Abstract
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.
Highlights
Content-based 3D shape retrieval is a key research topic, as the large and ever increasing number of available 3D models makes effectively searching for models with a desired shape an increasingly important task
Lian et al [3] gave a method which computes a canonical form for a mesh using the method of Elad and Kimmel [4] to map the geodesic distances between every pair of points on the surface to 3D Euclidean distances using multidimensional scaling (MDS)
We evaluated the distance matrices produced using each of these results using five quantitative measures of how well they perform: nearest neighbour (NN), 1-tier, 2-tier, e-measure, and discounted cumulative gain (DCG); see [2] for a description of these measures and their use in assessing shape retrieval performance
Summary
Content-based 3D shape retrieval is a key research topic, as the large and ever increasing number of available 3D models makes effectively searching for models with a desired shape an increasingly important task. A view-based method is used to perform shape retrieval The drawback of this method is the high, super-quadratic, computational cost of geodesic distance computation, which requires the models to be simplified to approximately 2000 vertices to achieve a reasonable run-time. Instead of mapping geodesic distances to Euclidean distances, we instead maximise the Euclidean distances between a subset of feature points while attempting to preserve the original mesh edge lengths These feature points are selected based upon the conformal factor of the vertices [5]. We are able to produce canonical forms for the dataset used by Lian et al, but without the need to simplify the models first Another way in which greater speed can be put to use is to allow a larger number of meshes to be compared within a fixed time budget if the search space is a large database
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