Three dimensional transparent structure segmentation and multiple 3D motion estimation from monocular perspective image sequences

A three dimensional scene can be segmented using different cues, such as boundaries, texture, motion, discontinuities of the optical flow, stereo, models for structure, etc. We investigate segmentation based upon one of these cues, namely three dimensional motion. If the scene contain transparent objects, the two dimensional (local) cues are inconsistent, since neighboring points with similar optical flow can correspond to different objects. We present a method for performing three dimensional motion-based segmentation of (possibly) transparent scenes together with recursive estimation of the motion of each independent rigid object from monocular perspective images. Our algorithm is based on a recently proposed method for rigid motion reconstruction and a validation test which allows us to initialize the scheme and detect outliers during the motion estimation procedure. The scheme is tested on challenging real and synthetic image sequences. Segmentation is performed for the Ullmann's experiment of two transparent cylinders rotating about the same axis in opposite directions

Robust Motion Segmentation from Pairwise Matches

In this paper we address a classification problem that has not been considered before, namely motion segmentation given pairwise matches only. Our contribution to this unexplored task is a novel formulation of motion segmentation as a two-step process. First, motion segmentation is performed on image pairs independently. Secondly, we combine independent pairwise segmentation results in a robust way into the final globally consistent segmentation. Our approach is inspired by the success of averaging methods. We demonstrate in simulated as well as in real experiments that our method is very effective in reducing the errors in the pairwise motion segmentation and can cope with large number of mismatches

Better Feature Tracking Through Subspace Constraints

Feature tracking in video is a crucial task in computer vision. Usually, the tracking problem is handled one feature at a time, using a single-feature tracker like the Kanade-Lucas-Tomasi algorithm, or one of its derivatives. While this approach works quite well when dealing with high-quality video and "strong" features, it often falters when faced with dark and noisy video containing low-quality features. We present a framework for jointly tracking a set of features, which enables sharing information between the different features in the scene. We show that our method can be employed to track features for both rigid and nonrigid motions (possibly of few moving bodies) even when some features are occluded. Furthermore, it can be used to significantly improve tracking results in poorly-lit scenes (where there is a mix of good and bad features). Our approach does not require direct modeling of the structure or the motion of the scene, and runs in real time on a single CPU core.Comment: 8 pages, 2 figures. CVPR 201

Multi-body Non-rigid Structure-from-Motion

Conventional structure-from-motion (SFM) research is primarily concerned with the 3D reconstruction of a single, rigidly moving object seen by a static camera, or a static and rigid scene observed by a moving camera --in both cases there are only one relative rigid motion involved. Recent progress have extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid} relative motions in the scene), as well as {non-rigid SFM} (where there is a single non-rigid, deformable object or scene). Along this line of thinking, there is apparently a missing gap of "multi-body non-rigid SFM", in which the task would be to jointly reconstruct and segment multiple 3D structures of the multiple, non-rigid objects or deformable scenes from images. Such a multi-body non-rigid scenario is common in reality (e.g. two persons shaking hands, multi-person social event), and how to solve it represents a natural {next-step} in SFM research. By leveraging recent results of subspace clustering, this paper proposes, for the first time, an effective framework for multi-body NRSFM, which simultaneously reconstructs and segments each 3D trajectory into their respective low-dimensional subspace. Under our formulation, 3D trajectories for each non-rigid structure can be well approximated with a sparse affine combination of other 3D trajectories from the same structure (self-expressiveness). We solve the resultant optimization with the alternating direction method of multipliers (ADMM). We demonstrate the efficacy of the proposed framework through extensive experiments on both synthetic and real data sequences. Our method clearly outperforms other alternative methods, such as first clustering the 2D feature tracks to groups and then doing non-rigid reconstruction in each group or first conducting 3D reconstruction by using single subspace assumption and then clustering the 3D trajectories into groups.Comment: 21 pages, 16 figure

CUR Decompositions, Similarity Matrices, and Subspace Clustering

A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces $\mathscr{U}=\underset{i=1}{\overset{M}\bigcup}S_i$. The similarity matrices thus constructed give the exact clustering in the noise-free case. Additionally, this decomposition gives rise to many distinct similarity matrices from a given set of data, which allow enough flexibility to perform accurate clustering of noisy data. We also show that two known methods for subspace clustering can be derived from the CUR decomposition. An algorithm based on the theoretical construction of similarity matrices is presented, and experiments on synthetic and real data are presented to test the method. Additionally, an adaptation of our CUR based similarity matrices is utilized to provide a heuristic algorithm for subspace clustering; this algorithm yields the best overall performance to date for clustering the Hopkins155 motion segmentation dataset.Comment: Approximately 30 pages. Current version contains improved algorithm and numerical experiments from the previous versio