Multi-level Shape Recognition based on Wavelet-Transform. Modulus Maxima

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1 uti-eve Shape Recognition based on Waveet-Transform oduus axima Faouzi Aaya Cheikh, Azhar Quddus and oncef Gabbouj Tampere University of Technoogy (TUT), Signa Processing aboratory, P.O. Box 553, FIN Tampere, Finand {faouzi, azhar, Abstract In this paper we propose a new approach to shape recognition based on the waveet transform moduus maxima. And appy it to the probem of content-based indexing and retrieva of fish contours. The description scheme and the simiarity measure deveoped take into consideration the way our visua system perceives objects and compares them. The proposed scheme is invariant to transation, rotation, scae change and to noise corruption. oreover, this description scheme aows accurate reconstruction of the shape boundary from the feature vector used to describe it. The experimenta resuts and comparisons show the performance of the proposed techniue. 1. Introduction Since the eary 1990s, content-based indexing and retrieva (CBIR) of digita images became a very active area of research. Both industria and academic systems for image retrieva have been buit. ost of these systems (e.g. QBIC [1] from IB, Netra from UCSB, Virage from Virage Inc., UVIS [2] from TUT), support one or more of the foowing options: browse, search by exampe, search based on a singe or a combination of ow eve features. These features can be extracted from the image, such as coor, shape, texture, spatia ayout of objects in the scene or added to it after its capture, such as contextua information and keywords. In this paper we wi focus on one way of describing the shape feature of a given object. Therefore, our data consists of non occuded object boundaries, one object boundary per image. We are not concerned by the way these boundaries were obtained. The probem of automatic object recognition and simiarity estimation remains a hard probem even with such assumptions. ost peope assume that what we see is exacty what our eyes see and report to our brain. This is not uite true in fact, our brain adds very substantiay to the information it gets from the eye. It is even more interesting to know that the eye throws away much of the information it gets, eaving it to the brain to fi in additiona information in its own way [3]. This capabiity is hard-wired into our retinas. Connected directy to the rods and cones of the retina are two ayers of neurons that perform an operation simiar to the apacian. This operation is caed atera inhibition and heps us to extract boundaries and edges [4]. Therefore, in this paper we represent shapes by their outer boundary and not by the regions they contain. Hoffman et a. [5] argued that when the human visua system decomposes objects it does so at points of high negative curvature. Therefore, approximating curves by straight ines joining these high curvature points (HCP) retain the maxima amount of information necessary for successfu shape recognition. This can be expained by the fact that our visua system focuses on the singuarities and ignores smooth curves thanks to the atera inhibition. In the case of shape, high curvature points are robust features in the sense that they are invariant under transation, rotation and scae change [6, 7]. oreover, they provide reiabe cues regarding objects even under occusion and varying background eves [8]. Corner-based representation of objects reduces significanty the size of the feature vector representing the object-contour, whie sti keeping mach of the boundary information essentia to object recognition [4]. Therefore, object recognition techniues based on corner point matching have been used in machine vision appications [8, 9]. It can be seen that compexity of the agorithms proposed in [8, 9] increases exponentiay as the number of candidate objects increases. Therefore, these

2 techniues are not suitabe for arge image databases where thousands of images are invoved. Hwang and aat [10] proved that there coudn t be a singuarity without a oca maximum of the waveet transform at the finer scaes. Therefore, the seem to be very appropriate for the description of contours. oreover, -based descriptors, unike goba contour descriptors such as the Fourier descriptors, provide precise oca shape information. In this paper the importance of high curvature points and their ocations are estimated directy from the of the orientation profie of the contour. In this context we propose a robust waveet-based matching agorithm, which is suitabe for shape matching based on object contour. oreover, it is not very sensitive to noise and is invariant to transation, rotation and scae change. The agorithm uses to detect the ocation of high curvature points and to estimate the degree of simiarity between two shapes at these points. In this paper the performance of our approach is evauated for estimating the simiarity of natura objects. The retrieved images with the proposed approach are compared to those retrieved with the contour scae-space (CSS) techniue [16] and to a set of images retrieved by human users. 2. Waveet-based feature extraction and matching Waveet decomposition provides natura setting for the muti-eve image contour anaysis. Since waveet transform moduus maxima (), provide usefu information for curvature anaysis [11, 12], we propose to use it here for fast feature extraction. It has been shown in [13, 12] that biuadratic waveets, proposed by aat and Zhong [14], perform better than other waveets for corner detection appications. The boundary is tracked and its orientation profie is computed as in [15]. The orientation profie of each one of the two shapes is upsamped and interpoated in a way to have the same number of points for each contour. The Waveet transform of the orientation profie is computed for dyadic scaes from to 2. are then computed, see Figure 1, and ony those s arger than a certain threshod are considered important singuarities. Simiarity scores are then estimated at each eve of the decomposition independenty. And the overa simiarity measure is computed as the maximum vaue of the singe eve simiarity scores. Fast schemes for narrowing down the search space are becoming essentia in content-based retrieva systems due to the size of data sets under consideration. Here we used the aspect ratio γ to reduce the search space. Images with error on γ arger than a fixed threshod are discarded. The remaining candidates go through the second step of the retrieva process, where a set of ow-eve features is extracted at high curvature points and compared to those of the uery image. These ow-eve features are the ocations and the magnitudes of the waveet transform moduus maxima. 3. Agorithm 1. Seect candidate objects with aspect ratios simiar to the one of the uery object, 2. Consider ony greater than certain threshod T, 3. Compare of both uery image and the database, 4. Compute a simiarity score, at each eve, between the uery image and the image in the database, 5. The fina simiarity score is computed as the maximum of the scores at each eve. At each waveet decomposition eve, we characterize the uery image contour with two vectors, and, where, = [ m1 m 2 mm ] contains the m magnitudes of the and = [ p1 p 2 pm ] the m ocations of the high curvature points on the normaized contour. Simiary, at each decomposition eve, the candidate image contour is characterized with two vectors, and of ength n. Before starting the matching, feature vectors from the uery and candidate contours are shifted in a way to have their argest magnitude vaues aigned. Which means, that we start the matching process from the boundary points having the highest curvature at each decomposition eve. A vaid match between two high curvature points is found if the differences between their ocations and magnitudes are under the threshods T and T respectivey. eaning that we are trying to match every maximum within its neighborhood, in the other boundary. et K be the number of matched maxima. The simiarity score at eve, for = j,, 6, is computed as: 2 ( K ξ ) s = 100 ( ) m + n, (1) where, = K δm 2 δp i i ξ +, is the c i= 1 mean( mi, mi ) ength of the contours, δ mi andδ pi are the errors on magnitude and position for the i th matched maxima. ξ gives an idea on how good the match is between the two sets of points. c c

3 The ower eves are not considered in the matching process in order to make our measure unaffected by noise presence. The overa simiarity score is S = max( s ), for {4,5,6}, in our experiments we used eves 4, 5 and 6. This approach is simiar to the CSS techniue proposed by Abbasi et a. [8], however the proposed approach is more effective since the exact ocation of the HCP is determined with high precision by tracking the through the decomposition eves unti the origina contour. oreover it is faster, since few decomposition eves are needed, unike the CSS where the fu decomposition is reuired. oreover, by considering high curvature points ony, just the visuay important detais are used to estimate the simiarity of two contours and redundant information is discarded by ignoring smooth curves. The proposed techniue preserves most of the shape information, since the object contour can be accuratey reconstructed from its [15]. This approach coud be very easiy extended to the description and simiarity estimation of three-dimensiona objects. For each 3-D object severa contours woud be extracted from its projections. 4. Experimenta resuts In these experiments we used 1130 fish contour images, (see Section 6). The boundary of each fish in the database is represented by a seuence of 1000 points. The resuts of uerying the fish database with the image shown in Figure 2 are presented in Tabe 1. Where, the five most simiar images retrieved using the CSS agorithm, the matching resuts of human users and the proposed agorithm are shown. Three threshods were used in these experiments, T, T and T. T = 0. 6, separates high curvature points from insignificant singuarities which coud be present in the fish boundaries due to noise introduced during the acuisition or the contour extraction processes. T = 0. 2 and T = 20, are the toerated errors on the magnitude and the ocation of the waveet transform moduus maxima. We aowed an error of 5% on the bounding box γ. The shape of the neighborhood used is specified by the errors on the ocation and the magnitude and their reation. In our experiments we used a rectanguar neighborhood which puts no constraints on the vaues the magnitude and the ocation can take within the toerated rectange. One intuitive reation coud be T + T Cte, to aow arger error on the ocation when the magnitude error is sma and vise versa. The CSS resuts shown in Tabe 1, were obtained from the webbased demo avaiabe at: " VSSP/imagedb/dbase2.htm". From Tabe 1, one can easiy see that the proposed agorithm often produces resuts, which are cose to those seected by human users. The produced resuts are ceary better than those obtained by CSS. 5. Concusions In this paper we proposed a fast and robust retrieva agorithm for contour images. This techniue is invariant to transation, rotation, and scae change and noise corruption. oreover, it is simpe and thus suitabe for arge databases. We have compared this agorithm with scae space based techniue caed CSS [16] and against resuts produced by human observers. Tabe 1 shows that the resuts are encouraging. The proposed techniue preserves most of the shape information since the object contour can be accuratey reconstructed from its feature vector. 6. Acknowedgements Authors acknowedge Prof. F. okhtarian and S. Abbasi, for providing the test image database. Authors aso acknowedge Tampere Graduate Schoo in Information Science and Engineering (TISE) and Tampere Internationa Center for Signa Processing (TICSP) for providing the financia support for this research. 7. References [1] Niback, W. et a, The QBIC project; uerying images by content using coor, texture and shape, SPIE, Vo. 1908, [2] Aaya Cheikh, F., Cramariuc, B., Reynaud, C., Quinghong,., Dragos-Adrian, B., Hnich, B., Gabbouj,., Kerminen, P., äkinen, T. and Jaakkoa, H., "UVIS: A System for Content-Based Indexing and Retrieva in arge Image Databases," Proceedings of the SPIE/EI 99 Conference on Storage and Retrieva for Image and Video Databases VII, Vo. 3656, pp , San Jose, Caifornia, January [3] Godstein, E. B., Sensation and Perception, 5th Edition University of Pittsburgh Pubished by Wadsworth Pubishing, CB [4] Russ, J. C., The Image Processing Handbook, 3rd edition, CRC, Springer and IEEE Press inc., [5] Hoffman, D. D., and Richards, W. A., Parts of recognition, Cognition, Vo. 18, pp , [6] Attneave, F. Some informationa aspects of visua perception, Psychoogica Rev., 61, (3), pp , [7] Teh, C.H. and Chin, R. T., On the detection of dominant points on digita curves, IEEE Trans. PAI, vo. 11, pp , 1989.

4 [8] Han,. H. and Jang, D., The use of maximum curvature points for the recognition of partiay occuded objects, Pattern Recognition, vo. 23, pp , [9] Koch,. W. and Kashyap, R.., Using poygon to recognize and ocate partiay occuded objects, IEEE Trans. PAI, vo. 9, pp , [10] aat, S., A Waveet Tour of Signa Processing, 2nd Edition, Academic Press, [11] Quddus, A. and Fahmy,.., Fast waveet-based corner detection techniue, Eectronics etters, Vo. 35, pp , Feb [12] Quddus, A., Curvature anaysis using muti-resoution techniues, Ph.D. Thesis, King Fahd University of Petroeum and ineras, Dhahran, Saudi Arabia, [13] Quddus, A. and Fahmy,.., Corner detection using various waveets, accepted for the ICICS'99, December 1999, Singapore. [14] aat, S., G. and Zhong, S., Characterization of signas from mutiscae edges, IEEE Trans. on PAI, Vo. 14, pp , [15] ee, J. S., Sun, Y. N. and Chen, C. H., utiscae corner detection by waveet transform, IEEE Trans. on Image Processing, Vo. 4, pp , [16] Abbasi, S., F. okhtarian, and J. Kitter, Curvature Scae Space image in Shape Simiarity Retrieva, Springer Journa of utiedia Systems, Figure 1. Two fish contours and their corresponding. Figure 2. Query image

5 Tabe 1. Retrieva resuts obtained by the CSS, Human observers and the proposed agorithm. CSS Human Proposed agorithm Simiarity Scores with proposed ago