Robust Recovery of Subspace Structures by Low-Rank Representation

In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible errors as well. To this end, we propose a novel method termed Low-Rank Representation (LRR), which seeks the lowest-rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that LRR well solves the subspace recovery problem: when the data is clean, we prove that LRR exactly captures the true subspace structures; for the data contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for the data corrupted by arbitrary errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace segmentation and error correction, in an efficient way.Comment: IEEE Trans. Pattern Analysis and Machine Intelligenc

Enabling Depth-driven Visual Attention on the iCub Humanoid Robot: Instructions for Use and New Perspectives

The importance of depth perception in the interactions that humans have within their nearby space is a well established fact. Consequently, it is also well known that the possibility of exploiting good stereo information would ease and, in many cases, enable, a large variety of attentional and interactive behaviors on humanoid robotic platforms. However, the difficulty of computing real-time and robust binocular disparity maps from moving stereo cameras often prevents from relying on this kind of cue to visually guide robots' attention and actions in real-world scenarios. The contribution of this paper is two-fold: first, we show that the Efficient Large-scale Stereo Matching algorithm (ELAS) by A. Geiger et al. 2010 for computation of the disparity map is well suited to be used on a humanoid robotic platform as the iCub robot; second, we show how, provided with a fast and reliable stereo system, implementing relatively challenging visual behaviors in natural settings can require much less effort. As a case of study we consider the common situation where the robot is asked to focus the attention on one object close in the scene, showing how a simple but effective disparity-based segmentation solves the problem in this case. Indeed this example paves the way to a variety of other similar applications