An Improved Method of Edge Detection Based on Gabor Wavelet Transform

NEERAJ NEGI1, SANJAY MATHUR2

Electronics & Communication Engineering Department

College of Technology

Pantnagar-263145

INDIA 1nsnegi_ec@yahoo.com

2mathur_sanjay@rediffmail.com

Abstract—Edge detection is one of the important pre-processing steps in many of the image processing applications. Wavelet based edge detection is found to be a better technique for various applications. In this paper Gabor based wavelet transform is used for edge detection in Ultrasound as well as normal images. The Gabor based detection is able to filter from different directions and scales to determine the edges of the texture under perfect frequency. For performance evaluation peak signal to noise ratio, mean square error and normalized absolute error is considered and experimental results shows that compared with other traditional edge detection methods, the proposed approach is effective in edge detection and very much robust to noise reduction. Keywords— Edge detection, Gabor filter, image processing 1 Introduction The edges of an image are those points at which the luminous intensity changes sharply, which usually reflect important events and changes in properties of the world. So edge detection and extraction are of great importance to identify and understand the whole image and has been applied to many fields such as finger edge extraction and finger shape comparisons for persons identification [1,2], edge detection in human auditory cortex [3], tumor detection in magnetic resonance spectroscopic images [4], interface identification in multiphase flow [5], etc. Edge detection is mainly the measurement and detection of gray change of an image. Since the concept of edge detection was introduced by Julez in 1959 [6], many edge detection methods has been proposed in the last half century, such as Laplacian operator, Roberts operator, Sobel operator, Prewitt operator, Kirsch operator, Marr operator, Canny operator [7-8] and so on. But all these operators have no automatic zoom function and cannot show the edges of an image in different scales, which is very important to many fields. Such as the classic Canny operator, it requires the possible smallest scale filter which has the bad anti noise performance. But if large-scale filter is

chosen the extracted result will depart from the real location. Wavelet analysis, a new signal analysis technology following Fourier transform and short-time Fourier transform, is an effective tool for joint time-frequency analysis of non-stationary signal. The multi-resolution characteristics of wavelet transform can separate signals into different scales and frequencies to get local refine analysis, which can detect image edge accurately and inhibit noise as well. Edge detection of ultrasound images is a very difficult task because edge detection algorithm may be sensitive to noise. In this work, it is attempted to find edges in smooth images instead of the original ones to reduce the effect of noise, so Gabor wavelet based edge detection is used here, Gabor filter is the only filter with orientation selectivity that can be expressed as a sum of only two separable filters. It choose higher frequency information hence the edge is maximized. For rectangular domain we have to select four different orientations to obtain the edges along 0, 90, 270 and 360 degrees. This paper is organized as follows section II deals with edge detection using Gabor wavelet, section III deals with performance

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evaluation section IV deals with results and discussion and section V deals with conclusion.

2 Gabor Wavelet Based Edge Detection Gabor filter is basically a Gaussian with variances along x and y-axes, modulated by a complex sinusoid with centre frequencies U and V along x and y axes respectively. Gabor expansion is a time-frequency analysis method, which can be introduced in 1946 by Dennis Gabor [9]. This expansion introduces a time-localization Gaussian window function for extracting local information of signal with the form similar to the Fourier transform. The Gabor filter tries to search and investigate the intermediate representations which combine the information of both time/space information f and frequency information F. The goal is a simultaneous description of the temporal and spectral behaviour of a function or signal f, such a representation is essentially two dimensional, measuring both behaviour of the frequency w and time/space. Gabor is the only filter which is having the property of directionality. Gabor expansion is a time frequency analysis method which combines both the time/space and frequency information. Gabor expansion can be implemented as a multi-channel filter. g(x, y, ω ,θ ,σ)= exp(-( ))exp(i(ωxcos θ +ωysin θ)) (1) The Gabor filter can be mathematically represented as (1) where Gabor parameters like ω, θ and σ represents radial frequency, orientation and spatial extension respectively. Gabor filtered image is a super imposed image of four orientations 00, 450, 900, 1350 in rectangular domain. The central frequency is selected according to the image dimension. The radial frequencies are all 1 octave apart. Low frequency corresponds to smooth variations and constitutes the base of an image and high frequency presents the edge information which gives the detailed information in the image. Hence this study neglects the very low radial frequencies. Using these frequencies and orientations, the Gabor filter multichannel system can present an image in various orientation and frequencies. For performing edge detection operation on hexagonal domain using Gabor filters, the image is convolved with Gabor filter bank to obtain the Gabor filtered image along three different orientation. Then we find the edge detection of the resultant superimposed Gabor filtered image. Gabor function is the only function who can reach the

time-frequency uncertainty bounds, so it can work as a filter to realize texture segmentation and determine the edge of texture under optimal meaning time-frequency. When using Gabor filter, it will not be too sensitive to the effects of local lightening due to the removed dc component, as a result, we can select different directions and scales to get corresponding results, most of the edge points in different directions can be captured by the results of the filter. The result can not only describe( multi-scale gray) distributed information from different directions, but also tolerate images that have certain translation, rotation, brightness and scale change and so on.

3 Performance Evaluation In this work the performance of edge detection is computed in terms of Mean square error (MSE), Peak signal to noise ratio (PSNR), Mean average error (MAE) and Normalized absolute error (NAE). The following measures of performance are used for quantitative estimation of the performance and analysis of the proposed edge detection technique. (i) Mean Square Error

It is the cumulative squared error between the edge map of noisy image and the edge map of noiseless image and is given by the following equation: MSE = (2) where,

I(x,y) = edge map before noise,

I’(x,y) = edge map after noise,

M, N = dimensions of the image

D = 255 (for unit8 data type) or 1 (for double data type)

Lower the value of the mean square error better or

visually the superior is the edge map.

(ii) Peak Signal to Noise Ratio(PSNR)

It is the measure of the peak error in the signal and is

expressed mathematically by the following equation:

(3)

The higher the value of peak signal to noise ratio means

the ratio of the significant signal to noise is better.

(iii) Mean Average Error(MAE)

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The larger the value of mean average error (MAE)

means that image is of poor quality.MAE is defined as

MAE = (4)

(iv) Normalized Absolute Error(NAE)

The larger value of Normalized absolute error means

that image is of poor quality.NAE is defined as

NAE = (5)

4 Results and Discussion In the experimental process we are using

MATLAB software. The type and the intensity of the noise play a very important role in influencing the selection of suitable level of the scale for a particular noisy image. It can be inferred from this, that certain degree of trade off has to be maintained to obtain noise free, continuous and prominent edge map of an image clouded by a particular type and intensity of noise. The result shown in figure1 reveals the effect of proposed Gabor based edge detection algorithm on different types of noises. From the results, it can be observed that Gabor based edge detector works fine with Gaussian, salt and pepper noise and for speckle noise, and offers the required flexibility of variable scale to suppress the noise edges while retaining the significant and real edges.

Fig. 1: Effect of proposed Gabor based edge detection on different types of noises

(a) Salt and pepper noise with noise density = 0.05 (b) Speckle noise with mean = 0 and variance = 0.05 (c) Gaussian noise with mean = 0.01 and variance = 0.02

As already discussed that the classical edge

detector work fine with high quality images which is shown in figure2, but often are not good enough for noisy image, because they cannot distinguish edges of different significance. The results shown in figure 3 clearly highlights this comparison and it can be observed that edge map obtained from proposed Gabor based edge detector is much superior to the edge map obtained from classical edge detectors in case for noisy images. This owes to the fact that noise is eliminated and almost all the significant edges are retained in case of proposed Gabor based edge detectors for an increased intensity of noise and it is very clear from this result that Gabor edge detector is much more effective than canny edge detector on noisy images.

Fig.2: Comparison of proposed Gabor based vs. Classical edge detectors on normal images

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Fig. 3: Comparison of proposed Gabor based edge detector vs. Classical edge detector on noisy images (Gaussian noise with mean= 0.01 and variance=0.02)

Figure 4 shows some more results on different

images like Barbara image and Cameraman images appreciating the superiority of edge maps of noisy images obtained from the proposed edge detector over canny edge detector.

Fig. 4: Comparison Between DWT, Canny,Gabor based edge detectors on different images (Gaussian noise with mean = 0.01 and variance = 0.02)

Also the Qualitative Analysis is made for Ultrasound images, as we know that edge detection in Ultrasonic images is a very difficult task, so a qualitative comparison is made between the Canny edge detection and Gabor based edge detection for these images and it is clear from the figure 5 to figure 7 that Gabor based edge detection completely suppress the multiplicative noise present in the ultrasonic images as comparison to Canny edge detection technique and Dwt based edge detection technique. The qualitative judgement made visually based on the results obtained in figure 5,6,7,8,9,10.The quantitative parameter results obtained are tabulated in table1,2.

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Fig.5: Qualitative Analysis between Canny, DWT and Gabor based edge detection for Ultrasound image of Brain

Fig.6: Qualitative Analysis between Canny, DWT and Gabor based edge detection for Ultrasound image of a Baby

Fig.7: Qualitative Analysis between Canny, DWT and Gabor based edge detection for Ultrasound image of a Fetus Result of Qualitative Analysis for Normal Images

Fig. 8: Canny edge detection (Gaussian noise with mean = 0.01 and variance =0.02)

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Fig.9: DWT based edge detection (Gaussian noise with mean = 0.01 and variance =0.02)

Fig.10: Gabor based edge detection (Gaussian noise with mean = 0.01 and variance =0.02

Edge detector Canny DWT Gabor

MSE 0.205292 0.024902 0.022034

MAE 0.205292 0.024902 0.022034

NAE 1.008243 1.003073 0.820455

PSNR 61.883374 80.205999 81.269058

Table 1: Comparison of Quantitative Parameters for different Edge detector for Lena image (Gaussian noise with mean= 0.02 and variance=0.03)

The following inferences can be drawn from the qualitative judgment and quantitative judgments carried out.

Over all readability and the quality of the edge map using proposed Gabor based edge detector is much superior to the canny and DWT based edge detector.

Mean square error, Mean Average Error, Normalized Absolute Error and the Peak signal to noise ratio are much better for Gabor based edge detector against the canny and DWT based edge detector. The same can be appreciated from the plots given in figures 11, 12.

The proposed Gabor based edge detector separates detail coefficients at the time of decomposition, thus it has to eliminate the residual noise and insignificant edges from the approximation coefficients. This makes the proposed Gabor based edge detection much more computationally faster than canny edge detector.

Edge detector Canny DWT Gabor

MSE 0.263046 0.042511 0.29968

MAE 0.263046 0.042511 0.29968

NAE 1.092805 1.712354 0.916045

PSNR 59.730161 75.560780 78.597573

Table 2: Comparison of Quantitative Parameters for different Edge detector for Lena image (Gaussian noise with mean= 0.05 and variance=0.1)

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Edge detector

DWT based Gabor based

Dyadic scale MSE PSNR MSE PSNR S=1 0.049026 74.32218 0.030029 78.57990 S=3 0.048340 74.44469 0.028549 79.01892 S=5 0.046616 74.76017 0.027573 79.32123 S=7 0.043304 75.40015 0.026367 79.70952 S=9 0.038391 76.44618 0.023804 80.59791 S=11 0.033112 77.73120 0.020340 81.96379 S=13 0.028030 79.17821 0.016998 83.52269 S=15 0.024750 80.25938 0.015991 84.05317 S=17 0.021790 81.36583 0.014481 84.91507 S=19 0.019241 82.44611 0.013000 85.85161 Table 3: Comparison of MSE and PSNR for the Lena image (Gaussian noise with mean= 0.05 and variance=0.1) Edge detector

DWT based Gabor based

Dyadic scale

MSE PSNR MSE PSNR

S=1 0.063049 72.13719 0.038757 76.08774 S=3 0.061768 72.31559 0.040009 76.36372 S=5 0.056854 73.03554 0.036972 76.77333 S=7 0.052750 73.68641 0.033173 77.71521 S=9 0.044678 75.12898 0.028168 79.13576 S=11 0.036575 76.86704 0.024963 80.18473 S=13 0.028625 78.99574 0.021423 81.51306 S=15 0.024796 80.24433 0.018631 82.72608 S=17 0.021133 81.63140 0.017166 83.43735 S=19 0.018982 82.56399 0.015091 84.55647 Table 4: Comparison of MSE and PSNR for the Lena image (Gaussian noise with mean= 0.05 and variance=0.2) 5 Conclusions In the modern image processing, image edge is basic image features, and is the base of analysis for understanding image. The structure information of an object boundary status can be preserved by edge detection, and can provide the basis for image cutting and features extracting. Traditional methods for Edge detection, such as Prewitt, Sobel, Roberts, Canny are very sensitive to noise in the image, also time and memory consuming. They cannot distinguish edges of different significance as they primarily focus on the coupling between image pixels on a single scale. Wavelet transform has the spatial and the frequency domain characteristics and multiscale analysis abilities, and very suitable for image processing especially for detection of the sharp signals. The traditional wavelet transform is time and memory consuming. By applying

wavelet transform using Gabor filters it is possible to detect edges in different orientation so that it can give the correct edge information also it not only accurately detect the useful edge information but also have certain anti-noise ability, also by adjusting the parameters of Gabor wavelet it is possible to find optimum edge detection . Experimental results show that the edge detection using Gabor filter gives better performance in terms of PSNR and MSE.

Fig.11: Variation of MSE/MAE with different Scale Fig. 12: Variation of PSNR with different scale

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References: [1] Ching-Liang Su, Original Finger Image Extraction by Morphological Technique and Finger Image Comparisons for Persons' Identification. Journal of Intelligent and Robotic Systems. 2006, 45(1): 1-14 [2] Ching-Liang Su, Finger edge extraction and finger shape comparisons for person’s identification by using index, middle, and ring fingers. Applied Mathematics and Computation. 2007,10:1016 [3] M. Herdener et al., Bold correlates of edge detection in human auditory cortex. NeuroImage. 2007, 36: 194-201 [4] L. Görlitz, B.H. Menze, M. A. Weber, B.M. Kelm, F.A. Hamprecht, Semi-supervised Tumor. Detection in Magnetic Resonance Spectroscopic Images Using Discriminative Random Fields. F.A. Hamprecht. C. Schnörr, and B. Jähne (Eds.): DAGM 2007, LNCS 4713, pp. 224-233 [5] Yu Jianrong, Bu Fanliang, Li Wenli, Lu Xiaojun. Image Identifying &Analyzing System of Flowing Air Bubbles in Fluidized Bed. Chinese Journal of Scientific Instrument. 2005, 26(8) supplement: 667-668 [6] Julez, B., A Method of Coding TV Signals Based on Edge Detection. Bell System Tech. 1959, 38(4):1001-1020. [7] John Canny. A Computational Approach to Edge Detection. IEEE Transactions on Pattern Analysis and

Machine Intelligence. 1986, Pam1-8(6):679-698 [8] Jia Tianxu, Zheng Nanning. Multiscales Edges Detection Based On Bubble Wavelet. Chinese Acta Electronica Sinica, 1996, 24(4):117-119 [9] D. J. Gabor, “Theory of communication,” IEEE, vol. 93, no. 26, pp. 429–457, 1946 [10] Huang Hongqiong Tang Tianhao. The Medicine Image Edge Detection Based on Spline Wavelet Transform. Microcomputer Information. 2007, 23(4-3): 313-314 [11] Chi Chang-yan, Zhang Ji-xian and Liu Zheng-jun. “Study on methods of noise reduction in a stripped image”, The International archives of the photogrammetry, remote sensing and special Information Science, Beijing ,vol. 37, part B6b, 2008. [12] R. N. Czerwinski, D. L. Jones and W. D. O’Brien, “Detection of Line and Boundaries in Speckle Images-Application to Medical Ultrasound,” IEEE Transactions on Medical Imaging, vol.18(2), pp.126-136, [13] B. Lee, J. Yan and T. Zhuang, “A dynamic Programming based Algorithm for Optimal Edge Detection in Medical Images,” International Workshop on Medical Imaging and Augmented Reality, pp.193-198, 2001. [14] L. Fan, G. A. Braden and D. M. Herrington, “Nonlinear Wavelet Filters for Intracoronary Ultrasound Images,” Computers in Cardiology, pp.41-44, 1996. [15] S. P. Kozaitis, S. Udomhunsakul, R. H. Cofer, A. Agarawal, and S. Song, “Linear feature extraction using wavelet domain filters,” Proceeding SPIE, vol.4741, pp.290-295, 2002.

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