Stochastic Algorithms for Visual Tracking

1 Introduction and background.- 1.1 Overview.- 1.2 Active contours for visual tracking.- 1.2.1 Splines and shape space.- 1.2.2 Dynamical models using auto-regressive processes.- 1.2.3 Measurement methodology.- 2 The Condensation algorithm.- 2.1 The basic idea.- 2.2 Formal definitions.- 2.2.1 Technical detail: convergence of distribution-valued distributions.- 2.2.2 The crucial definition: how a particle set represents a distribution.- 2.3 Operations on particle sets.- 2.3.1 Multiplication by a function.- 2.3.2 Applying dynamics.- 2.3.3 Resampling.- 2.4 The Condensation theorem.- 2.5 The relation to factored sampling, or "where did the proof go?".- 2.6 "Good" particle sets and the effective sample size.- 2.6.1 The survival diagnostic.- 2.6.2 From effective sample size to survival diagnostic.- 2.6.3 Estimating the weight normalisation.- 2.6.4 Effective sample size of a resampled set.- 2.7 A brief history of Condensation.- 2.8 Some alternatives to Condensation.- 3 Contour likelihoods.- 3.1 A generative model for image features.- 3.1.1 The generic contour likelihood.- 3.1.2 The Poisson likelihood.- 3.1.3 The interior-exterior likelihood.- 3.1.4 The order statistic likelihood.- 3.1.5 The contour likelihood ratio.- 3.1.6 Results and examples.- 3.2 Background models and the selection of measurement lines.- 3.2.1 Discussion of the background model.- 3.2.2 Independence of measurement lines.- 3.2.3 Selection of measurement lines.- 3.3 A continuous analogue of the contour likelihood ratio.- 3.3.1 The continuous model.- 3.3.2 Likelihoods for HO and HB.- 3.3.3 Problems with the continuous ARP model.- 4 Object localisation and tracking with contour likelihoods.- 4.1 A brief survey of object localisation.- 4.2 Object localisation by factored sampling.- 4.2.1 Results.- 4.2.2 Interpretation of the gradient threshold.- 4.3 Estimating the number of targets.- 4.4 Learning the prior.- 4.5 Random sampling: some traps for the unwary.- 4.6 Tracker initialisation by factored sampling.- 4.6.1 Kalman filter tracker.- 4.6.2 The Condensation tracker.- 4.7 Tracking using Condensation and the contour likelihoods.- 4.7.1 The robustified colour contour likelihood.- 4.7.2 Implementation of a head tracker.- 5 Modelling occlusions using the Markov likelihood.- 5.1 Detecting occluded objects.- 5.2 The problem with the independence assumption.- 5.3 The Markov generative model.- 5.4 Prior for occlusions.- 5.5 Realistic assessment of multiple targets.- 5.5.1 Explanation of results.- 5.5.2 Experimental details.- 5.6 Improved discrimination with a single target.- 5.7 Faster convergence using importance sampling.- 5.8 Random samples using MelvIe.- 5.9 Calculating the partition functions.- 5.10 Further remarks.- 6 A probabilistic exclusion principle for multiple objects.- 6.1 Introduction.- 6.2 A generative model with an exclusion principle.- 6.2.1 Description of the generative model.- 6.2.2 Likelihoods derived from the generative model.- 6.2.3 Where does the "exclusion principle" come from?.- 6.2.4 The full likelihood.- 6.3 Tracking multiple wire-frame objects.- 6.4 Tracking multiple opaque objects.- 7 Partitioned sampling.- 7.1 The need for partitioned sampling.- 7.2 Weighted resampling.- 7.3 Basic partitioned sampling.- 7.4 Branched partitioned sampling.- 7.5 Performance of partitioned sampling.- 7.6 Partitioned sampling for articulated objects.- 7.6.1 Results: a vision-based drawing package.- 8 Conelusion?.- Appendix A.- A.1 Measures and Metrics on the configuration space.- A.2 Proof of the interior-exterior likelihood.- A.3 Del Moral's resampling lemma and its consequences.- Appendix B.- B.1 Summary Of Notation.