Invariant feature extraction for 3D model retrieval: An adaptive approach using Euclidean and topological metrics

With the fast development of 3D model construction and widespread popularity of 3D graphic engines, more applications employ 3D geometric models to provide an interactive environment. As the number of 3D models increases, some 3D model retrieval systems have been proposed for indexing and matching these models. An important issue in a retrieval system is feature extraction. An efficient and invariant feature is a global shape distribution that collects some geometric properties of a model. The D2 shape descriptor by Osada et al. is a one-dimensional histogram of Euclidean distances between two random points. Although the D2 is effective for some cases, it changes when the model deforms. We propose two shape descriptors in this paper: GD, which is the topological metric, and ASF, which combines both Euclidean and topological metrics. The topological metric is an invariant deformation factor. The two features are also robust against common geometric processing, including scaling, rotation, resampling, compression, and remeshing. In experiments, we implement these methods and confirm their feasibility.