CSDL Home IEEE Transactions on Pattern Analysis & Machine Intelligence 2014 vol.36 Issue No.08 - Aug.
Issue No.08 - Aug. (2014 vol.36)
Cristina Garcia-Cardona , Institute of Mathematical Sciences at Claremont Graduate University, Los Angeles,
Ekaterina Merkurjev , Department of Mathematics at University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles,
Andrea L. Bertozzi , Department of Mathematics at University of California, Los Angeles, 405 Hilgard Avenue, Los Angeles,
Arjuna Flenner , Naval Air Warfare Center, China Lake,
Allon G. Percus , Institute of Mathematical Sciences at Claremont Graduate University, Los Angeles,
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.
Laplace equations, Minimization, Image segmentation, Equations, TV, Vectors, Government,high-dimensional data, Segmentation, Ginzburg-Landau functional, diffuse interface, MBO scheme, graphs, convex splitting, image processing
Cristina Garcia-Cardona, Ekaterina Merkurjev, Andrea L. Bertozzi, Arjuna Flenner, Allon G. Percus, "Multiclass Data Segmentation Using Diffuse Interface Methods on Graphs", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.36, no. 8, pp. 1600-1613, Aug. 2014, doi:10.1109/TPAMI.2014.2300478