1. A Perceptual Shape Descriptor
Nafiz ARICA, Fatoş T. YARMAN-VURAL
METU, Department of Computer Engineering
{nafiz,
METU, Department of Computer Engineering

2. 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

3. 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

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

5. 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

6. 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

7. 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

8. 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

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

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

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

12. 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

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

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

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

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

17. 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

18. 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 /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