Euclidean-distance-based canonical forms for non-rigid 3D shape retrieval

Retrieval of 3D shapes is a challenging problem, especially for non-rigid shapes. One approach giving favourable results uses multidimensional scaling (MDS) to compute a canonical form for each mesh, after which rigid shape matching can be applied. However, a drawback of this method is that it requires geodesic distances to be computed between all pairs of mesh vertices. Due to the super-quadratic computational complexity, canonical forms can only be computed for low-resolution meshes. We suggest a linear time complexity method for computing a canonical form, using Euclidean distances between pairs of a small subset of vertices. This approach has comparable retrieval accuracy but lower time complexity than using global geodesic distances, allowing it to be used on higher resolution meshes, or for more meshes to be considered within a time budget.