Ranch Y. Q. Lai

Ranch Y. Q. Lai, Pong C. Yuen

We propose a Projected Proximal Point Algorithm (ProPPA) for solving a class of optimization problems. The algorithm iteratively computes the proximal point of the last estimated solution projected into an affine space which itself is parallel and approaching to the feasible set. We provide convergence analysis theoretically supporting the general algorithm, and then apply it for solving $\ell_1$-minimization problems and the matrix completion problem. These problems arise in many applications including machine learning, image and signal processing. We compare our algorithm with the existing state-of-the-art algorithms. Experimental results on solving these problems show that our algorithm is very efficient and competitive.

Ranch Y. Q. Lai, Pong C. Yuen, K. W. Lee et al.

Character posing is of interest in computer animation. It is difficult due to its dependence on inverse kinematics (IK) techniques and articulate property of human characters . To solve the IK problem, classical methods that rely on numerical solutions often suffer from the under-determination problem and can not guarantee naturalness. Existing data-driven methods address this problem by learning from motion capture data. When facing a large variety of poses however, these methods may not be able to capture the pose styles or be applicable in real-time environment. Inspired from the low-rank motion de-noising and completion model in \cite{lai2011motion}, we propose a novel model for character posing based on sparse coding. Unlike conventional approaches, our model directly captures the pose styles in Euclidean space to provide intuitive training error measurements and facilitate pose synthesis. A pose dictionary is learned in training stage and based on it natural poses are synthesized to satisfy users' constraints . We compare our model with existing models for tasks of pose de-noising and completion. Experiments show our model obtains lower de-noising and completion error. We also provide User Interface(UI) examples illustrating that our model is effective for interactive character posing.