We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding Lov\'asz extensions and the squared Euclidean norm, leading to algorithms requiring total variation oracles of the summand functions; without further assumptions, these more complex oracles require many calls to the simpler minimization oracles often available in practice. In this paper, we consider a modified convex problem requiring constrained version of the total variation oracles that can be solved with significantly fewer calls to the simple minimization oracles. We support our claims by showing results on graph cuts for 2D and 3D graphs.

Particle filtering is known as a robust approach for motion tracking by vision, at the cost of heavy computation in a high dimensional pose space. In this work, we describe a number of heuristics that we demonstrate to jointly improve robustness and real-time for motion capture. 3D human motion capture by monocular vision without markers can be achieved in realtime by registering a 3D articulated model on a video. First, we search the high-dimensional space of 3D poses by generating new hypotheses (or particles) with equivalent 2D projection by kinematic flipping. Second, we use a semi-deterministic particle prediction based on local optimization. Third, we deterministi-cally resample the probability distribution for a more efficient selection of particles. Particles (or poses) are evaluated using a match cost function and penalized with a Gaussian probability pose distribution learned off-line. In order to achieve real-time, measurement step is parallelized on GPU using the OpenCL API. We present experimental results demonstrating robust real-time 3D motion capture with a consumer computer and webcam.