Journal
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume 36, Issue 8, Pages 1600-1613Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2014.2300478
Keywords
Segmentation; Ginzburg-Landau functional; diffuse interface; MBO scheme; graphs; convex splitting; image processing; high-dimensional data
Funding
- ONR [N000141210838, N000141210040, N0001413WX20136]
- AFOSR MURI [FA9550-10-1-0569]
- US National Science Foundation (NSF) [DMS-1118971, DMS-0914856]
- US Department of Energy (DOE) Office of Science's ASCR program in Applied Mathematics
- W.M. Keck Foundation
- NSF
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1118971] Funding Source: National Science Foundation
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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.
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