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Volume 1 No. 1 APRIL 2011 ARPN Journal of Systems and Software ©2010-11 AJSS Journal. All rights reserved http://www.scientific-journals.org Performance Evaluation of Shape Analysis Techniques S.Selvarajah Department of Physical Science, Vavuniya Campus of the University of Jaffna, Vavuniya, Sri Lanka shakeelas@mail.vau.jfn.ac.lk S.R. Kodituwakku Department of Statistics & Computer Science, University of Peradeniya, Sri Lanka. salukak@pdn.ac.lk ABSTRACT Shape is one of the important features used in Content Based Image retrieval (CBIR) systems. The shape of the object is a binary image representing the object. They are broadly categorized into two groups: contour-based and region-based shape descriptors. An experimental comparison of a number of different shape features for CBIR is presented in this paper. The objective of this research is to determine which shape feature or combination of features is most efficient in representing the images. In this paper, we first present the comparison of individual shape features and then the comparison of combined shape features. For the experiments, publicly available image databases are used and the retrieval performance of the features is analyzed in detail. The article is concluded by stating which shape features perform well for CBIR. Keywords- Colour moments, directional edges, non-directional edges 1. INTRODUCTION A basic requirement of an image database is to perform searches based on content for images. Shape is one of the very powerful image descriptor [5, 10, 12, 22]. Shape processing plays important role in several applications, particularly in computer vision, such as object recognition, image retrieval and processing of pictorial information. Shape is probably the most important property that is perceived about objects. It allows predicting more facts about an object than other features such as color. Therefore, shape recognition is crucial for object recognition. In some applications, it may be used as the only feature to recognize images. Logo recognition is one such example [1, 2, 10]. This paper presents the comparison of individual Shape analysis methods analyze the objects in an shape features and combined shape features. For the image. The shape of the object is a binary image experiments, publicly available image databases are used representing the object. They are broadly categorized into and the retrieval performance of the features is analyzed in two groups: contour-based and region-based shape detail. The article is concluded by stating which shape descriptors. Figure 1 shows different available methods features perform well for CBIR. that fall into these two categories. The contour-based descriptors concentrate on the boundary lines while the 2. METHODS AND MATERIALS region-based descriptors consider on the whole area of the object. For retrieving images based on the shape feature, some simple geometric features can be used [1]. This section summarizes such simple shape descriptors and the other techniques used. 2.1. Materials In order to analyze the performance of shape feature, the following are considered. 12 Volume 1 No. 1 APRIL 2011 ARPN Journal of Systems and Software ©2010-11 AJSS Journal. All rights reserved http://www.scientific-journals.org 2.1.1. Simple Shape Descriptors The M. K. Hu’s traditional invariant moments Area, circularity, eccentricity, major axis orientation, Euler Number and Perimeter are the common The two dimensional traditional Geometric shape parameters considered. Moments of order p+q of intensity function f(x, y) are defined as: 2.1.2. Shape Signature +∞ +∞ m pq = ∫ ∫ x y f(x, y)dxdy p, q = 0,1,2 p p (1) A shape signature maps a two dimensional shape −∞ −∞ to a one dimensional function derived from shape These are not invariant. boundary points. Centroidal profile, complex coordinates, centroidal distance, tangent angle, cumulative angle, The intensity function gives the intensity of the curvature, area and chord-length are the shape descriptors point (x, y) in image space. In case of the binary image, analyzed [2, 4]. These are considered as they are scale f(x, y) takes the value of 1 when the pixel (x, y) represents invariant translations. objects or noise and takes zero when it is part of the background. 2.1.3. Moments When the geometric moments m pq given in For both contour and region of a shape, one can equation (1) are referred to the object centroid (x c , y c ) use moment’s theory, an integrated theory from they become the Central Moments and are given by: mathematics and physics, to analysis the object. Boundary moments can be used to reduce the dimensions of the +∞ +∞ boundary representation. Assume that the shape boundary has been represented as a shape signature z(i), the rth μ pq = ∫ ∫ (x - x − ∞− ∞ c ) P (y - y c ) Q f(x, y)dxdy (2) moment mr and central moment μ r [3, 4, 5, 6, 8] can be m m estimated as x c = 10 , y c = 01 m 00 m 00 1 N m r = ∑ [z(i)]r N i =1 , In practical applications, the equations (1) and (2) 1 N μ r = ∑ [z(i) − m1 ] r are discritized for binary images according to the N i =1 following formulae. where N is the number of boundary points. m pq = ∑∑ x P y Q f(x, y) The normalized moments x y mr = mr , μr = μr are invariant to translation, μ pq = ∑∑ (x − x c ) P (y - y c ) Q f(x, y) μ2 μ2 r/2 r/2 x y rotation and scaling. Less noise-sensitive shape descriptors can be obtained from Where m pq and μ pq are computed by sweeping the image space. 1/2 The total area of the object is given by m 00 and (μ 2 ) F1 = m1 the Central Moments μ pq are invariant to translation. They may be normalized to turn invariant to area scaling μ3 μ4 through the relation. The set of seven lowest order F2 = and F3 = rotation, translation and scale invariants up to the third 3/2 2 (μ 2 ) (μ 2 ) order is given by: φ1 = η 20 + η 02 Region moments can be classified into two categories, invariant moments [3] and Zernike moments [6]. φ 2 = (η 20 − η 02 ) 2 + 4η11 2 φ 3 = (η 30 − 3η 12 ) 2 + (η 03 − 3η 21 ) 2 φ 4 = (η 30 + η 12 ) 2 + (η 03 + η 21 ) 2 13 Volume 1 No. 1 APRIL 2011 ARPN Journal of Systems and Software ©2010-11 AJSS Journal. All rights reserved http://www.scientific-journals.org φ5 = (η 30 − 3η12 )(η 30 + η12 )[(η 30 + η12 ) 2 − 3(η 21 + η 03 ) 2 ] S11 = A42 × A22 + c.c = + (3η 21 − η 03 )(η 21 + η 03 ) × [3(η 30 + η12 ) − (η 03 + η 21 ) ] 2 2 30 {( 4 µ04 − 40 ) + 3( µ 20 − µ02 )](µ02 − µ 20 ) π2 φ6 = (η 20 − η 02 )[(η30 + η12 ) − (η 03 + η 21 ) ] + 2 2 + 4 µ11[4( µ31 + µ13 ) − 3µ11 ]} 4η11 (η 30 + η12 )(η 03 + η 21 ) 2.1.4. Scale Space Method φ7 = (3η 21 − η03 )(η30 + η12 )[(η30 + η12 ) 2 − 3(η03 + η 21 ) 2 ] + (3η12 − η30 )(η03 + η 21 ) × [3(η30 + η12 ) 2 − (η03 + η 21 ) 2 ] The problem of noise sensitivity and boundary variations in most spatial domain shape methods inspire Zernike moments invariants expressed in the use of scale space analysis [13, 14, 15, 16, 17]. The scale space representation of a shape is created by tracking terms of usual moment the position of inflection points in shape boundary filtered by low-pass Gaussian filters of variable widths. The second, third and fourth moments are defined by the following formulae. 2.1.5. Chain Code representation Second order Chain code represents an object by a sequence of S1 = A20 = 3[2( µ 20 + µ 02 ) − 1] / π , unit-size segments with a given orientation. In this representation, an arbitrary curve is represented by a 2 sequence of small vectors of unit length and a limited set S 2 = A22 = 9[2( µ 20 + µ02 ) 2 + 4( µ11 ) 2 ] / π 2 of possible directions. Therefore, this approach is called as unit-vector method. In chain code representation scheme, Third order a digital boundary of an image is superimposed with a grid, the boundary points are approximated to the nearest 2 S3 = A33 = 16[2( µ03 + 3µ 21 ) 2 + ( µ30 − 3µ12 ) 2 ] / π 2 grid point, and then a sampled image is obtained. From a selected starting point, a chain code can be generated by 2 using 4-directional or 8-directional chain code. N- S 4 = A31 = 144[2( µ03 + µ 21 ) 2 + ( µ30 + µ12 ) 2 ] / π 2 directional (N>8 and N=2k) chain code is also possible; it is called general chain code [11]. S5 = ( A33 ) × ( A31 )3 + c.c = 13824 {( µ03 − 3µ 21 )( µ03 + µ 21 ) × [( µ03 + µ 21 ) 2 − 3( µ30 + µ 21 ) 2 ] 2.1.6. Chain Code Histogram (CCH) π4 − (( µ30 − 3µ 21 )( µ30 + µ12 ) × [( µ30 + µ12 ) 2 − 3( µ03 + µ21 ) 2 ])} The CCH is independent of the choice of the starting point. It is a translation and scale invariant shape S6 = ( A31 ) × A22 + c.c 2 descriptor. It can be made invariant to rotations of 90 864 = {( µ02 − µ 20 )( µ03 + µ 21 ) 2 − ( µ30 + µ12 ) 2 ] degrees irrespective of the number of directions in a chain π3 code. + 4 µ11 ( µ03 + µ 21 )( µ30 + µ12 )} This shape descriptor is based on Freeman chain code. The Freeman chain code is an ordered sequence of n Fourth order links {ci i = 1,2,......, n} where c i is a vector 2 connecting neighboring edge pixels. The directions of S7 = A44 c i are coded with integer values k=0, 1,….., K-1 (K is = 25[( µ 40 − 6 µ 22 + µ04 ) 2 + 16( µ31 − µ13 ) 2 ] / π 2 the number of directions) in a counterclockwise sense starting from the direction of the positive x-axis. S 8 = A42 = 25{[ 4( µ 04 − µ 40 ) + 3( µ 20 − µ 02 )}2 2 The CCH is calculated from the chain code of a contour. The CCH is a discrete function + 4{4( µ 31 + µ13 ) − 3µ11 ]2 } / π 2 nk S9 = A40 = 5[6( µ 40 + 2 µ 22 + µ 40 ) − 6( µ 20 + µ02 ) + 1] / π p(k) = where n k is the number of chain code values S10 = ( A44 ) × ( A42 ) 2 + c.c = n k in the chain code, and n is the number of links in a chain 250 (( µ 40 − 6µ 22 + µ04 ) × {4( µ04 − µ 40 ) + 3( µ 20 + µ02 )]2 code [12, 21]. π3 - 4[4( µ31 + µ13 ) − 3µ11 ]2 } − 16[4( µ04 − µ 40 ) + 3( µ 20 − µ02 )] × [4( µ31 + µ13 ) - 3µ11 ]( µ31 − µ13 )) 14 Volume 1 No. 1 APRIL 2011 ARPN Journal of Systems and Software ©2010-11 AJSS Journal. All rights reserved http://www.scientific-journals.org 2.1.7. Fourier Descriptors then each point of A must be within distance d of some point of B, and there is also some point of A that is exactly Shape signatures are very sensitive to noise. Any distance d from the nearest point of B ( the most small change in the boundary leads to a large error in the mismatched point). The Hausdorff distance H (A, B) is the matching. Fourier Descriptors [4, 7] are used to overcome maximum of h (A, B) and h (B, A). this problem. Fourier transform of the signature s (t) is defined as 2.1.10 Similarity measurements 1 N − j2π2π u n = ∑ s(t)exp( ) N t =1 N Eight similarity measurements have been proposed [9]. In this work, we use fixed threshold, Sum- of-Squared-Differences (SSD) and sum-of-Absolute The u n , n=1, 2,……N are called Fourier Descriptors and Differences (SAD) methods. are denoted as FDn. n −1 2 SSD ( f q , f t ) = ∑ ( f q [i ] − f t [i ]) 2.1.8. Grid Method i =o n −1 The grid shape descriptor is proposed by Lu and SAD( f q , f t ) = ∑ (1 f q [i ] − f t [i ]) Sajjanhar [13, 20]. A grid of cells is overlaid on a shape i =o , where and the grid is then scanned from left to right and top to bottom. The result of this process is a bitmap. The cells f q f t represent query feature vector, and database feature covered by the shape are assigned 1 and those not covered vectors and n is the number of features in each vector. by the shape are assigned 0. The shape can then be represented as a binary feature vector. The binary 2.2. Methodology Humming distance is used to measure the similarity between two shapes. Since the spatial distribution of gray values defines the qualities of texture, the binary images are used 2.1.9. Hausdorff Distance for experimentation. In order to evaluate the efficiency of the shape features, features defined in the previous section The Hausdorff distance is a measure defined are used. The sum-of-squared-difference (SSD) and sum- between two point sets for representing a model and an of-absolute-difference (SAD) are used to measure the image. This distance can be used to determine the degree similarity between query image and the database images. of resemblance between two objects in a shape that are The MPEG7_CE-Shape-1_Part_B image database that superimposed on one another. The key advantages of this contains 1403 images with GIF format is used for approach are: (i) relative insensitivity to small experimentation. perturbations of the image, (ii) simplicity and speed of For each image, shape features have been computation, (and) (iii) naturally allowing for portions of computed and stored in a database. The shape features one shape to be compared with another [19]. such as area, CCH, Hausdorff distance and so forth are Given two finite point sets computed for images in the database and the computed A = {a 1 ,......a p } and B = {b1 ,.......b q } the Hausdorff values are stored in a database. The absolute difference of the feature vector values of the query image and database distance is defined as images are also calculated. After that, in order to identify the relevant images, SAD and SSD are used. The average H(A, B) = max(h(A, B), h(B, A)) precision of retrieved images for each feature is computed and recorded for analysis and comparison purposes. where h(A, B) = max min a − b In image retrieval based on simple shape a∈A b∈B descriptors, area, circularity, eccentricity, major axis orientation, Euler Number and perimeter are calculated for where a − b is any metric between the points a and b. query image as well as the database images. Then the relevant images are retrieved by combining all these For simplicity, a − b = (x 2 − x 1 ) 2 + (y 2 − y1 ) 2 simple shape parameters. which is the Euclidean distance between a(x1, y1) and To calculate the shape signature, the first step is to extract the shape boundary points. Then the complex b(x2, y2). coordinates are calculated by using the following formula. The function h (A, B) is called the directed Hausdorff distance from A to B. It identifies the point a ∈ A that is farthest from any point of B, and measures the distance from a to its nearest neighbor in B. That is if h(A,B)=d, 15 Volume 1 No. 1 APRIL 2011 ARPN Journal of Systems and Software ©2010-11 AJSS Journal. All rights reserved http://www.scientific-journals.org z (t ) = [ x(t ) − xc ] + i[ y (t ) − yc ] assigned. By performing this binary feature vector is obtained for the object. Relevant images are identified by where calculating the eccentricity. In Hausdorff distance based shape description, 1 N xc = ∑ x(t ) N t =1 before calculating the Hausdorff distance, edges of the image are detected. Then the Hausdorff distance is calculated by using the formula mentioned in section 1 N yc = ∑ y(t ) N t =1 2.1.9. To identify the similar images, minimum and maximum Hausdorff distance values of images are considered. If Min_Hausdorff distance <= Max_Hausdorff distance for an image, it is taken as a similar image. The central distance shape signature feature is calculated The first step of the process of computing CSS is same as that is used in computing FD. The output of is the by r (t ) = ([ x(t ) − x c ] + [ y (t ) − y c ] . 2 2 boundary coordinates (x (t), y (t)), t= 0, 1, 2, …, N-1. The second step is the scale normalization which The curvature function is calculated by using sampled the entire shape boundary into fixed number of points so that shapes with different number of boundary K (t ) = θ (t ) − θ (t − 1) , where points can be matched. The normalization is done by an equal arc length sampling technique. The equal arc length sampling best preserves the y (t ) − y (t + w) θ (t ) = tan −1 ( ), boundary topological structure. The two main steps in the x(t ) − x(t + w) process are the CSS contour map computation and CSS peaks extraction. where w is the jumping step in selecting next pixel. In our The CSS contour map is a multi-scale organization of the inflection points (or curvature zero- case we selected w as 1. crossing points). To calculate the CSS contour map, curvature is first derived from shape boundary points (x (t) The cumulative angular function was calculated by y (t)), t = 0, 1, 2, …, N-1. Curvature zero-cross points are located in the φ (t ) = [θ (t ) = θ (0)] mod(2π ) shape boundary. The shape is then evolved into next scale Lt , by applying Gaussian smooth. New curvature zero- ψ (t ) = φ ( )+t crossing points are located at the each evolving scale. 2π This process is continued until no curvature zero- crossing points are found. The CSS contour map is where L is the perimeter of the shape boundary. composed of all curvature zero-crossing points zc (t, σ), In CCH based feature description method, where t is the location and σ is the scale at which the zc morphological closing operation (dilation followed by point is obtained. erosion) is applied to the binary image. Then contour The peaks or the local maxima of the CSS image is obtained by subtracting the closed image from contour map are then extracted out and sorted in dilated image. After that the Gaussian filter is applied to descending order of σ. obtain the Gaussian smooth image. For the smoothed The next step is to normalize all the obtained image, the CCH is calculated as described in section 2.1.6. CSS peaks. The average height of all the peaks is From the extracted shape boundary coordinates, extracted from the database which is used for the peak the shape signatures are derived. Then the shape is normalization. Finally, the normalized CSS peaks are used sampled to fixed number of points. After that Discrete as CSS descriptors to index the shape. Fourier Transform is applied to calculate the Fourier descriptors (FD). Since all four shape signatures are not invariant to all three transformations: translation, rotation 3. RESULTS AND DISCUSSION and scale, the rotation invariant FDs are obtained by taking the magnitude values of them. For scale invariant The shape features mentioned in section 2 are FDs, the magnitude values of all other descriptors are used to retrieve images and to compare the performance of divided by the magnitude value of the second descriptor. individual and combined shape features. In this In Grid Based method, after identifying the object experiment, only the top 50 images are chosen as the the rotation and scale normalization is done. Then the retrieval results. Test results for some of the individual normalized object is mapped on a grid of fixed cell size shape features are shown in Figures 2, 3, 4 and 5. The first 2x2. After that the grid is scanned and assigned either one image of these resultant images is the query image. The or zero. If the cells depending on the number of pixels in results for combinations of features are given in Table 1. the cell which are inside the object are greater than a predefined threshold, one is assigned. Otherwise zero is 16 Volume 1 No. 1 APRIL 2011 ARPN Journal of Systems and Software ©2010-11 AJSS Journal. All rights reserved http://www.scientific-journals.org Table 1: An average retrieval accuracy of combined texture features Average Feature/ Combined Feature Precision Simple Shape Descriptors(SSD) 0.22 Shape Signature(SS) 0.28 Hu’s invariant moments(HM) 0.44 Figure 3: First 50 retrieved images for the feature Zernike moments(ZM) 0.49 M.K.Hu’s traditional invariant moments Scale Space Method(CSS) 0.50 Chain Code representation(CC) 0.35 Chain Code Histogram (CCH) 0.40 Fourier Descriptors(FD) 0.52 Grid Method(GM) 0.25 Hausdorff Distance(HD) 0.46 SSD+SS 0.30 SSD+HM 0.45 Figure 4: First 50 retrieved images for the feature CCH. SSD+ZM 0.49 SSD+FD 0.54 Figure 5: First 50 retrieved images for the feature Hausdorff Distance 4. CONCLUSIONS An experimental comparison of a number of Figure 2: First 50 retrieved images for the feature different shape features for content-based image retrieval Simple Descriptors. was carried out. Both contour-based and region-based methods were considered for retrieval. The retrieval efficiency of the shape features was investigated by means of relevance. According to the results obtained it is difficult to claim that any individual feature is superior to 17 Volume 1 No. 1 APRIL 2011 ARPN Journal of Systems and Software ©2010-11 AJSS Journal. All rights reserved http://www.scientific-journals.org others. The performance depends on the spatial 11. Rui Y. and Huang T. S (1997), Image retrieval: distribution of images. The test results indicated that Past, Present, and Future, Journal of Visual Fourier Descriptors perform well compared to other Communication and Image Representation. individual features. In most of the image categories, Scale Space Method and Zernike moments feature also showed 12. H. Freeman, On the encoding of arbitrary better performance. The performance of Fourier geometric con1gurations, IRE Trans. Electron. Descriptors and can be improved by combining with Comput. EC-10 (1961) 260–268. simple descriptors. 13. Cui Ming; Peter Wonka; Anshuman Razdan; REFERENCES Jiuxiang Hu, A New Image Registration Scheme Based on Curvature Scale Space Curve 1. Dengsheng Zhang, Guojun Lu, Review of Shape Matching. representation and description techniques, Pattern Recognition 37 (2004) 1 –19. 14. F. Mokhtarian & A. K. Mackworth. .A theory of multiscale, curvature-based shape representation 2. John M. Z. Jr. and Sitharama S. I. (2000). An for planar curves. IEEE Trans. Pattern Analysis information theoretic approach to content based and Machine Intelligence 14, pp. 789.805, 1995. image retrieval, 2000. 15. H. Asada and M. Brady. The Curvature Primal 3. Ming-Kuei HU, Visual Pattern Recognition by Sketch. MIT AI Memo 758, 1984. Moment Invariants, IRE transactions on information theory. 16. T. Lindeberg. Scale-space: A Framework for Handling Image Structures at Multiple Scales. 4. David McG. Squire, Terry M. Caelli, Invariance Proc. CERN School of Computing, Egmond aan Signatures: Characterizing contours by their Zee, The Netherlands, 8-21 September, 1996. departures from invariance. 17. F. Mokhtarian, S. Abbasi and J. Kittler. Robust 5. Herbert Freeman, Computer Processing of Line- and Efficient Shape Indexing Through Curvature Drawing Images, Computing Surveys, Vol. 6, Scale Space. Proc. British Machine Vision No. I, March 1974. Conference, pp.53-62, Edinburgh, UK 1996. 6. Richard J. Prokop, Anthony P. Reevees, A 18. S. Abbasi, F. Mokhtarian and J. Kittler. Survey of Moment-Based Techniques for Curvature Scale Space Image in Shape Unoccluded Object Representation and Similarity Retrieval. Multimedia Systems, Recognition. 7:467-476, 1999. 7. D.S. Zhang, G. Lu, A comparative study of 19. Hausdorff Distance for Shape Matching, Hacer Fourier descriptors for shape representation and Şengül AKAÇ, Dilay BİNGÜL, May 2010. retrieval, in: Proceedings of the Fifth Asian Conference on Computer Vision (ACCV02), 20. Cyrus Shahabi · Maytham Safar, An Melbourne, Australia, January 22–25, 2002, pp. experimental study of alternative shape-based 646–651. image retrieval techniques, Multimedia Tools Application, DOI 10.1007/s11042-006-0070-y. 8. R.C. Gonzalez, R.E. Woods, Digital Image Processing, Addison-Wesley, Reading, MA, 21. G. Lu and A. Sajjanhar. On Performance 1992, pp. 502–503. Measurement of Multimedia Information Retrieval Systems. In Proc. of International 9. Dengsheng Zhang and Guojun Lu, Evaluation of Conference on Computational Intelligence and similarity measurement for image retrieval, Multimedia Applications, pp.781-787, Australia, IEEE Int. Conf. Neural Networks & Signal Feb. 9-11, 1998. Processing Nanjing, China, December 14-17, 22. 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12
Performance Evaluation of Shape Analysis Techniques
S.Selvarajah
Department of Physical Science,
Vavuniya Campus of the University of Jaffna, Vavuniya, Sri Lanka
shakeelas@mail.vau.jfn.ac.lk
S.R. Kodituwakku
Department of Statistics & Computer Science,
University of Peradeniya, Sri Lanka.
salukak@pdn.ac.lk
ABSTRACT
Shape is one of the important features used in Content Based Image retrieval (CBIR) systems. The shape of the object is a binary image representing the object. They are broadly categorized into two groups: contour-based and region-based shape descriptors. An experimental comparison of a number of different shape features for CBIR is presented in this paper. The objective of this research is to determine which shape feature or combination of features is most efficient in representing the images. In this paper, we first present the comparison of individual shape features and then the comparison of combined shape features. For the experiments, publicly available image databases are used and the retrieval performance of the features is analyzed in detail. The article is concluded by stating which shape features perform well for CBIR.

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