Novel Image Representation and Description Technique using Density Histogram of Feature Points

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1 Novel Iage Representation and Description Technique using Density Histogra of Feature Points Keneilwe ZUVA Departent of Coputer Science, University of Botswana, P/Bag UB, Gaborone, Botswana and Tranos ZUVA Departent of Coputer Systes Engineering, Tshwane University of Technology, Private Bag X680, Pretoria 000, South Africa and Queen Miria SELLO Departent of Coputer Science, University of Botswana, P/Bag UB, Gaborone, Botswana ABSTRACT This paper introduces novel object shape representation using Density Histogra of Feature Points (DHFP). We use silhouette iages where the iage region ξ consists of only those pixels that correspond to points on the object and have a value one () indicating on pixels. We count the nuber of on pixels in a rectangle boundary around the centroid, in the event that there are no on pixels in a rectangle boundary then the value is zero and the rectangle boundaries that are outside the grid are represented by a duy nuber. A siilarity easure is used to calculate the probability of two iage objects being siilar. Depending on the value of the probability then a dissiilar can be calculated. This ethod showed iproved retrieval rate due its selective way of calculating dissiilarity of object shapes. Analytic analysis was done to justify our ethod, experients were conducted and we tabulated the results. Keywords: Density Histogra, Siilarity, Dissiilarity, Shape representation, and Silhouette iages. INTRODUCTION With vast collection of digital iages on personal, institutional coputers and on the Internet, the need to find a particular iage or a collection of iages of interest has increased treendously. This has otivated the researchers to find efficient, effective and accurate algorith that is doain independent for representation, description and retrieval of iage(s) of interest. There have been any algoriths that have been developed to represent, describe and retrieve iages using their visual features (shape, colour, texture) [5][6][8][0][]. Visual feature representation and/or description play(s) a very iportant role in iage classification, recognition and retrieval. A successful iage representation and description is dependent on the following: the selection of suitable iage feature(s) to encode the quantification of these features []. Shape representation and description has been doinant in research area of iage processing because shape is considered to be the basis of huan visual recognition []. The shape representation can be classified as Region based or Contour based representation. The contour based techniques use the boundary of shape to describe an object. It is coonly believed that huan beings can differentiate objects by their boundaries or contours [0]. Usually ost objects for shapes with defined contours, aking the use of these techniques ost appealing. The techniques can generally be applied to different application areas with a considerable success. The techniques have a low coputation coplexity as copared to region based techniques and they are sensitive to noise. Soe of the techniques in this group are as follows just to ention a few and are well described in [6] are: Copactness, Eccentricity, Shape signature, Hausdoff Distance, Fourier Descriptors and Wavelet Descriptor. The region based shape representation uses the boundary pixels and the interior pixels of the shape. This group of shape representation algoriths are robust to noise, shape distortion and they are applicable to generic shapes []. Soe of the techniques in this

2 groun [6] are: Geoetric oents, Legendre oents, Zernike oents, Generic Fourier Descriptor and Object representation by the density of feature points. In this paper we propose a novel iage representation and description technique using Density Histogra of Feature Points (DHFP) representation of an iage object. This ethod iitates huan visualization of iage object shape and atching siilar object shapes.. SHAPE REPRESENTATION BY THE ENHANCED DENSITY HISTOGRAM OF FEATURE POINTS (EDHFP) This ethod describes the feature points within the rectangle boundary in an iage grid. Assue we have a silhouette object shape segented by soe eans such as Chan & Vese Active Contour without Edges and let the feature points set P ( (intensity function) of the object shape be defined as P( such that i p ( i,,... n where n Eq. () We find the centroid of the object shape. The following forulae will be used to calculate the centroid [4][7]: x c,0 0,0 y c 0, 0,0 Eq. () Eq. (3) where,0, 0,, 0, 0 are derived fro the silhouette oents given by x y P( x y, Eq. (4) The following theores will guarantee the uniqueness and existence of silhouette oents: Uniqueness Theore Assuing that the intensity function P ( is a piecewise continuous and bounded in the region ξ, the oent sequence { } is uniquely deterined by the intensity i, j function P( and conversely. Existence Theore Assuing that the intensity function P ( is a piecewise continuous and bounded in the region ξ, the oents, of all orders exist and finite. Thus for silhouette iage P (, 0, 0 the oent of zero order represents the geoetrical area of the iage region and,,0 0, oent of first order represents the intensity oent about the y-axis and x-axis of the iage respectively. The centroid x, y ) gives the geoetrical centre of the iage region. ( c c Suppose the size of the grid occupied by the object shape is NXN. The vector diension to represent the density of object shape will be N-. In reality we are going to have a vector diension of N, the last eleent represents the nuber of vector eleents that describe the object shape within the grid. The centroid calculated by the two forulas above () and (3) is x, y ). Fro the centroid we count the ( c c nuber of on pixels in the rectangle boundaries in steps of one successively fro the centroid. Soe rectangle boundaries are incoplete but we count the on pixels in the in the grid. The nuber of on pixel in each and every rectangle boundary is denoted as n, n,... n where is the nuber of rectangle boundaries fro the centroid. If is less than N- ( < N-) it eans the rectangle boundaries fall outside the grid where there is no iage object. The positions of the vector that fall outside the grid, we represent the with duy nuber for exaple pi an irrational nuber. In the event that there are no on pixels in a rectangle boundary within the grid we put zero. Since all the pixels of the iage contribute in calculating the centroid, it eans the deviation of the point is inial. The vector representation of the object shape of our ethod should have all or soe of the following: Zeros-indicating no on pixels in a partial or coplete rectangle boundary within the grid Natural nubers indicating nuber of on pixels in partial or coplete rectangle boundary within the grid Duy nuber > 4N or an irrational nuber for rectangle boundary outside the grid Exaple (Representing an object shape) Supposed we have the following object shape features on a grid given in table. 0,0,0,0 3,0 4,0 0,,, 3, 4, 0,,, 3, 4, 0,3,3,3 3,3 4,3

3 0,4,4,4 3,4 4,4 Figure. Segented object shape The bolded indicate the on pixels. The size of the grid occupied by the object shape is 5X5. It eans the vector diension to represent the density of object shape in grid will be four (4). The centroid calculated by the two forulas above () and (3) is (3, ), the centroid pixel is in italics. The first rectangle boundary is ade up of the following pixel (,), (3,), (4,), (4,), (4,3), (3,3), (,3), (,) and there are seven on pixels that constitute our first eleent of the vector. The vector that represents object shape above is ( 7, 7,, Pi), using EDHFP Since rectangle boundary 4 is outside the grid then a duy nuber is used, in this case pi is the nuber used in EDHFP. 3. SIMILARITY OF SILHOUETTE IMAGES Supposed we have two geoetrical objects shapes defined as P ( are called siilar if they both have the sae shape. The objects shapes are ade up of pixels ( wherei,,... nand n and wherei,,... nand n ( respectively with intensity value one (). Unifor scaling is done to all our objects shapes therefore in reality we are finding objects shapes that are congruent to each other. If the two objects shapes are congruent then the distribution of pixels and the area are the sae in the two objects shapes. We also regard that congruent shapes are siilar shapes with a scale factor of one aking siilarity of shapes ore generic terinology to use. Siilarity is defined [9] as: Having two subsets P ( of Euclidean space n R are called siilar if f : P Q such that for any two points x and y that belong to P we have d( f ( x), f ( ) rd(, Eq. (5) where d( is the Euclidean distance fro x to y. P( are called siilar if P( is the iage of Q( under such a siilarity. In our case r= thus there exist isoetry f. The following condition will be fulfilled d ( P, Q) 0 Eq. (6) d is invariant under a chosen group of transforations G if for all f G, d( f ( P), f ( Q)) d( P, Q). This is a requireent for object shape recognition under affine transforation [9]. The acquisition of the iage using different caera enabled devices and the segentation technique used akes the objects shapes not to be exactly the sae causing probles in iage retrieval. Any sall change in the object shape causes changes in the siilarity distance. One point that should not deviate uch due to soe inor distortion in the object shape is the centroid due to the fact that every pixel of the object shape contributes in calculating it. So if P( are siilar then The centroid is approxiately the sae in relation to pixels that ake up the object shape due to the fact that siilar objects shapes have the sae shape. The area of two objects shapes are approxiately the sae because they are apped in the sae grid of NXN. The centroid is the point of reference when generating the rectangles. It eans the nuber of rectangles in each object shape is the sae in the grid in the event of objects shapes with the sae centroid. The distribution of pixels in both objects shapes that are siilar is the sae thus we can establish a pattern of nuber of pixels within each and every rectangle generated fro the centroid of the object shape. Knowing the pattern for P( then we know approxiately the pattern for Q (. Then the following hold for siilarity of objects shapes Nuber of pixels ( ( nuber of pixels ( ( ) in P( ) in Q ( is equal to Centroid of P( in relation to ( is also the centroid of Q( in relation to ( The nuber of rectangles generated in P( is also the sae nuber generated in Q ( The nuber of pixels of the object shape in each rectangle in P( is also the nuber of pixels in each rectangle in Q (

4 In easuring the dissiilarity on objects shapes, the fundaental concept is to copare corresponding rectangles in each object shape to find out the difference in the corresponding rectangles. The following dissiilarity easureent techniques in [][3] were experiented with in our ethod L p L Minkowski faily and faily siilarity distance easures. Dissiilarity Measureent We use the Euclidean L. When we have two vectors representing two object shapes and the vectors are V xi and V y i where i=,,...n, n The dissiilarity between the two object shapes is given by [3][] as: s n, V ) V, V ( xi yi ) i d ( V. Eq. (7) Applying the Euclidean siilarity distance to our ethod, the duy value is used in calculating the distance and is taken as zero. Siilarity Measureent p s s s p q r s Eq. (0) Where p = nuber of rectangles occupied by both objects objects s = nuber of rectangles not occupied by both q = nuber of rectangles occupied by object and not by object r = nuber of rectangles occupied by object and not by object When s 5then there is a higher probability of the s 0. two objects to be siilar, if not then it is very unlikely for the objects to siilar to each other. Exaple (Calculating Siilarity and Dissiilarit Suppose the two object shapes are represented as follows: The object shape being queried is V EDHFP V (4,3,4,, pi,pi) V (4,,5,3,5, pi) We calculate siilarity easure ss as follows: p = 4, s =, q = 0, r = using the forula above we have s s indicating a high probability of siilarity between the two objects. We can now calculate the dissiilarity of the two objects using the Euclidean distance forula. d s (4 4) (3 ) (4 5) ( 3) 5 0 d s 8 So that is the dissiilarity of the two object shapes. 4. EXPERIMENTATION Our ain objective is to find the effectiveness of the representation algoriths DHFP in retrieval of iage objects. We used the Euclidean Dissiilarity in retrieving siilar iage objects after calculating their likelihood of being siilar. We created iage database of shoes iage shapes. Soe of the iage objects were not rotated lossless at 90, 80 and 70 degrees that eans degradation of the iage object shapes occurred during rotation. The query iages were captured using different caera enabled devices. The iages objects were of different diensions MXN or NXN where M and N belong to natural nubers. The iages that we used were only having one iage object with a hoogeneous background. We then segented the iage object shape by a 45X45 grid. All iages were converted to gray scale iages. After segentation the output was a binary iage object (silhouette). They were then represented using our ethod the novel DHFP. We easured the accuracy of our syste by calculating the recall, the precision and effectiveness. The following forulas were used [8] recall A N A precision A C Eq. () Eq. ()

5 N A B Eq. (3) Where A is the nuber of relevant iage objects retrieved, B is the nuber of relevant iage objects not retrieved and C is the nuber of not relevant iage objects retrieved. 5. RESULTS The results obtain fro coparing the two ethods are as follows: Grid size 45X45 Average Recall % Average Precision % Table : The average precision of the ethod with the grid size of 45X45 6. SUMMARY AND CONCLUSION Fro our results we can conclude that EDHFP ethod of iage object representation was able to retrieve huanbeings perceived siilar iage object shapes. The cobination of siilarity and dissiilarity easures ade our syste to have a high precision values. The researchers found an efficient, effective and accurate algorith that are doain independent for representation, description and retrieval of iage(s) of interest. This was deduced fro the retrieval results. 7. REFERENCES [4] J. FLUSSER, T. SUK, & B. ZITOVA, Moents and oent invariants in pattern recognition. West Sussex: John Wiley & Sons Ltd 009. [5] Y. LI,. & L. GUAN, An effective shape descriptor for the retrieval of natural iage collections. Paper presented at the. Proceedings of the IEEE CCECE/CCGEI, Ottawa 006. [6] Y. MINGQIANG, K. KIDIYO, & R. JOSEPH, A survey of shape feature extraction techniques. Paper presented at the Pattern Recognition, 008. [7] R. MUKUNDAN, & K. R. RAMAKRISHNAN, Moent functions in iage analysis: theory and applications. Singapore: World Scientic Publishing Co. Pte. Ltd [8] M. X. RIBEIRO, J. MARQUES, A. J. M. TRAINA, & C. T. JR, Statistical Association Rules and Relevance Feedback: Power Allies to Iprove the Retrieval of Medical Iages. Proceedings of the 9th IEEE Syposiu on Coputer-Based Medical Systes, 006. [9] R. C. VELTKAMP & L. J. LATECKI, Properties and Perforance of Shape Siilarity Measures. Lecture notes in coputer science: 006, pp. -9. [0] D. ZHANG, & G. LU, Review of shape representation and description techniques. Pattern Recognition Society, 37: 004, pp. -9. [] X. ZHENG, S. A. SHERRILL-MIX, & Q. GAO, Perceptual shape-based natural iage representation and retrieval. Paper presented at the Proceedings of the IEEE International Conference on Seantic Coputing, 007. [] E. M. CELEBI, & A. Y. ASLANDOGAN, A coparative Study of Three Moent-Based Shape Descriptors. Proceedings of the International Conference on Inforation Technology: Coding and Coputing, 005. [] S. H. CHA, Coprehensive Survey on Distance/Siilarity Measures between Probability Density Functions. International Journal of Matheatical Models and Methods in Applied Sciences, (4), 007, pp [3] C. C. CHEN & H.-T. CHU, Siilarity Measureent Between Iages. Paper presented at the Proceedings of the 9th Annual International Coputer Software and Applications Conference, 005.

COLOR HISTOGRAM AND DISCRETE COSINE TRANSFORM FOR COLOR IMAGE RETRIEVAL

COLOR HISTOGRAM AND DISCRETE COSINE TRANSFORM FOR COLOR IMAGE RETRIEVAL 1 Te-Wei Chiang ( 蔣德威 ), 2 Tienwei Tsai ( 蔡殿偉 ), 3 Jeng-Ping Lin ( 林正平 ) 1 Dept. of Accounting Inforation Systes, Chilee Institute