3D Shapes Isometric Deformation Using in-tSNE

Isometric shapes share the same geometric structure, and all possible bendings of a given surface are considered to have the same isometric deformation. Therefore, we use the inner distance to describe the isometric geometric structure. The inner distance is defined as the length of the shortest path between landmark points with the bending stability. Stochastic neighbor embedding algorithm t-SNE is a manifold embedding algorithm to visualize high-dimensional data by giving each data point a location in a two or three-dimensional map. Then, t-SNE is applied to 3D shapes isometric deformation in which Euclidean distances in high-dimensional space are replaced by inner distances. We can use this isometric deformation to describe invariant Signatures of surfaces, so that the matching of nonrigid shapes is better.