Marius-Calin Silaghi

Local and Global Skeleton Fitting Techniques for Optical Motion Capture

Identifying a precise anatomic skeleton is important in order to ensure high quality motion capture. In this paper we discuss two skeleton fitting techniques based on 3D optical marker data. First a local technique is proposed based on relative marker trajectories. Then it is compared to a global optimization of a skeleton model. Various proposals are made to handle the skin deformation problem. Index Terms--skeleton fitting, motion capture, optical markers.

Consistency Maintenance for ABT

One of the most powerful techniques for solving centralized constraint satisfaction problems (CSPs) consists of maintaining local consistency during backtrack search (e.g. [11]). Yet, no work has been reported on such a combination in asynchronous settings. The difficulty in this case is that, in the usual algorithms, the instantiation and consistency enforcement steps must alternate sequentially. When brought to a distributed setting, a similar approach forces the search algorithm to be synchronous in order to benefit from consistency maintenance. Asynchronism [24,14] is highly desirable since it increases flexibility and parallelism, and makes the solving process robust against timing variations. One of the most well-known asynchronous search algorithms is Asynchronous Backtracking (ABT). This paper shows how an algorithm for maintaining consistency during distributed asynchronous search can be designed upon ABT. The proposed algorithm is complete and has polynomial-space complexity. Since the consistency propagation is optional, this algorithms generalizes forward checking as well as chronological backtracking. An additional advance over existing centralized algorithms is that it can exploit available backtracking-nogoods for increasing the strength of the maintained consistency. The experimental evaluation shows that it can bring substantial gains in computational power compared with existing asynchronous algorithms.

Numerical Constraint Satisfaction Problems with Non-isolated Solutions

In recent years, interval constraint-based solvers have shown their ability to efficiently solve complex instances of non-linear numerical CSPs. However, most of the working systems are designed to deliver point-wise solutions with an arbitrary accuracy. This works generally well for systems with isolated solutions but less well when there is a continuum of feasible points (e.g. under-constrained problems, problems with inequalities). In many practical applications, such large sets of solutions express equally relevant alternatives which need to be identified as completely as possible. In this paper, we address the issue of constructing concise inner and outer approximations of the complete solution set for non-linear CSPs. We propose a technique which combines the extreme vertex representation of orthogonal polyhedra 1,2,3, as defined in computational geometry, with adapted splitting strategies 4 to construct the approximations as unions of interval boxes. This allows for compacting the explicit representation of the complete solution set and improves efficiency.

Approximation Techniques for Non-linear Problems with Continuum of Solutions

Most of the working solvers for numerical constraint satisfaction problems (NCSPs) are designed to delivering point-wise solutions with an arbitrary accuracy. When there is a continuum of feasible points this might lead to prohibitively verbose representations of the output. In many practical applications, such large sets of solutions express equally relevant alternatives which need to be identified as completely as possible. The goal of this paper is to show that by using appropriate approximation techniques, explicit representations of the solution sets, preserving both accuracy and completeness, can still be proposed for NCSPs with continuum of solutions. We present a technique for constructing concise inner and outer approximations as unions of interval boxes. The proposed technique combines a new splitting strategy with the extreme vertex representation of orthogonal polyhedra [1,2,3], as defined in computational geometry. This allows for compacting the representation of the approximations and improves efficiency.

Asynchronous Search for Numeric DisCSPs

In Distributed CSPs (DisCSPs), agents maywant to keep parts of their problem secret but accept to cooperate by exchanging proposals. Asynchronism in solving DisCSPs [1] increases flexibility, parallelism, and robustness. Enumerative algorithms apply for discrete problems with small domains. Our goal is to develop asynchronous algorithms that can deal with numeric constraints. Centralized techniques for CSPs with continuous domains interleave (dichotomous) splitting of the search space with forms of bound consistency. Consecutive numerical values are aggregated into intervals. As a first step towards our goal, we have developed Asynchronous Aggregation Search (AAS) [1], allowing agents to asynchronously propose subspaces of their search space. Agents propose splits of domains that ensure the feasibility of their subproblem. Then we have proposed DMAC, allowing to maintain bound (or arc) consistency in AAS [1]. Dichotomous splits are generally only partially sound splits since the agent proposing them does not necessarily have its constraints fully satisfied by them. The simplest and most widely used strategy for partially sound splits is the dichotomous one, but the technique we propose next can similarly deal with more complex splitting strategies.

Visualization of Local Movements for Optimal Marker Positioning

Motion Capture has been adopted for the production of highly realistic movements, as well as for the clinical analysis of pathological motions. In both cases, a skeleton model has to be identified to derive the joint motion. The optical technology has gained a large popularity due to the high precision of its marker position measurements. However, when it comes to building the skeleton frames out of the 3D marker positions, significant local skin deformations may penalize the quality of the model reconstruction. In this paper we exploit a local fitting tool to visualize the influence of skin deformation on marker movements. Such a knowledge can in turn improve the layout of optical markers. We illustrate our viewpoint on motions of the upper-torso.

Ways of Maintaining Arc Consistency in Search Using the Cartesian Representation

The search space of constraint satisfaction problems (CSPs) can be reduced by using value interchangeability. This notion consists of aggregating subsets of values that behave similarly on the future branches of the search. BT-CPR [8], is a typical backtracking algorithm using value interchangeability. It uses the Cartesian product representation of the search space (CPR) which aggregates partial solutions and proves particularly useful for finding and representing all solutions of a CSP. It is assessed that maintaining arc-consistency (MAC) is the most efficient general algorithm for solving hard problems. A few work on combining MAC with CPR exists. In this paper we study comparatively two other possible alternatives of MAC-CPR.

Intelligent Domain Splitting for CSPs with Ordered Domains

This paper presents intelligent domain splitting, an approach for searching in CSPs with ordered domains. The technique has a particular strength for finding all solutions. It represents the search space by aggregations obtained through the cooperation of two known clustering concepts, namely intervals and cross-products. Intelligent domain splitting searches for solutions by iteratively breaking up the space into smaller subspaces in a meaningful way. The proposed backtracking technique benefits from the strengths of Hull-consistency (i.e. 2B-consistency [4]) and of the Cartesian product representation [2]. The algorithm can be applied to general systems of constraints with explicit representations. Even though designed for generating all solutions, it also proves useful for finding the first solution of hard problems, as shown by preliminary experiments.