Tensor Voting: A Perceptual Organization Approach to Computer Vision and Machine Learning

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Morgan & Claypool Publishers, 2007 - Computers - 126 pages
This lecture presents research on a general framework for perceptual organization that was contacted mainly at the Institute for Robotics and Intelligent Systems of the University of Southern California. It is not written as a historical recount of the work, since the sequence of the presentation is not in chronological order. It aims at presenting an approach to a wide range of problems in computer vision and machine learning that is data-driven, local and requires a minimal number of assumptions. The tensor voting framework combines these properties and provides a unified perceptual organization methodology applicable in situations that may seem heterogeneous initially. Authors Philippos Mordohai and Gerard Medioni show how several problems can be posed as the organization of the inputs into salient perceptual structures, which are inferred via tensor voting. The book extends the original tensor voting framework with the addition of boundary inference capabilities, a novel re-formulation of the framework applicable to high-dimensional spaces and the development of algorithms for computer vision and machine learning problems. The authors provide complete analysis for some problems and briefly outline the approach for other applications and provide references to relevant sources.
 

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Contents

Introduction
1
12 APPROACH
4
13 OUTLINE
6
TENSOR VOTING
9
22 TENSOR VOTING IN 2D
12
222 Second Order Voting in 2D
13
223 Voting Fields
16
224 Vote Analysis
18
432 The Voting Process
52
433 Vote Analysis
55
45 COMPUTER VISION PROBLEMS IN HIGH DIMENSIONS
59
453 Texture Synthesis
61
46 DISCUSSION
62
Dimensionality Estimation Manifold Learning and Function Approximation
63
51 RELATED WORK
65
52 DIMENSIONALITY ESTIMATION
69

226 Quantitative Evaluation of Saliency Estimation
19
23 TENSOR VOTING IN 3D
20
231 Representation in 3D
21
232 Voting in 3D
23
233 Vote Analysis
25
234 Results in 3D
26
Stereo Vision from a Perceptual Organization Perspective
27
32 RELATED WORK
29
33 OVERVIEW OF OUR APPROACH
31
34 INITIAL MATCHING
32
35 SELECTION OF MATCHES AS SURFACE INLIERS
35
36 SURFACE GROUPING AND REFINEMENT
37
37 DISPARITY ESTIMATION FOR UNMATCHED PIXELS
40
38 EXPERIMENTAL RESULTS
41
39 DISCUSSION
43
310 OTHER 3D COMPUTER VISION RESEARCH
46
3102 Tracking
47
Tensor Voting in N D
49
42 LIMITATIONS OF ORIGINAL IMPLEMENTATION
50
43 TENSOR VOTING IN HIGHDIMENSIONAL SPACES
51
53 MANIFOLD LEARNING
71
54 MANIFOLD DISTANCES AND NONLINEAR INTERPOLATION
73
55 GENERATION OF UNOBSERVED SAMPLES AND NONPARAMETRIC FUNCTION APPROXIMATION
78
56 DISCUSSION
83
Boundary Inference
87
62 FIRSTORDER REPRESENTATION AND VOTING
89
621 FirstOrder Voting in High Dimensions
92
63 VOTE ANALYSIS
93
64 RESULTS USING FIRSTORDER INFORMATION
97
65 DISCUSSION
99
Figure Completion
101
72 OVERVIEW OF THE APPROACH
103
73 TENSOR VOTING ON LOW LEVEL INPUTS
104
75 EXPERIMENTAL RESULTS
106
76 DISCUSSION
111
Conclusions
113
References
115
Author Biographies
125
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