our model isolate a special Gabor function for every visual scale in the image and thus consider that the different visual scale images will correspond to a special filtering of the retinal image to extract a set of edges relevant to that special function and independently to another set of edges. The retina seems to represent the possible levels of contrast at

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different scales in the image rather independent of smooth illumination variations. The proposed model that is described in this paper improves structure of the Canny edge detector by using the model of respective fields (RF) in the retina and primary visual cortex. The paper is organized as follows: In section 2, Canny edge detection method is described briefly. In Section 3, we review the modelling of the retina and simple cell in VI by Gabor function. Section 4, presents proposed edge detection model. Experimental results are presented in section 5. Finally, a discussion and a conclusion complete the paper .

2. Canny Edge Detection

Canny developed a computational approach to edge detection upon establishing three criteria related to the performance of an edge detector, that is, an edge detector should provide good detection, good localization, and only one response to a single edge [8]. Canny algorithm smoothes image by Gaussian filter, calculates the magnitude and direction of gray level gradient, has the non-maxima suppression on gradient magnitude, detects and connects the edge from the candidate points by the high and low thresholds [17]. Fig.l shows the basic steps of Canny algorithm.

2. 1

Calculate Magnitude Gradient and Direction

Non-maximum Suppression

Dual Thresholding

Edge Tracking and Connection

Fig. 1: Basic steps of Canny algorithm

Gaussian smoothing filter

The process of image smoothing by Gaussian filter means to remove image noise. Using Gaussian function,

convolution carried out on original image with variance of ()c . Gaussian function is defined by (1) :

1 [ x2+y2 ] G(x'Y)= --2 exp - 2 27reJ 2eJ

(1)

Gradient vector : V G = laG I ax J aG lay

(2)

Parameter cr stands for the width of the Gaussian filter, meaning smoothness. The larger the cr, the wider the frequency band of Gaussian filter. Parameter cr can be adjusted according to the various images.

2.2 Calculation of the Gradient Magnitude and the

Edge Direction

Canny algorithm basically finds edges where the grayscale intensity of the image varies alot. These areas are found by determining gradients of the image. Gradients at each pixel in the smoothed image are determined by applying what is known as the Sobel­operator. First step is to approximate the gradient in the x­and y-direction respectively by applying the kernels shown in Equation (3).

KGx = [=� � �l KGy = [� � � 1 -1 0 1 -1 -2 - 1 (3)

The gradient magnitudes (also known as the edge strengths) can then be determined as an Euclidean distance measured by applying the law of Pythagoras as shown in Equation (4). It is sometimes simplified by applying Manhattan distance measure as shown in Equation (5) to reduce the computational complexity.

(4)

(5)

where:

Gx and Gy are the gradients in the x- and y-direction respectively. The direction of the edges must be determined and stored as shown in Equation (6).

e=arctan [� l IGxl

(6)

2.3 Non-maximum Suppression

In order to determine the edge of the image, the roof ridge of gradient magnitude image shall be refined. Only the local maximum of the magnitude shall be kept, that is, non-maxima shall be suppressed to get the refined edge.

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Canny operator has an interpolation, along the gradient direction, in the gradient magnitude image G and a 2x2 neighborhood of the center point (i,j). If the gradient magnitude of the point M(i,j) is greater than the two adjacent interpolation in the direction of 9(i,j), the point (i,j) will be marked as the candidate edge point, Otherwise is marked as non-edge point.

2.4 Dual thresholding, edge tracking and

connection

The traditional Canny operator, by dual threshold method, detects and connects edge points from the candidates points. It is more robust. The steps are:

Step 1. Set manually the high threshold Th and low threshold T, ; Step 2. Scan image. Choose any pixel (i,j) in the candidate edge image M. calculate its gradient magnitude M(i,j). If gradient magnitude M(i,j) > TIP the point will be marked as edge point; If gradient magnitude MCi,j) < T,), the point will be marked as non-edge point;

if MCi,j) is between Th and T, , the point will be marked as suspect, and should be decided about it based on the connectivity of the edge. If the adjacent pixels are the edge points, the point will be marked as the edge point. Otherwise, as non-edge point.

Step 3. Connect through the marked Edge points to get the final edge detection image.

Fig. 2 shows the complete edge detection process on the test image including all intermediate results.

(a) (b) (c)

(d) (e)

Fig. 2: All steps of the Canny edge detection. (a) Original image.

(b) Smoothed image. (c) Gradient magnitude. (d) Non-maximum

suppression and dual thresholding. ( e) Edges after tracking and

connection

3. The model of retina and primary visual cortex

simple cells

The preprocessing unit at the front end of the visual pathway consists of a synaptic connection among photoreceptor cells (rod and cone cells), bipolar cells and ganglion cells. The unit has three parts: a linear model for visual input, a threshold transform of the neuron spike firing train and multiple-scale filtering. Generally, it is assumed that a light-intensity array image U(x,y) as the visual input can be usually expressed as a linear combination by cascade connection between photoreceptor cells (rod and cone cells), bipolar cells and ganglion cells. Retina ganglion cells receive the input signals from photoreceptor cells and bipolar cells and convert them into a spatial sum. Only the ganglion cells having a spatial sum over a threshold are being fired. Electrophysiological experiments have confirmed that information on multiple scales, such as edges and contours, is transferred by M cells and information on a fine scale such as texture and facial expression, is transferred by P cells [18]. Therefore, multiple-scale properties of receptive fields in ganglion cells and LGNs should also be taken into account. In the early 1980s, Marr gave a clear explanation on a neurobiological basis for the use of the Laplacian operator of Gaussian function V2G (r / a") to accurately describe the properties. He used this filter for preprocessing since it can simulate ON­center and OFF-center receptive fields of ganglion cells and cells in a LGN. Marr discussed the plausibility of using the filter in information processing along the visual pathway. Of course, the DoG function (difference of two Gaussian functions) and Gabor function can also be used as the filter function [19]. As originally described by Hubel and Wiesel [20], the primary visual cortex is composed of "hypercolumns", which consist of cells which respond to the same spatial position in the retina, but with different orientation preferences, and "orientation columns" which consist of cells responding to the same orientation but with different position in the visual space. The model assumes that orientation selectivity varies gradually within an hypercolumn: Hence, two consecutive excitatory neurons in the hypercolumn have orientation preferences which differ by 15 deg. As it is well known, cortical cells receive their afferent inputs from cells in the LGN [21]. In the present model, we assume that the receptive field (RF) of each cortical cell consists of a central ON region (that is, a region excited by light) surrounded by two lateral OFF regions (excited by darkness). Each region is elongated along a preferred orientation. According to Jones and Palmer, these spatial RFs can be reproduced fairly well using a Gabor function [22]. If we consider a cortical cell whose RF is centered at the position xc, yc of the visual image, with preferred orientation e, the receptive field assumes the following expression:

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Where:

2 2 2 u + r v u = RO exp( - 2 ) cos(2.7Z" A + tp)

2(j

(7)

Equation (7) represents the Gabor function; (8) and (9) describe a rotation of the RF by an angle e around the central point of coordinate (xc, yc). x,y represent a generic coordinate in the input image, (j is spatial variances, which establish the dimension of the RF in the preferred and non-preferred orientations, and A is a spatial wavelength, which determines the width of the ON and OFF subregions. y is the ratio of the length in the major axis direction to that in the minor axis direction, usually set as the constant 1 , <p is the phase (when <p=O;n, R (x, y) is symmetric(even) about the origin; when <p=­(n/2);(n/2), R (x , y) is symmetric( odd) about the origin and otherwise, R (x, y) is asymmetric), e is the preferred orientation .Starting from (7)-(9), the input to the cortical cell t is obtained by performing the inner product of the visual image I , and the receptive field R i.e.,

t(x ,Y ,8) = JJI(x ,y )R(x -x ,y -y ,8)d d ::::: c c c c x y M N

== L LI(mLlx,n�y)R(mLlx -x ,n�y -y ,8)Llx�y m=1 n=l c C

(10)

where the two sums in the right hand side of (10) signify that the two-dimensional integral has been approximated with the histogram method, and �x, �y represent the dimensions of the single pixel in the input image. N and M are the number of pixels in the horizontal and vertical directions. Fig. 3 illustrates receptive fields (Gabor functions), Receptive field sizes range from 1 to 4 degrees at four different orientations. Simple cell like responses are obtained by directly filtering the input image with an array of Gabor filters at different orientations and different scales; spatial frequency Ie is held constant (see Fig. 4).

4. Multi-scale and Multi-directional edge

detection model

The Multi-scale and Multi-directional (MSMD) edge detection strategy is depicted in Fig. 5. We have merged two classical approaches from edge detection and vision science literature (Canny edge detector and model of retina and simple cells). First, we arranged the Gabor filters to form a pyramid of scales (in n degree steps) and we considered m orientations (ranging from 00 to 1800 in 180/m 0 intervals), thus leading to n.m different

•

•

•

• �

I

II

II I

�

,

,

,

- �

.... ,

... , - ,

Fig. 3: Receptive fields (Gabor functions: 4 scales and 4 orientations).

Fig. 4: Filtering of the input image using Gabor filters in different

orientations and scales.

receptive field types (m orientations x n scales). The gradient magnitude is estimated by computing the sum of responses of all Gabor filters, as shown in equation (11), and corresponding angles is assumed as the angle of the highest gradient magnitude . Then, for gradient image, non-maximum suppression operator and normalization are employed. All other units are similar to the Canny operator as shown in Fig. 5 .

n m

IG(x ,y) = L L Abs(t"i ,A.8, .n/2(x ,y») ;=1 k=1

5. Experimental results

(11)

In this section, the edge detection model has been applied on synthetic and natural images in order to evaluate the proposed model. Fig. 6(a) shows a synthetic image with a size of 800x800 to compare the performance of our model and canny edge detector.

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Non-maximum Suppression

Fig. 5: Multi-scale and Multi-directional (MSMD) edge-detection model

The edge-detection results using canny detector and proposed model are shown in Fig. 6(b) and (e) respectively. In this experiment, the parameters used in the Canny edge detector are two Tc thresholds (the low threshold and the high threshold) and the standard deviation O"c of a Gaussian filter. The high threshold and the low threshold are set to 0.5 and 0.2, respectively, and the standard deviation is set to 0.5 . Because of its constant standard deviation, Canny operator cannot detect edges in low spatial frequency regions or smoothed edges. However MSMD model is able to detect edges in all spatial frequency bands. In this experiment, the thresholds in both approaches set to 0.5. Fig. 6(b) shows a natural image with a size of SOOxSOO and its resulting edge maps are shown in Fig. 6( d) and (t). In this case, Tc = 0.15 , T MSMIJ = 0.15, 0"1 = 1 ,O"c = O.S, n=4, m=4, so that the best performance for edge detection is obtained. To evaluate the accuracy of different edge-detectors, we use the receiver operating characteristic (ROC) curve to measure the edge-detection accuracy which shows our model can achieve a better performance in terms of detection and localization accuracy, (see Fig. 7).

6. Discussion

The original motivation for the research was to obtain a comprehensive model for edge-detection that would be a perfectly parameter-less structure . Most of existing

(a) (b)

(c) (d)

(e) (t) Fig. 6: Comparison between Multi-scale and Multi-directional model

and Canny operator. (a),(b) Original images. (c),(d) Canny detection.

(e),(f) Multi-scale and Multi-directional detection

02 • ., � 024 Q) �O.22

'iii o 02 fi.

0.12

ROCclfie

Fig. 7: ROC curves of our Multi-scale and Multi-directional (MSMD)

model edge detector and the Canny edge detector

edge-detector algorithms are dependent on their input parameters. Obviously, in this case the human visual system is the best solution available, and psychophysical and neurobiological observations suggest a multi-scale and multi-directional processing mechanism that could be responsible for edge-detection and other functions in the retina and visual cortex . in this paper, the scale variations

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and angular variations are modelled by standard deviation (]' and angle (] of the Gabor function, respectively. In order to detect edges at fine and coarse scales (thin and thick edges) it is necessary to use both small and larger filters, However, if (]' is set to a much larger value, edge localization may be lead to distortion. On the other hand, increasing the number of preferred orientation m , leads to better localization performance. Obviously, the runtime required by our model with using the 2-D convolution operation is larger than that of required by the Canny edge detector. The Canny edge detector is restricted to be optimum for step edges and is structured to utilize the first derivative of a Gaussian impulse response, however, by adjusting the Gabor function parameters, it is possible to achieve better results for other edge profiles. As a result, the dependence between (j , e, A"T and even between all parameters should be investigated in the future work.

7. Conclusion

In this paper, we have proposed an edge-detection model inspired by multi-scale and multi-directional analysis in the human visual system. The model in its initial form uses a very simple set of operators such as Sum and Max operator to combine Gabor filter outputs, similar to biological neurons. This model for edge­detection performs better than the classical Canny edge detector and is a starting point to create a parameter-less edge detector.

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