Nearness to Local Subspace Algorithm for Subspace and Motion Segmentation

TL;DR

This paper introduces a reliable clustering algorithm for high-dimensional data from unions of subspaces, demonstrating state-of-the-art motion segmentation results on the Hopkins 155 Dataset.

Contribution

The paper proposes a new nearness to local subspace algorithm that effectively segments data from unions of subspaces, especially in noisy conditions, with superior performance in motion segmentation.

Findings

Achieved 99.43% accuracy in two-motion segmentation

Achieved 98.69% accuracy in three-motion segmentation

Overall segmentation accuracy of 99.24% on Hopkins 155 Dataset

Abstract

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.