Nearness to Local Subspace Algorithm for Subspace and Motion Segmentation

There is a growing interest in computer science, engineering, and mathematics for modeling signals in terms of union of subspaces and manifolds. Subspace segmentation and clustering of high dimensional data drawn from a union of subspaces are especially important with many practical applications in computer vision, image and signal processing, communications, and information theory. This paper presents a clustering algorithm for high dimensional data that comes from a union of lower dimensional subspaces of equal and known dimensions. Such cases occur in many data clustering problems, such as motion segmentation and face recognition. The algorithm is reliable in the presence of noise, and applied to the Hopkins 155 Dataset, it generates the best results to date for motion segmentation. The two motion, three motion, and overall segmentation rates for the video sequences are 99.43%, 98.69%, and 99.24%, respectively

The low-rank decomposition of correlation-enhanced superpixels for video segmentation

Low-rank decomposition (LRD) is an effective scheme to explore the affinity among superpixels in the image and video segmentation. However, the superpixel feature collected based on colour, shape, and texture may be rough, incompatible, and even conflicting if multiple features extracted in various manners are vectored and stacked straight together. It poses poor correlation, inconsistence on intra-category superpixels, and similarities on inter-category superpixels. This paper proposes a correlation-enhanced superpixel for video segmentation in the framework of LRD. Our algorithm mainly consists of two steps, feature analysis to establish the initial affinity among superpixels, followed by construction of a correlation-enhanced superpixel. This work is very helpful to perform LRD effectively and find the affinity accurately and quickly. Experiments conducted on datasets validate the proposed method. Comparisons with the state-of-the-art algorithms show higher speed and more precise in video segmentation

Symmetric low-rank representation for subspace clustering

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple subspaces through the self-expressiveness property of the data. In particular, the SLRR method considers a collaborative representation combined with low-rank matrix recovery techniques as a low-rank representation to learn a symmetric low-rank representation, which preserves the subspace structures of high-dimensional data. In contrast to performing iterative singular value decomposition in some existing low-rank representation based algorithms, the symmetric low-rank representation in the SLRR method can be calculated as a closed form solution by solving the symmetric low-rank optimization problem. By making use of the angular information of the principal directions of the symmetric low-rank representation, an affinity graph matrix is constructed for spectral clustering. Extensive experimental results show that it outperforms state-of-the-art subspace clustering algorithms.Comment: 13 page

Satellite Articulation Sensing using Computer Vision

Autonomous on-orbit satellite servicing benefits from an inspector satellite that can gain as much information as possible about the primary satellite. This includes performance of articulated objects such as solar arrays, antennas, and sensors. A method for building an articulated model from monocular imagery using tracked feature points and the known relative inspection route is developed. Two methods are also developed for tracking the articulation of a satellite in real-time given an articulated model using both tracked feature points and image silhouettes. Performance is evaluated for multiple inspection routes and the effect of inspection route noise is assessed. Additionally, a satellite model is built and used to collect stop-motion images simulating articulated motion over an inspection route under simulated space illumination. The images are used in the silhouette articulation tracking method and successful tracking is demonstrated qualitatively. Finally, a human pose tracking algorithm is modified for tracking the satellite articulation demonstrating the applicability of human tracking methods to satellite articulation tracking methods when an articulated model is available

Subspace Segmentation And High-Dimensional Data Analysis

This thesis developed theory and associated algorithms to solve subspace segmentation problem. Given a set of data W={w_1,...,w_N} in R^D that comes from a union of subspaces, we focused on determining a nonlinear model of the form U={S_i}_{i in I}, where S_i is a set of subspaces, that is nearest to W. The model is then used to classify W into clusters. Our first approach is based on the binary reduced row echelon form of data matrix. We prove that, in absence of noise, our approach can find the number of subspaces, their dimensions, and an orthonormal basis for each subspace S_i. We provide a comprehensive analysis of our theory and determine its limitations and strengths in presence of outliers and noise. Our second approach is based on nearness to local subspaces approach and it can handle noise effectively, but it works only in special cases of the general subspace segmentation problem (i.e., subspaces of equal and known dimensions). Our approach is based on the computation of a binary similarity matrix for the data points. A local subspace is first estimated for each data point. Then, a distance matrix is generated by computing the distances between the local subspaces and points. The distance matrix is converted to the similarity matrix by applying a data-driven threshold. The problem is then transformed to segmentation of subspaces of dimension 1 instead of subspaces of dimension d. The algorithm was applied to the Hopkins 155 Dataset and generated the best results to date