Manifold embedding for shape analysis

Shape analysis played important role in computer vision based tasks. The importance of shape information relies that it usually contains perceptual information, and thus can be used for high level visual information analysis. Currently, there are many ways that shapes can be represented as a structural manner using graphs. Hence shapes can be analyzed by using graph methods. This paper describes how graph-spectral methods can be used to transform the node correspondence problem into one of point-sets alignment. We commence by using the ISOMAP algorithm to embed the nodes of a graph in a low-dimensional Euclidean space. With the nodes in the graph transformed to points in a metric space, we can recast the problem of graph-matching into that of aligning the point-sets. Here we use semidefinite programming to develop a robust point-sets correspondences algorithm. Variations in graph structure using the covariance matrix for corresponding embedded point-positions is captured. We construct a statistical point distribution model for the embedded node positions using the eigenvalues and eigenvectors of the covariance matrix. We show how to use this model to project individual graph, i.e. shape into the eigenspace of the point position covariance matrix. We illustrate the utility of the resulting method for shape analysis and recognition on COIL and MPEG-7 databases.