Grating cell operator features for oriented texture segmentation

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1 Appeared in in: Proc. of the 14th Int. Conf. on Pattern Recognition, Brisbane, Austraia, August 16-20, 1998, pp Grating ce operator features for oriented texture segmentation P. Kruizinga and N. Petkov Institute of Mathematics and Computing Science and Centre for High Performance Computing University of Groningen P.O. Box 800, 9700 AV Groningen, The Netherands Abstract The performance of two we-known texture operators based on Gabor-energy and the cooccurrence matrix) is compared with the performance of a new, bioogicay motivated texture operator, the grating ce operator, which was proposed esewhere by the authors. The comparison is made using a new quantitative method, based on the Fisher criterion. Together with some cassification resuts comparison experiments the comparison shows a cear superiority of the new operator in oriented texture probems. 1. Introduction Texture is an important part of the visua word of animas and men and their visua systems successfuy detect, discriminate and segment texture. Reativey recenty progress was made concerning structures in the brain which are presumaby responsibe for texture processing. Von der Heydt et a. [19] reported on the discovery of a new type of orientation seective neuron in areas V1 and V2 of the visua cortex of monkeys which they caed grating ce. Grating ces respond vigorousy to gratings of bars of appropriate orientation, position and periodicity. In contrast to other orientation seective ces, grating ces respond very weaky or not at a to singe bars which do not make part of a grating. This behaviour of grating ces cannot be expained by inear fitering foowed by haf-wave rectification as in the case of simpe ces, neither can it be expained by threestage modes of the type used for compex ces. Esewhere we proposed a mode of this type of ce and demonstrated the advantages of grating ces with respect to the separation of texture and form information [9, 16]. In this paper we use the output of grating ce operators as texture features and compare them with commony used texture features as cooccurrence matrix and Gabor-energy features. For this comparison a new method is proposed which enabes a quantitative evauation of the texture discrimination properties of feature extraction operators. The method differs from the commony used texture feature performance evauation method which is based on the comparison of cassification resuts [1, 3, 13, 17, 20]. The probem with the traditiona comparison method is that it mixes together the performance of a cassifier with the discrimination properties of the feature operator. Furthermore, it does not give an estimation of the reiabiity of cassification: for instance, two different operators can give rise to the same number of miscassified pixes when appied to two different texture images, but this does not mean that they wi perform equay in future cassification tasks with other images of the same textures. Consequenty, a method is needed in which the performance of a cassifier can be separated from the discrimination properties of the feature operator and in which the spread in the discrimination properties can be quantified in order to estimate the reiabiity of cassification. 2. Grating ce mode Our mode of grating ces consists of two stages [16]. In the first stage, the responses of so-caed grating subunits are computed using as input the computed responses of centre-on and centre-off simpe ces with symmetrica receptive fieds for a computationa mode of simpe ces, see [15]). The mode of a grating subunit is conceived in such a way that the unit is activated by a set of three bars with appropriate periodicity, orientation and position. In the second stage, the responses of grating subunits of a given preferred orientation and periodicity are summed together within a certain area to compute the response of a grating ce. This mode is next expained in more detai: A quantity, caed the activity of a grating subunit with position, preferred orientation and preferred grating periodicity, is computed as

2 Z foows:! #"%$'&) +*, -/ "%$763 8*, -/ ) a) input and 0 is a threshod parameter with a vaue smaer than C ) and the auxiiary quantities * 5 D - and 2 are computed as foows: near 1 e.g. 0 * - Q 9 Ä Q 9 Ä f - 5 D E7FDG :IH JK JK, LNMPO DQ3QR A5S T=U WVX <Y, [Z\ S T=U ] A5U^`_ avbc <Y PZd U^e_ ] g <?>h< <ia ja B 2) b) c) centre-on responses centre-off responses M M M -3-1 M M M Figure 1. Luminance distribution aong a norma to a set of three square bars a), and the distribution of the computed responses of centre-on b) and centre-off c) simpe ces aong this ine. 1 where H J J, LNM is the output of a simpe ce operator 1 of preferred orientation and periodicity at position c Q Q and 2 '\E7FIG : *, - O 3) The quantities *, are reated to the activities of simpe ces with symmetric receptive fieds aong a ine segment of ength >N passing through point c in orientation. This segment is divided in intervas of ength and the maximum activity of one sort of simpe ces, centre-on f - or centre-off f -, is determined in each interva. * I, nm)o, for instance, is the maximum activity of centre-on simpe ces in the corresponding interva of ength ; * 5 D nm is the maximum activity of centre-off simpe ces in the adjacent interva, etc. Centre-on and centre-off simpe ce activities are aternatey used in consecutive intervas. 2 is the maximum among the above interva maxima. Roughy speaking, the concerned grating ce subunit wi be activated if centre-on and centre-off ces of the same preferred orientation and spatia frequency p are aternatey activated in intervas of ength aong a ine segment of ength >N centred on point and passing in direction. This wi, for instance, be the case if three parae bars with spacing and orientation of the norma to them are encountered Fig.1). In contrast, the condition is not fufied by the simpe ce activity pattern caused by a singe bar or two bars, ony. In the next, second stage of the mode, the response qr of a grating ce is computed by weighted summation of the responses of the grating subunits. At the same 1 Hafwave rectified convoution of the image with a 2D Gabor function see [15, 16] for further detais). time the mode is made symmetrica for opposite directions by taking the sum of grating subunits with orientations and Z. q s3tvu m?wnxy,x J{z} j~ w} y, Jez{ w z J J J J ƒ 3 5 Q Q a 4) The weighted summation is a provision made to mode the spatia summation properties of grating ces with respect to the number of bars and their ength as we as their unmoduated responses with respect to the exact position phase) of a grating. The parameter determines the size of the area over which effective summation takes pace. A vaue of ˆ resuts in a good approximation of the spatia summation properties of grating ces. For further detais we refer to [16]. The grating ce operator is avaiabe on the internet [10]. 3. Texture features and the Fisher criterion The quantities computed with the grating ce operators can be used as texture features. We next compare the foowing set of features: Grating ce operator features: A set of grating ce operators with eight different preferred orientations and three preferred spatia-frequencies is appied to an image, yieding a vector of 24 features in each point. Gabor-energy features: A popuar set of texture features is based on the use of Gabor fiters [7]. In

3 m m œ T1 T2 T3 T4 T5 T6 T7 T8 T9 T T T T T T T T Tabe 1. The Fisher criterion for pairs of texture images cacuated on the basis of feature vectors obtained with the grating ce operator. this case, an image is fitered with a set of Gabor fiters with different orientations, spatia frequencies and phases. Using eight orientations and three preferred spatia-frequencies and combining the resuts of symmetric and anti-symmetric fiters, this muti-channe fitering scheme yieds a feature vector of 24 Gaborenergy quantities. The same preferred orientations and spatia-frequencies are used as the ones of the grating ce operators. Cooccurrence matrix features: A cassic method for texture segmentation is based on the gray-eve cooccurrence matrices [6]. In each point of a texture image, a set of gray-eve cooccurrence matrices is cacuated for different orientations and inter-pixe distances. From these matrices, a number of features is extracted which characterise the neighbourhood of the concerned pixe. In our experiments eight gray-eve cooccurrence matrices were cacuated in each point using a neighbourhood of size AŒ A. From each of the matrices three features energy, inertia and entropy) were extracted resuting in a vector of 24 features in each image point. The feature vectors computed at different points of a texture using a given operator are not identica. They rather form a custer in the muti-dimensiona feature space. The arger the distance between two custers which correspond to two different types of texture, the better the discrimination properties of the texture operator which produced the feature vectors. The distance has, of course, to be reated to the size of the custers. In order to determine the distance between two custers of feature vectors, it is sufficient to ook at the projection of the -dimensiona feature space onto a one-dimensiona space, under the assumption that this projection maximises the separabiity of the custers in the one-dimensiona space. A inear transformation that reaizes this projection was first introduced by Fisher [4] and is caed Fisher s inear discriminant function. It has the foowing form: Ž p < % 8 p, where and p are the means of the two custers and p is the inverse of the pooed covariance matrix. Fisher s inear discriminant function is invariant under any nonsinguar inear transformation. Figure 2. The nine test images of oriented textures, enumerated T1 through T9 eft to right and top to bottom. The projection of the feature vectors onto the projection ine maximises the so-caed Fisher criterion [5]! š ) jœ where and are the standard deviations of the distributions of the projected feature vectors of the respective cus- šÿž ters and and, are the projections of the means 8 and is positive definite, the difference. Since the matrix, is aways positive. The Fisher criterion expresses the distance between two custers reative to their compactness

4 T1 T2 T3 T4 T5 T6 T7 T8 T9 T T T T T T T T Tabe 2. The Fisher criterion for pairs of texture images cacuated on the basis of feature vectors obtained with the Gabor-energy operator. in one singe quantity. 4. Performance evauation and comparison The performance of the grating ce operator is evauated according to the Fisher criterion by the separabiity of nine test images, each containing a singe oriented texture Fig.2). The separabiity is measured in the foowing way: a set of 24 different grating ce operators is appied to each image. In this way each image point is assigned a feature vector of 24 grating ce operator coefficients. The pooed covariance matrix is cacuated for each pair of images using 1000 sampe feature vectors from each image. Then the feature vectors are projected on a ine using Fisher s inear discriminant function and the Fisher criterion is evauated in the projection space. Tabe 1 shows the vaues of the Fisher criterion for each pair of the test images. The minimum vaue isted is >@, which means that for a image pairs, the projected feature vector distributions wi at most overap for Iª. Therefore a custers of feature vectors can be separated ineary. Note that the feature vectors of each custer are taken from an image that contains merey one texture. This means that it is a priori known to which custer the feature vector sampes beong to, resuting in a good estimate of the covariance matrix. The vaues obtained with the Gabor-energy features isted in Tabe 2) are a smaer than the ones obtained with the grating ce features. On average the Fisher criterion for the Gabor-energy features is more than two times smaer than for the grating ce features. Anyhow, the Fisher criterion is sti arge enough to distinguish the custers. The Gabor-energy features are therefore suitabe for the cassification of a texture images as a whoe, i.e. cassification of an entire texture image based on the distribution of a arge number of projected feature vectors. For the segmentation of a texture image into regions containing the same texture, i.e. for the cassification of the individua pixes, the intercuster distance is not sufficienty arge as can be seen from Figure 3. The quaity of the cooccurrence matrix features is even worse in comparison to the Gabor-energy features. Though the inter-custer distance is arge enough for cassification of texture images as a whoe Tabe 3), the features are inappropriate for cassification of singe pixes. Figure 3 shows the resuts of pixe cassification using K-means custering of the generated feature vectors. It further demonstrates the superiority of grating ce operator features to Gabor-energy and cooccurrence matrix features. In a future work, the authors wi compare the grating ce operator with the operators and methods proposed by Unser [18], Laws [11] and Mitche [12], the fracta dimension approach [14], a method based on GOP Genera Operation Processor) operations [8], gray eve differences, centre-symmetric covariance features, oca binary patterns [17] and Markov random fieds [2]. References [1] R. Conners and C. Harow. A theoretica comparison of texture agorithms. IEEE Transactions on Pattern Anaysis and Machine Inteigence, 23): , [2] G. Cross and A. Jain. Markov random fied texture modes. IEEE Transactions on Pattern Anaysis and Machine Inteigence, 51):25 39, [3] J. Du Buf, M. Kardan, and M. Spann. Texture feature performance for image segmentation. Pattern Recognition, 23: , [4] A. Fisher. The mathematica theory of probabiities, voume 1. Macmian, New York, [5] K. Fukunaga. Introduction to statistica pattern recognition. Academic Press, [6] R. Haraick, K. Shanmugam, and I. Dinstein. Textura features for image cassification. IEEE Transactions on Systems, Man and Cybernetics, 36): , 1973.

5 T1 T2 T3 T4 T5 T6 T7 T8 T9 T T T T T T T T Tabe 3. The Fisher criterion for pairs of texture images cacuated on the basis of feature vectors obtained with the cooccurrence matrix operator. Figure 3. Resuts of segmentation experiments using the K-means custering agorithm. The eftmost image shows an input image containing nine different textures. The exact segmentation of the input image is shown in the second image from the eft. The three right-most images show the segmentation resuts based on the grating ce operator features midde coumn), the Gabor-energy features second coumn from the right) and the cooccurence matrix features right-most coumn). [7] A. Jain and F. Farrokhnia. Unsupervised texture segmentation using gabor fiters. Pattern Recognition, 2412): , [8] H. Knutsson and G. Granund. Texture anaysis using twodimensiona quadrature fiters. In IEEE Workshop CA- PAIDM, Pasadena, CA, [9] P. Kruizinga and N. Petkov. A computationa mode of periodic-pattern-seective ces. In J. Mira and F. Sandova, editors, Proc. IWANN 95, Lecture Notes in Computer Science, vo.930, pages Springer-Verag, [10] P. Kruizinga, N. Petkov, and U. Hettema. The grating ce operator interactive software impementation. imaging/grcop.htm. [11] K. Laws. Textured image segmentation. Technica Report USCIPI 940, Image Processing Institute, University of Southern Caifornia, [12] O. Mitche, C. Myers, and W. Boyne. A max-min measure for image texture anaysis. IEEE Transactions on Computing, C-2: , [13] P. Ohanian and R. Dubes. Performance evauation for four casses of textura features. Pattern Recognition, 258): , [14] S. Peeg, J. Naor, R. Hartey, and D. Avnir. Mutipe resoution texture anaysis and cassification. IEEE Transactions on Pattern Anaysis and Machine Inteigence, 6: , [15] N. Petkov. Bioogicay motivated computationay intensive approaches to image pattern recognition. Future Generation Computer Systems, 11: , [16] N. Petkov and P. Kruizinga. Computationa modes of visua neurons speciaised in the detection of periodic and aperiodic oriented visua stimui: bar and grating ces. Bioogica Cybernetics, 762):83 96, [17] O. Picher, A. Teuner, and B. Hosticka. A comparison of texture feature extraction using adaptive gabor fitering, pyramida and tree structured waveet transforms. Pattern Recognition, 295): , [18] M. Unser. Loca inear transforms for texture measurements. Signa Processing, 11:61 79, [19] R. von der Heydt, E. Peterhans, and M. Dürsteer. Periodicpattern-seective ces in monkey visua cortex. Journa of Neuroscience, 12: , [20] Z. Wang, A. Guerriero, and M. Desario. Comparison of severa approaches for the segmentation of texture images. Pattern Recognition Letters, 175): , 1996.