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Non rigid representation
When a sucient description of the object cannot be obtained using simple geometric elements, non rigid representation and silhouette based tracking methods are needed. An example of such requirements is shown in Figure 2.2. This modelling oers an accurate shape description based on object edges and contour. In practice this tracking scheme is used when the complete region of the object is required and oers exibility to handle a great variety of shapes. Within this category we distinguish between two dierent tracking approaches, namely shape matching and contour tracking. The shape matching approach, as any template matching technique, aims to nd the image regions that show high similarity with the object model. The object silhouette is searched in the current frame based on a set of templates representing the silhouette at the previous frames. A smooth variation of the shape is assumed from a frame to the next one. The matching mechanism is mainly formulated as a distance minimisation or matching score optimisation, with dierent metrics such as Bhattacharya distance, cross-correlation or Kullback-Leibler divergence [15].
The contour tracking approach, in contrast with the template matching, makes the contour shape evolve pixel by pixel until it ts the actual position of the object. Starting from the previous contour, the algorithms iteratively modify this contour either by expanding or shrinking some parts of it until getting the best conguration for the current frame. One major limitation is that contour tracking imperatively requires overlapping of two consecutive contours; which makes this technique unusable in case of abrupt motion. The contour evolution can be carried out using deterministic gradient descent for minimisation of a contour energy functional [121]. The tracking problem can be also considered as an estimation problem within a state space model corresponding to the shape and motion parameters of the contour [42] and solved using Kalman lters or particle lters.
Rigid representation
Rigid representation concerns applications where tracking accurately the object shape is not mandatory. It consists in a simpler object representation based on basic geometric forms (points, rectangles, ellipses etc.) and an easier problem statement. This representation is not restricted to objects with xed shapes, it is also applicable to other types of object when considering only the global variation of the original shape : rotation, scale and other ane transformations. Within this category we can distinguish between two main subcategories: point representation and kernel representation. Point tracking consists in making the correspondence between detected points of interest. In each frame the objects are represented by points provided by a detection process, and the tracker aims to match the corresponding points between successive frames to obtain the object trajectories. An example of pointcorrespondence is shown in Figure 2.3 where the tracker computes trajectories of points located on a rotating ball and a dish. This tracking scheme highly depends on the detection algorithm that returns the object location at each image frame. The correspondence problem is solved either in a deterministic way or using statistical methods.
Sequential importance sampling (SIS)
SIS is a modied importance sampling method that enables to sample from q(x0:tjy1:t) without modifying the previously simulated trajectories (i.e. the past samples x0:t1). For that purpose, we consider an importance function which can be written recursively as: q(x0:tjy1:t) = q(x0:t1jy1:t1) q(xtjx0:t1; y1:t)
Table of contents :
List of Figures
1 Introduction
Nomenclature
2 About Visual tracking
2.1 Denition and challenges of visual tracking
2.2 Classication of visual tracking methods
2.2.1 Non rigid representation
2.2.2 Rigid representation
2.3 Context of the work
2.4 Chapter Conclusion
3 Sequential Monte Carlo methods
3.1 Bayesian estimation
3.2 Particle Filtering
3.2.1 Importance sampling
3.2.2 Sequential importance sampling (SIS)
3.2.3 The weight degeneracy problem
3.2.4 Resampling
3.2.5 Choice of the importance function
3.2.6 Auxiliary particle lter (APF)
3.2.7 Marginal particle lter (MPF)
3.3 Sequential Markov chain Monte Carlo Methods
3.3.1 MCMC methods
3.3.2 Sequential MCMC
3.3.3 Choice of the proposal
3.3.4 Adaptive MCMC
3.4 Chapter Conclusion
4 SMC methods applied to visual tracking
4.1 Introduction
4.2 Problem formulation
4.2.1 State model
4.2.2 Dynamic model and prior density
4.2.3 Observation model and likelihood
4.2.3.1 Appearance models
4.2.3.2 Detection information
4.3 Selected models for single object tracking
4.4 Chapter Conclusion
5 Near Optimal Particle Filters
5.1 Optimal proposals
5.1.1 Optimal importance function for PFs
5.1.1.1 Specic cases
5.1.1.2 General case
5.1.1.3 Suboptimal strategies – state of the art
5.1.2 Optimal proposal for sequential MCMC
5.1.2.1 Suboptimal strategies – state of the art
5.2 Proposed approach : approximation of the optimal proposals
5.2.1 Information exploited for sampling
5.2.2 Simplifying assumptions
5.2.3 Approximations of the distributions of interest
5.3 The near optimal particle lter and its variants
5.3.1 Near optimal particle lter (NOPF)
5.3.2 Near optimal auxiliary particle lter (NOAPF)
5.3.3 Near optimal marginal particle lter (NOMPF)
5.3.3.1 First algorithm
5.3.3.2 Second algorithm
5.4 The near optimal sequential MCMC (NOMCMC)
5.4.1 First algorithm
5.4.2 Second algorithm
5.5 Conclusion
6 Application to abrupt motion tracking
6.1 Performance metrics
6.2 Tracking algorithms
6.2.1 Basic SMC methods
6.2.2 SMC methods to approach the optimal proposal
6.2.3 SMC methods to deal with abrupt motion
6.2.4 General experimental settings
6.3 Performance of near optimal SMC methods
6.3.1 Test Sequences
6.3.2 Performance of the NOPF
6.3.3 Performance of the NOMCMC
6.3.4 Comparison of the dierent near optimal SMC methods
6.3.4.1 Benets of particle preselection in NOAPF
6.3.4.2 Computational time
6.4 Comparison with the state-of-the-art methods for abrupt motion tracking
6.4.1 Test sequences
6.4.2 Performance comparison
6.5 Chapter Conclusion
7 Multiple object tracking
7.1 Related work
7.2 Near optimal proposal for multi-object tracking
7.2.1 Problem formulation – Tracking of multiple independent objects
7.2.2 Multiple independent near optimal particle lters
7.2.3 Joint near optimal particle lter
7.2.4 Experimental results
7.3 MOT using the local particle lter
7.3.1 Problem formulation – Tracking of multiple interacting objects
7.3.2 The local particle lter
7.3.3 Experimental results
7.4 Chapter Conclusion
8 Conclusions and perspectives
9 Résumé en Français
9.1 Contexte de la thèse
9.2 État de l’art
9.3 La loi de proposition « Near Optimal »
9.3.1 Loi de proposition optimale
9.3.2 Approximation de la loi de proposition optimale
9.3.3 Variantes de l’algorithme NOPF
9.4 Application au suivi des mouvements abrupts
9.4.1 Comparaison du NOPF avec des PFs standards
9.4.2 Comparaison avec des algorithmes de référence
9.5 Application au suivi multi-objets
9.5.1 Algorithme NOPF pour le suivi multi-objets
9.5.2 Local PF pour le suivi multi-objets
9.6 Conclusion
Appendix A
References
