Recovery of Non-Rigid Structure Based on Sparse Coding

3D non-rigid recovery is a problem of recovering the real shape of 3D deformable object by using some kinds of algorithms. This paper proposes a novel approach to recovery of non-rigid structure using sparse coding in trajectory space. In order to overcome the difficulty of defining the size of trajectory bases, the sparse coding method is used to construct an over-complete atom dictionary replacing the truncated trajectory bases. Experimental results show that the proposed method does better in solving the 3D non-rigid reconstruction than traditional trajectory basis method and it is also very easy to implement. This paper presents the new thought preliminarily and introduces a simple but effective solution for recovering the structure of the non-rigid objects. Introduction 3D non-rigid reconstruction is a classical computer vision problem and it is very important when dealing with 3D object simulation problem. Commonly, one prevalent solution for solving this problem is considering the deformable object as a linear combination of some shape bases. And this method worked well in the motion scenes which contain a series of simple action. However, it has shortcomings that it would be hard to recover the structure of a complex motion sequence. For this reason, Akhter et al. [1] introduced a commonly method that reconstructs the 3D object in trajectory space instead of shape space. At the same time, lots of experiments have shown that this approach did well with long complex motion sequences because these measurement trajectory curves were not dependent on each other in trajectory space. The efficiency of the trajectory basis method relies on two factors: the type of the trajectory basis and the number of the bases. It has been proved that the discrete cosine transform (DCT) basis was more suitable to be defined as a general basis [2]. However, we should know that, though DCT basis has been proved to be better than the others on the whole, it still could not be suitable for every motion sequence. On the other hand, a small size of trajectory basis number K may lead to a big ignorance of much important information of the motion sequences, while a big K may lead to a large number of unknown factors and the system of equations would be ill-posed. This paper introduces to apply sparse coding algorithms to the non-rigid structure recovery problem. In this process, a set of over-complete bases called atom dictionary is predefined to estimate the deformable object with sparse coefficients. An advantage of the sparse approach is that it is not restricted to only one trajectory basis function and may use two or more incoherent basis functions. It is very useful to recovering the trajectory curves which is complex. What’s more, since the goal of sparse approximation is to represent trajectory sequences as a sparse combination of all atoms, it’s no need to predefine the number of trajectory bases size. The paper is organized as follows. In Section 2, a novel method of sparse approximation is proposed, and some definitions and assumptions on this topic are given. Next the Algorithm Solutions are presented in Section 3. And Section 4 shows the experiment results obtained by using the proposed method. Finally, a conclusion of this paper is provided in section 5. Sparse Approximation Method The measurement projective trajectories are contained in a 2F×P matrix W as follows: International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 1384