Real-time 3D reconstruction of non-rigid shapes with a single moving camera

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper describes a real-time sequential method to simultaneously recover the camera motion and the 3D shape of deformable objects from a calibrated monocular video. For this purpose, we consider the Navier-Cauchy equations used in 3D linear elasticity and solved by finite elements, to model the time-varying shape per frame. These equations are embedded in an extended Kalman filter, resulting in sequential Bayesian estimation approach. We represent the shape, with unknown material properties, as a combination of elastic elements whose nodal points correspond to salient points in the image. The global rigidity of the shape is encoded by a stiffness matrix, computed after assembling each of these elements. With this piecewise model, we can linearly relate the 3D displacements with the 3D acting forces that cause the object deformation, assumed to be normally distributed. While standard finite-element-method techniques require imposing boundary conditions to solve the resulting linear system, in this work we eliminate this requirement by modeling the compliance matrix with a generalized pseudoinverse that enforces a pre-fixed rank. Our framework also ensures surface continuity without the need for a post-processing step to stitch all the piecewise reconstructions into a global smooth shape. We present experimental results using both synthetic and real videos for different scenarios ranging from isometric to elastic deformations. We also show the consistency of the estimation with respect to 3D ground truth data, include several experiments assessing robustness against artifacts and finally, provide an experimental validation of our performance in real time at frame rate for small mapsPeer ReviewedPostprint (author's final draft

Disturbance Grassmann Kernels for Subspace-Based Learning

In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers, e.g., Support Vector Machines (SVMs). However, the existing discriminative algorithms mostly ignore the instability of subspaces, which would cause the classifiers misled by disturbed instances. Thus we propose considering all potential disturbance of subspaces in learning processes to obtain more robust classifiers. Firstly, we derive the dual optimization of linear classifiers with disturbance subject to a known distribution, resulting in a new kernel, Disturbance Grassmann (DG) kernel. Secondly, we research into two kinds of disturbance, relevant to the subspace matrix and singular values of bases, with which we extend the Projection kernel on Grassmann manifolds to two new kernels. Experiments on action data indicate that the proposed kernels perform better compared to state-of-the-art subspace-based methods, even in a worse environment.Comment: This paper include 3 figures, 10 pages, and has been accpeted to SIGKDD'1

Depth Superresolution using Motion Adaptive Regularization

Spatial resolution of depth sensors is often significantly lower compared to that of conventional optical cameras. Recent work has explored the idea of improving the resolution of depth using higher resolution intensity as a side information. In this paper, we demonstrate that further incorporating temporal information in videos can significantly improve the results. In particular, we propose a novel approach that improves depth resolution, exploiting the space-time redundancy in the depth and intensity using motion-adaptive low-rank regularization. Experiments confirm that the proposed approach substantially improves the quality of the estimated high-resolution depth. Our approach can be a first component in systems using vision techniques that rely on high resolution depth information

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio