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E-raamat: Stochastic Algorithms for Visual Tracking: Probabilistic Modelling and Stochastic Algorithms for Visual Localisation and Tracking

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A central problem in computer vision is to track objects as they move and deform in a video sequence. Stochastic algorithms -- in particular, particle filters and the Condensation algorithm -- have dramatically enhanced the state of the art for such visual tracking problems in recent years. This book presents a unified framework for visual tracking using particle filters, including the new technique of partitioned sampling which can alleviate the "curse of dimensionality" suffered by standard particle filters. The book also introduces the notion of contour likelihood: a collection of models for assessing object shape, colour and motion, which are derived from the statistical properties of image features. Because of their statistical nature, contour likelihoods are ideal for use in stochastic algorithms. A unifying theme of the book is the use of statistics and probability, which enable the final output of the algorithms presented to be interpreted as the computer's "belief" about the state of the world. The book will be of use and interest to students, researchers and practitioners in computer vision, and assumes only an elementary knowledge of probability theory.
Introduction and background
1(7)
Overview
2(1)
Active contours for visual tracking
3(5)
Splines and shape space
4(1)
Dynamical models using auto-regressive processes
5(1)
Measurement methodology
6(2)
The Condensation algorithm
8(30)
The basic idea
8(3)
Formal definitions
11(5)
Technical detail: convergence of distribution-valued distributions
14(1)
The crucial definition: how a particle set represents a distribution
15(1)
Operations on particle sets
16(8)
Multiplication by a function
17(1)
Applying dynamics
18(2)
Resampling
20(4)
The Condensation theorem
24(1)
The relation to factored sampling, or ``where did the proof go?''
25(1)
``Good'' particle sets and the effective sample size
26(9)
The survival diagnostic
28(3)
From effective sample size to survival diagnostic
31(2)
Estimating the weight normalisation
33(1)
Effective sample size of a resampled set
33(2)
A brief history of Condensation
35(2)
Some alternatives to Condensation
37(1)
Contour likelihoods
38(27)
A generative model for image features
38(16)
The generic contour likelihood
42(3)
The Poisson likelihood
45(1)
The interior-exterior likelihood
46(3)
The order statistic likelihood
49(1)
The contour likelihood ratio
50(1)
Results and examples
51(3)
Background models and the selection of measurement lines
54(6)
Discussion of the background model
55(1)
Independence of measurement lines
55(2)
Selection of measurement lines
57(3)
A continuous analogue of the contour likelihood ratio
60(5)
The continuous model
60(2)
Likelihoods for Ho and HB
62(1)
Problems with the continuous ARP model
63(2)
Object localisation and tracking with contour likelihoods
65(27)
A brief survey of object localisation
65(3)
Object localisation by factored sampling
68(7)
Results
70(3)
Interpretation of the gradient threshold
73(2)
Estimating the number of targets
75(4)
Learning the prior
79(1)
Random sampling: some traps for the unwary
80(4)
Tracker initialisation by factored sampling
84(2)
Kalman filter tracker
85(1)
The Condensation tracker
85(1)
Tracking using Condensation and the contour likelihoods
86(6)
The robustified colour contour likelihood
86(3)
Implementation of a head tracker
89(3)
Modelling occlusions using the Markov likelihood
92(20)
Detecting occluded objects
92(2)
The problem with the independence assumption
94(1)
The Markov generative model
95(1)
Prior for occlusions
96(3)
Realistic assessment of multiple targets
99(3)
Explanation of results
99(1)
Experimental details
100(2)
Improved discrimination with a single target
102(1)
Faster convergence using importance sampling
103(4)
Random samples using MCMC
107(2)
Calculating the partition functions
109(1)
Further remarks
110(2)
A probabilistic exclusion principle for multiple objects
112(12)
Introduction
112(2)
A generative model with an exclusion principle
114(4)
Description of the generative model
114(1)
Likelihoods derived from the generative model
115(1)
Where does the ``exclusion principle'' come from?
116(2)
The full likelihood
118(1)
Tracking multiple wire-frame objects
118(1)
Tracking multiple opaque objects
119(5)
Partitioned sampling
124(20)
The need for partitioned sampling
124(3)
Weighted resampling
127(3)
Basic partitioned sampling
130(1)
Branched partitioned sampling
131(2)
Performance of partitioned sampling
133(1)
Partitioned sampling for articulated objects
134(10)
Results: a vision-based drawing package
138(6)
Conclusion?
144(2)
Appendix A 146(7)
A.1 Measures and metrics on the configuration space
146(1)
A.2 Proof of the interior-exterior likelihood
147(2)
A.3 Del Moral's resampling lemma and its consequences
149(4)
Appendix B 153(2)
B.1 Summary of notation
153(2)
Bibliography 155(10)
Index 165