• Publication
  • PrePrints
  • Abstract - Multiclass Data Segmentation Using Diffuse Interface Methods on Graphs
 This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Multiclass Data Segmentation Using Diffuse Interface Methods on Graphs
PrePrint
ISSN: 0162-8828
We present two graph-based algorithms for multiclass segmentation of high-dimensional data on graphs. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation and graph cuts. A multiclass extension is introduced using the Gibbs simplex, with the functional’s double-well potential modified to handle the multiclass case. The first algorithm minimizes the functional using a convex splitting numerical scheme. The second algorithm uses a graph adaptation of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates between diffusion and thresholding. We demonstrate the performance of both algorithms experimentally on synthetic data, image labeling, and several benchmark data sets such as MNIST, COIL and WebKB. We also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph Laplacian, and take advantage of the sparsity of the matrix. Experiments indicate that the results are competitive with or better than the current state-of-the-art in multiclass graph-based segmentation algorithms for high-dimensional data.
Index Terms:
high-dimensional data,Segmentation,Ginzburg-Landau functional,diffuse interface,MBO scheme,graphs,convex splitting,image processing
Citation:
Arjuna Flenner, Ekaterina Merkurjev, Allon Percus, Andrea Bertozzi, "Multiclass Data Segmentation Using Diffuse Interface Methods on Graphs," IEEE Transactions on Pattern Analysis and Machine Intelligence, 04 Feb. 2014. IEEE computer Society Digital Library. IEEE Computer Society, <http://doi.ieeecomputersociety.org/10.1109/TPAMI.2014.2300478>
Usage of this product signifies your acceptance of the Terms of Use.