31 research outputs found
Shape Interaction Matrix Revisited and Robustified: Efficient Subspace Clustering with Corrupted and Incomplete Data
The Shape Interaction Matrix (SIM) is one of the earliest approaches to
performing subspace clustering (i.e., separating points drawn from a union of
subspaces). In this paper, we revisit the SIM and reveal its connections to
several recent subspace clustering methods. Our analysis lets us derive a
simple, yet effective algorithm to robustify the SIM and make it applicable to
realistic scenarios where the data is corrupted by noise. We justify our method
by intuitive examples and the matrix perturbation theory. We then show how this
approach can be extended to handle missing data, thus yielding an efficient and
general subspace clustering algorithm. We demonstrate the benefits of our
approach over state-of-the-art subspace clustering methods on several
challenging motion segmentation and face clustering problems, where the data
includes corrupted and missing measurements.Comment: This is an extended version of our iccv15 pape
The Geometry of Dynamic Scenes - On Coplanar and Convergent Linear Motions Embedded in 3D Static Scenes
In this paper, we consider structure and motion recovery for scenes consisting of static and dynamic features. More particularly, we consider a single moving uncalibrated camera observing a scene consisting of points moving along straight lines converging to a unique point and lying on a motion plane. This scenario may describe a roadway observed by a moving camera whose motion is unknown. We show that there exist matching tensors similar to fundamental matrices. We derive the link between dynamic and static structure and motion and show how the equation of the motion plane (or equivalently the plane homographies it induces between images) may be recovered from dynamic features only. Experimental results on real images are provided, in particular on a 60-frames video sequence
DUST: dual union of spatio-temporal subspaces for monocular multiple object 3D reconstruction
© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.We present an approach to reconstruct the 3D shape of multiple deforming objects from incomplete 2D trajectories acquired by a single camera. Additionally, we simultaneously provide spatial segmentation (i.e., we identify each of the objects in every frame) and temporal clustering (i.e., we split the sequence into primitive actions). This advances existing work, which only tackled the problem for one single object and non-occluded tracks. In order to handle several objects at a time from partial observations, we model point trajectories as a union of spatial and temporal subspaces, and optimize the parameters of both modalities, the non-observed point tracks and the 3D shape via augmented Lagrange multipliers. The algorithm is fully unsupervised and results in a formulation which does not need initialization. We thoroughly validate the method on challenging scenarios with several human subjects performing different activities which involve complex motions and close interaction. We show our approach achieves state-of-the-art 3D reconstruction results, while it also provides spatial and temporal segmentation.Peer ReviewedPostprint (author's final draft