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Multi-class Graph Mumford-Shah Model for Plume Detection Using the MBO scheme

  • Huiyi Hu
  • Justin Sunu
  • Andrea L. Bertozzi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8932)

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.

Keywords

graph segmentation Mumford-Shah total variation MBO Nyström hyper-spectral image 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Huiyi Hu
    • 1
  • Justin Sunu
    • 2
  • Andrea L. Bertozzi
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Institute of Mathematical ScienceClaremont Graduate UniversityUSA

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