ABSTRACT
This chapter discusses the problem of 3D shape matching. Recent advancements in shape acquisition technology have led to the capture of large amounts of 3D data. The major difficulties in shape registration arise due to: variation in the shape acquisition techniques, local deformations in nonrigid shapes, large acquisition discrepancies, and local scale change. It presents an intrinsic approach for unsupervised 3D shape registration first proposed. The chapter discusses the problem of exact graph isomorphism and existing solutions. It deals with dimensionality reduction using the graph Laplacian in order to obtain embedded representations for 3D shapes. The chapter discusses the PCA of graph embeddings and proposes a unit hyper-sphere normalization for these embeddings along with a method to choose the embedding dimension. It introduces the formulation of maximum subgraph isomorphism before presenting a two-step method for 3D shape registration. The chapter describes a 3D shape registration approach that computes dense correspondences between two articulated objects.
