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

BAS: A shape Descriptor with Beam Angle Statistics 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

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

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

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

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

METU, Department of Computer Engineering 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

METU, Department of Computer Engineering 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

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

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

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

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

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

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

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

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

METU, Department of Computer Engineering Comparison Best Studies in MPEG 7 CE Shape 1; Data Set Shape Context Tangent Space Curvature Scale Space Zernika Moments Wavelet DAG SBA with length 40 SBA with length 60 Part A1 _ 88.65 89.76 92.54 88.04 85 89.32 90.87 Part A2 100 99.37 99.60 97.46 99.82 Part B 76.51 76.45 75.44 70.22 67.76 60 81.04 82.37 Part C 92 96 94.5 93 83 93.5 METU, Department of Computer Engineering

Performance Evaluation (1) Average performance with the average over the three parts; Total Score1 = 1/3 A + 1/3 B + 1/3 C Tangent Space Curvature Scale Space Zernika Moments Wavelet DAG SBA with length 40 SBA with 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 Score2 = 840/2241 A + 1400/2241 B+ 1 / 2241 C Tangent Space Curvature Scale Space Zernika Moments Wavelet DAG SBA with length 40 SBA with length 60 Total Score 2 83.16 82.62 79.92 77.14 69.38 86.12 87.27 METU, Department of Computer Engineering