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

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 Nystrom 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.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 2014
Accession Number
ADA612745

Entities

People

  • Andrea Bertozzi
  • Huiyi Hu
  • Justin Sunu

Organizations

  • University of California, Los Angeles

Tags

DTIC Thesaurus Topics

  • Algebra
  • Algorithms
  • Applied Computer Science
  • Computer Science
  • Computer Vision
  • Convex Sets
  • Detection
  • Dynamics
  • Eigenvectors
  • Equations
  • Image Processing
  • Image Segmentation
  • Long-Wavelength Infrared Radiation
  • Mathematics
  • Physics
  • Physics Laboratories
  • Sequences

Fields of Study

  • Computer science

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Computer Vision.
  • Graph Algorithms and Convex Optimization.