Effects of Different Gabor Filter Parameters on Image Retrieval by Texture

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1 Effects of Different Gabor Filter Parameters on Image Retrieval b Teture Lianping Chen, Guojun Lu, Dengsheng Zhang Gippsland School of Computing and Information Technolog Monash Universit Churchill, Victoria, 3842, Australia {Lianping.Chen, Guojun.Lu, Dengsheng.Zhang}@infotech.monash.edu.au Abstract Gabor filter is widel used to etract teture features from images for image retrieval. A number of parameters (number of scales and orientations and filter mask size are used in the Gabor Filter. In the reported work so far, these parameters seem to be chosen without proper eplanations. In this paper, we investigate the effects of different Gabor filter parameters on teture retrieval.. Introduction Teture is an important feature of images. In recent ears, the multichannel Gabor decomposition becomes ver popular for teture analsis. Gabor filter resembles the characteristics of simple visual cortical cells [, 2] and is widel used to etract teture features from images for either teture segmentation [3, 4, 5] or image retrieval [6, 7, 8], Among man others, the most successful results are reported b Ma & Manjunath [7, 8], which has shown that image retrieval using Gabor features outperforms that using pramid-structured wavelet transform (PWT features, tree-structured wavelet transform (TWT features and multiresolution simultaneous autoregressive model (MR-SAR features. Their contribution is also adopted b MPEG-7 as one of teture descriptors [9]. A number of parameters are used in the Gabor Filter. However, in the reported work so far, these parameters seem to be chosen without proper eplanations. Perona [] just lists the number of scales and orientations used in a variet of sstems. Numbers run from four to eleven scales and from two to eighteen orientations. Moreover, there is no research found on how to select filter mask size so far. In this paper, we investigate the effects of different Gabor filter parameters on teture retrieval. In practice, it is a compromise to choose number of filters and filter mask size to balance the effectiveness and efficienc of teture retrieval. The rest of the paper is organized as follows: Section 2 introduces the fundamental of Gabor filters, and Section 3 presents the eperimental results and analsis. In Section 4, a summar is given. 2. Gabor filter 2. Fundamentals Gabor filters are a group of wavelets. A set of filtered images is obtained b convolving the given image with Gabor filters. Each of these images represents the image information at a certain scale and at a certain orientation. From each filtered image, Gabor features can be calculated and used to retrieve images. For a given image I(, with size P Q, its discrete Gabor wavelet transform is given b a convolution: G (, = s t * I ( s, t ψ ( s, t where, s and t are the filter mask size variables, and * ψ is the comple conjugate of ψ which is a class of self-similar functions generated from dilation and rotation of the following mother wavelet: ψ(, = 2 2 ep[ ( + ] ep( j2πw 2 2 2π 2 where W is called the modulation frequenc. ψ(, is a Gaussian modulated b a comple sinusoid [5]. The selfsimilar Gabor wavelets are obtained through the generating function: ψ (, = a m ψ ( ~, ~

2 where m and n specif the scale and orientation of the wavelet respectivel, with m =,, M-, n =,, N-, and M is the number of scales, N is the number of orientations. ~ m = a ( cosθ + sinθ ~ m = a ( sinθ + cosθ f = (µ,, µ,,, µ (M-(N-, (M-(N-. We follow [6] for rotation normalization and similarit measurement. 2.3 Parameters where a > and θ = nπ/n. In the above equations, there are following parameters to The variables in the above equations are defined as follows: be selected. M and N are the numbers of scales and orientations respectivel. The filter mask dimension size is s*t. The filter mask size needs not to be square, but this a = (U h /U l M, is usuall the case []. If the filter is centred on a piel, it W n = a m U l must be odd dimensions. We shall assume this to be the ( a + 2ln 2 case in our discussion., n =, m 2 π a ( a U l, n = 2 π U h 2π tan( ( 2N 2ln 2 2π, n where a is a scale factor. U h represents the highest centre frequenc and U l is the lowest centre frequenc of interest. The values of and characterize the spatial etent and bandwidth of the filter in and directions respectivel. 2.2 Teture representation 2 Filters with U l, the lowest centre frequenc, and U h, the highest centre frequenc, are centred in the frequenc domain at distances U l and U h from the origin, respectivel. The upper limit frequenc for U h is [2], and the low limit one for U l is. In realit, it is ver rare to have this kind of images with onl maimum or minimum frequenc. Moreover, as far as the cost of computation and storage space is concerned, different centre frequenc to be selected does not make an difference. We follow [6, 8] to choose U h = and U l =.5. In this work, we just focus on three parameters: number of scales, number of orientations and filter mask size to determine the effects of different Gabor filter parameters on teture retrieval. After appling Gabor filters on the image with different orientation at different scale, we obtain an arra of 3. Eperimental results magnitudes: E( n = G (,, 3. Setup m =,,, M-; n =,,, N- These magnitudes represent the energ content at different scale and orientation of the image. The main purpose of teture-based retrieval is to find images or regions with similar teture. The following mean µ and standard deviation of the magnitude of the transformed coefficients are used to represent the teture feature of the region: E( n µ = P Q = ( G (, µ P Q A feature vector f (teture representation is created using µ and as the feature components [6, 8]. M scales and N orientations are used and the feature vector is given b: 2 All images used for this eperiment are from Brodatz [3]. In Brodatz, there are 2 52*52 Brodatz teture images, each is cut into 6 28 *28 sub tetures to create a database composed of 792 tetures, plus some deliberatel rotated tetures with a total of 852 tetures. Ever teture is used as a quer, and the average precision-recall is used as an overall performance measurement. 3.2 Sstem structure The complete sstem structure used in our test is outlined in Figure.. It consists of following steps: parameters selection, Gabor filters and Gabor features generation, rotation normalization, and image retrieval.

3 For ever scale and orientation Parameters selection Gabor filter Gabor feature Feature Vector (scale*orientation*2 Rotation normalization (circular shift Image Retrieval convolving the filter with the image µ Figure. Sstem structure used in our test 3.3 Performance for different scales and orientations Gabor filter is a frequenc and orientation selective Gaussian envelope. The set of scale channels can be configured to capture a specific band of frequenc components from an image. The set of the orientational channels are used to etract directional features. The number of multichannels or called filters is the product of number of scales and number of orientations. We change scales and orientations while filter mask size is kept unchanged. In Figure 2, the curve for brof3s6o4 represents filter mask size of 3*3, scale of 6 and orientation of 4 (the number of filters is 24, for Brodatz image database. The first observation is that the performance of the retrieval, even with the same number of filters, is affected b different combinations of scales and orientations. The eperimental results also suggest that the bigger number of scales and orientations, or more precisel, the more filters, doesn t alwas mean to have a better performance, as shown in Figure 2. Brof3s6o6 has almost the same performance as brof3s6o4 but more computationall epensive. In the meantime, Figure 2 points out, that the small number of filters does not give us a better performance either. Brof3s6o4 has a higher performance than brof3s4o3. Therefore, the best performance was achieved b having the parameter settings of 6 scales and 4 orientations for filter mask size 3*3. The possible reasons and analsis are summarized as below: Daugman [4] showed that for two-dimensional Gabor functions, the uncertaint relations u /(4*π and v /(4*π limit the joint resolution in the 2D space and the 2D frequenc domains, where [, ] gives the resolution in space domain and [ u, v] gives the resolution in frequenc domain. Therefore, raising the resolution in space domain will lead to diminishing the resolution in frequenc domain. Thus such filters can negotiate the inescapable trade-offs for resolution in different was. For eample, sharp spatial resolution in the direction (at the epense of orientation selectivit or sharp spatial resolution in the direction (at the epense of spatial-frequenc selectivit or scale selectivit. Furthermore, we can also design a filter for greater resolution in the spatial domain b reducing the standard deviation of the 2D Gaussian envelope along both spatial dimensions. However, decreasing the effective spatial area of the filter has the inevitable result of increasing its effective area in the frequenc domain, thereb decreasing its spatial frequenc (e.g. scale and orientation selectivit. Such a division of labor among filters permits the etraction of different spatial-spectral information from the image. Therefore, the scale and orientation selectivit has to be considered simultaneousl. This has been discussed in detail in [4]. The number of filters has to be reasonable. Besides, the more filters we have, the more detailed and redundant representation of the image we get. But this ma not result in better retrieval performance because similar features ma now be captured b different filters. In contrast, fewer filters cannot give us enough detailed representation of the images. Thus, the number of filters should be neither too big nor too small. The same observations can be made from Figures 3-5 that the combination of scale 6 and orientation 4 is the best choice for filter mask size 9*9, 33*33 and 6*6 respectivel, considering both the retrieval effectiveness and the computational cost.. brof3s4o3 brof3s8o3 brof3s6o4 brof3s6o6. Figure 2. Average precision-recall with filter mask size 3*3, number of filters 2, 24 and 96 in combinations of 4*3, 8*3, 6*4 and 6*6 respectivel.

4 brof9s4o3 brof9s8o3 brof9s6o4 brof9s6o6 brof6s4o3 brof6s8o3 brof6s6o4 brof6s6o6.... Figure 3. Average precision-recall with filter mask size 9*9, number of filters 2, 24 and 96 in combinations of 4*3, 8*3, 6*4 and 6*6 respectivel. Figure 5. Average precision-recall with filter mask size 6*6, number of filters 2, 24 and 96 in combinations of 4*3, 8*3, 6*4 and 6*6 respectivel. Actuall, a series of eperiments has been carried out to test the performance for different combinations of the parameters. The results also coincide with the aforementioned. 3.4 Performance for different filter mask size. brof33s4o3 brof33s8o3 brof33s6o4 brof33s6o6. Figure 4. Average precision-recall with filter mask size 33*33, number of filters 2, 24 and 96 in combinations of 4*3, 8*3, 6*4 and 6*6 respectivel. The eperimental results with filter mask size changing onl are presented in Figure 6. The best performance was achieved b setting the filter mask size 3*3 whereas the worst performance was the one for filter size 6*6. This can be eplained as follows: In convolution, the calculation performed at a piel is a weighted sum of gre levels from a neighbourhood surrounding a piel. Gre levels taken from the neighbourhood are weighted b coefficients that come from a matri or convolution kernel. In our case, the coefficients of the Gabor filter are the convolution kernel. Therefore, the kernel s dimension or the filter mask size defines the size of the neighbourhood in which calculations take place. As filter mask size increases, the computed value of the convolution at a point is determined b a larger neighbourhood of image piels. So if the neighbourhood is too large, the convolution value at a point is determined b this larger neighbourhood possibl with some unrelated image piels, especiall for non-homogeneous patterns. The retrieval cannot be accurate. Likewise, if the neighbourhood is too small and perhaps some related image piels are missing. As a result, the effective

5 retrieval cannot be achieved either. Therefore, the filter size should not be too large or too small. Figure 6 suggests that brof9s6o4 performs nearl the same as brof3s6o4 does, but the former decreases greatl when the recall comes to. The filter mask size 3*3 is the best selection for our database. The filter mask size also influences the computational cost. brof3s6o4 brof8s5o6.. brof6s6o4 brof33s6o4 brof3s6o4 brof9s6o4 Figure 7. Average precision-recall on Brodatz Images with our optimal parameters filter size 3*3, scale 6 and orientation 4 and parameters filter size 8*8, scale 5 and orientation 6 selected in [9]. 3.6 Consideration of computation and storage space requirements. Figure 6. Average precision-recall on Brodatz Images with filter mask size 6*6, 33*33, 3*3, 9*9, number of filters 24 in combination of scale 6, orientation Overall effects of different scales and orientations and filter mask size Based on the discussion in Section 3.3 and 3.4, the best combination of parameters is scale 6, orientation 4, with 24 filters, and filter mask size 3*3. Figure 7 shows the result using our selected parameters and the ones (filter size 8*8, scale 5 and orientation 6 used in [9] for Brodatz images. It is evident from the presented results that none of the combinations thus far are better than the one we selected. In order to get the Gabor features, images must be convolved with all the filters. More importantl, the convolution takes a lot of time because of the large image size and the computational compleit. To achieve fast speed in large images, convolution implementations in spatial domain can be substituted b the multiplications in frequenc domain. The general process of the convolution requires appling FFT (Fast Fourier Transform and IFFT (Inverse Fast Fourier Transform on the source image and Gabor filters [5,6]. We know that the time compleit of the FFT and IFFT is O(S 2 log 2 S, where S *S is the image size. For each filter, the bigger filter mask size (set of the filter coefficients, the more time compleit needed to get it. Furthermore, the more Gabor Filters, the more compleit and storage space needed to compute and store the coefficients and the feature vectors. So the parameters selection is important. Our findings are reasonable regarding the computation and storage cost. 4. Summar The success of an effective and efficient teture image retrieval using Gabor filters depends essentiall on the proper choice of A suitable filter mask size, and An appropriate number of filters with proper combination of number of scales and orientations

6 Especiall for filter mask size, ver little work has been done so far. But it reall affects the performance and the computational cost substantiall when different values are used. However, the selection of the filter parameters heavil depends on the characteristics of the tetures in the database. Our test data are based on Brodatz tetures. The best combination of parameters, filter mask size 3*3, scale 6 and orientation 4 (24 filters, might not work ver well on ever individual image, but the give better results when all images in the database are considered. Since most research on teture is conducted on the Brodatz teture collection b researchers, we believe that our findings are also representative, and furthermore, ver useful for further teture analsis, such as teture segmentation etc. References [] Daugman, J.G., Two-dimensional spectral analsis of cortical receptive field profiles, Vision Research, Vol. 2, pp , 98. [2] S. Marcelja, Mathematical description of the responses of simple cortical cells, J. Opt. Soc. Amer., vol. 7, no., pp , 98. [3] A. K. Jain and F. Farrokhnia, Unsupervised teture segmentation using Gabor filters, Pattern Recognition, Vol. 24 no. 2, pp , 99. [4] Dunn, D. and Higgins, W.E., Optimal Gabor filters for Teture Segmentation, IEEE Transactions on Image Processing, Vol. 4, No. 7, pp , Jul 995. [5] Dunn, D., Higgins, W.E. and Wakele, J., Teture segmentation using 2-D Gabor elementar functions, IEEE Transactions on Pattern Analsis and Machine Intelligence, Vol. 6, No. 2, pp. 3-49, Feb [6] Dengsheng Zhang, Guojun Lu, Content-based image retrieval using Gabor teture features, In Proc. Of First IEEE Pacific- rim Conference on Multimedia (PCM, pp.-9, Fargo, ND, USA, June -3, 2. [7] P. Wu, B.S.Manjunath, S.D. Newsam and H.D.Shin, "A Teture Descriptor for Image Retrieval and Browsing", Computer Vision and Pattern Recognition Workshop, Fort Collins, CO, USA, June 999. [8] B.S.Manjunath and W.Y. Ma, "Teture features for browsing and retrieval of image data", IEEE Transactions on Pattern Analsis and Machine Intelligence (PAMI, vol.8, no.8, pp , Aug 996. [9] B.S. Manjunath, Phillipe Salembier, Thomas Sikora, Introduction to MPEG-7 : multimedia content description interface, Chichester; Milton (Qld. : Wile, 22. [] Perona, P., Deformable kernels for earl vision, IEEE Transactions on Pattern Analsis and Machine Intelligence, Volume: 7, Issue: 5, pp , Ma 995. [] Nick Efford, Digital image processing : a practical introduction using Java, Harlow New York : Addison-Wesle, 2. [2] Yossi Rubner and Carlo Tomasi, Perceptual metrics for image database navigation, Boston, Mass.; London: Kluwer Academic, c2. [3] P. Brodatz, Tetures: A Photographic Album for Artists and Designers. New York: Dover, 966. [4] Daugman, J.G., Uncertaint relation for resolution in space, spatial-frequenc, and orientation optimized b twodimensional visual cortical filters, Journal of the Optical Societ of America, Vol. 2, pp. 6-69, 985. [5] Tan, T.N. and A.G. Constantinides (99. Teture analsis based on a human visual model, Proc. ICASSP9, pp [6] R. C. Gonzalez, R. E. Woods, Digital image processing, 2 nd edition, Upper Saddle River, N.J. Prentice Hall, c22.