Complex Fiedler Vectors for Shape Retrieval

Abstract

Abstract. Adjacency and Laplacian matrices are popular structures to use as representations of shape graphs, because their sorted sets of eigenvalues (spectra) can be used as signatures for shape retrieval. Unfortunately, the descriptiveness of these spectra is limited, and handling graphs of different size remains a challenge. In this work, we propose a new framework in which the shapes (3D models in our test corpus) are represented by multi-labeled graphs. A Hermitian matrix is associated to each graph, in which the entries are defined such that they contain all information stored in the graph edges. Additional constraints ensure that this Hermitian matrix mimics the well-studied spectral behaviour of the Laplcian matrix. We therefore use the Hermitian Fiedler vector as shape signature during retrieval. To deal with graphs of different size, we efficiently reuse the calculated Fiedler vector to decompose the graph into a limited number of non-overlapping, meaningful subgraphs. Retrieval results are based on both complete matching and subgraph matching.

Unsupervised Clustering of Human Pose Using Spectral Embedding

“…The information encoded in the eigenvectors of the Laplacian has been used for shape registration [6] and clustering. Veltkamp et al [7] developed a shape retrieval method using a complex Fielder vector of a Hermitian property matrix. Recent spectral approaches use the eigenvectors corresponding to the k smallest eigenvalues of the Laplacian matrix to embed the graph onto a k dimensional Euclidian space [8], [9].…”