A Perceptual Shape Descriptor Nafiz ARICA Fato T

A Perceptual Shape Descriptor Nafiz ARICA, Fatoş T. YARMAN-VURAL METU, Department of Computer Engineering {nafiz, vural}@ceng. metu. edu. tr METU, Department of Computer Engineering 1

BAS: A shape Descriptor with Beam Angle Statistics l l l Represents each boundary point with the statistics of the beam angles in a set of neighborhood, Elaborates the idea of using the statistics of the representations at all scales, Avoids heuristics or threshold values for selecting a representation at an “appropriate” scale, Insensitive to distortions, rotation, translation and scale, Measures similarity by elastic matching. METU, Department of Computer Engineering 2

Beams at Boundary Points Beams, are the lines connecting a point with the rest of the points on the boundary. beams of the point p(i) is the set of lines Vi+j and Vi-j are the forward and backward vectors connecting p(i) with, p(i+j) and p(i-j), for j=1, …N/2 METU, Department of Computer Engineering 3

Kth Order Neighborhood System For each neighborhood system K, there is only one pair of beams, METU, Department of Computer Engineering 4

Beam Angle For the point p(i), the angle between the beams in the kth order neighborhood system: METU, Department of Computer Engineering 5

Plots of CK(i)’s with fix K values k=N/40 k=N/10 k=N/40 : N/4 METU, Department of Computer Engineering 6

What is the most appropriate value for K which discriminates the shapes in large database and represents the shape information at all scale ? Answer: Find a representation which employs the information in CK(i) for all values of K. Output of a stochastic process at each point METU, Department of Computer Engineering 7

C(i) is a Random Variable of the stochastic process which generates the beam angles mth moment of random variable C(i) Each boundary point i is represented by the moments of C(i) METU, Department of Computer Engineering 8

First three moments of C(i)’s METU, Department of Computer Engineering 9

Correspondence of Visual Parts and Insensitivity to Affine Transformation METU, Department of Computer Engineering 10

Robustness to Polygonal Approximation Robustness to Noise METU, Department of Computer Engineering 11

Similarity Measurement Elastic Matching Algorithm – Similarity Measurement method – Application of dynamic programming – Minimize the distance between two patterns by allowing deformations on the patterns. – Cost of matching two items is calculated by Euclidean metric. – Robust to distortions – promises to approximate human ways of perceiving similarity METU, Department of Computer Engineering 12

TEST RESULT FOR MPEG 7 CE PART A-1 Robustness to Scaling METU, Department of Computer Engineering 13

TEST RESULT FOR MPEG 7 CE PART A-2 Robustness to Rotation METU, Department of Computer Engineering 14

TEST RESULT FOR MPEG 7 CE PART B Similarity-based Retrieval METU, Department of Computer Engineering 15

TEST RESULT FOR MPEG 7 CE PART C Motion and Non-Rigid Deformations METU, Department of Computer Engineering 16

Comparison l Best Studies in MPEG 7 CE Shape 1; Data Set Shape Tangent Curvature Zernika Wavelet DAG SBA with length 40 length 60 Context Space Scale Space Moments Part A 1 _ 88. 65 89. 76 92. 54 88. 04 85 89. 32 90. 87 Part A 2 _ 100 99. 37 99. 60 97. 46 85 99. 82 100 Part B 76. 51 76. 45 75. 44 70. 22 67. 76 60 81. 04 82. 37 Part C 94. 5 93. 5 _ 92 96 93 83 93 METU, Department of Computer Engineering 17

Performance Evaluation (1) Average performance with the average over the three parts; Total Score 1 = 1/3 A + 1/3 B + 1/3 C Tangent Curvature Zernika Wavelet DAG SBA with Space Scale Space Moments length 40 length 60 Total Score 1 87. 59 88. 67 86. 93 84. 50 76 90. 80 91. 69 (2) Average performance with the average over the number of queries; Total Score 2 = 840/2241 A + 1400/2241 B+ 1 / 2241 C Tangent Curvature Zernika Wavelet DAG Space Scale Space Moments Total Score 2 83. 16 82. 62 SBA with length 40 length 60 79. 92 77. 14 69. 38 86. 12 87. 27 METU, Department of Computer Engineering 18