Multiclass Data Segmentation using Diffuse Interface Methods on Graphs

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. 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 is a 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, grayscale and color images, 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 multiclass segmentation algorithms.Comment: 14 page

Cortical spatio-temporal dimensionality reduction for visual grouping

The visual systems of many mammals, including humans, is able to integrate the geometric information of visual stimuli and to perform cognitive tasks already at the first stages of the cortical processing. This is thought to be the result of a combination of mechanisms, which include feature extraction at single cell level and geometric processing by means of cells connectivity. We present a geometric model of such connectivities in the space of detected features associated to spatio-temporal visual stimuli, and show how they can be used to obtain low-level object segmentation. The main idea is that of defining a spectral clustering procedure with anisotropic affinities over datasets consisting of embeddings of the visual stimuli into higher dimensional spaces. Neural plausibility of the proposed arguments will be discussed

Index Trees for Efficient Deformable Shape-based Retrieval

An improved method for deformable shape-based image indexing and retrieval is described. A pre-computed index tree is used to improve the speed of our previously reported on-line model fitting method; simple shape features are used as keys in a pre-generated index tree of model instances. In addition, a coarse to fine indexing scheme is used at different levels of the tree to further improve speed while maintaining matching accuracy. Experimental results show that the speedup is significant, while accuracy of shape-based indexing is maintained. A method for shape population-based retrieval is also described. The method allows query formulation based on the population distributions of shapes in each image. Results of population-based image queries for a database of blood cell micrographs are shown.Office of Naval Research (Young Investigator Award, N00014-96-1-066); National Science Foundation (IIS-9624168, EIA-9623865