Multi-class Graph Mumford-Shah Model for Plume Detection using the MBO Scheme

Abstract

Abstract. We focus on the multi-class segmentation problem using the piecewise constant Mumford-Shah model in a graph setting. After formulating a graph version of the Mumford-Shah energy, we propose an efficient algorithm called the MBO scheme using threshold dynamics. Theoretical analysis is developed and a Lyapunov functional is proven to decrease as the algorithm proceeds. Furthermore, to reduce the computational cost for large datasets, we incorporate the Nyström extension method which efficiently approximates eigenvectors of the graph Laplacian based on a small portion of the weight matrix. Finally, we implement the proposed method on the problem of chemical plume detection in hyper-spectral video data.

Detecting plumes in LWIR using robust nonnegative matrix factorization with graph-based initialization

“…Recently, Nyström method has been developed for the hyperspectral data, 18 and then was employed in more recent TV-based clustering. 3,19 Let W be the similarity matrix of the data matrix B, which can be rearranged and partitioned as the following block-matrix form…”

“…Some related work using the same LWIR data includes simultaneous spectral analysis from multiple videos 18 and TV-based clustering methods. 3,19 The paper is organized as follows. The graph based initialization method combining the Nyström method and LPA is presented in Section 2.…”