A 3-D Search Engine based on Fourier Series ⋆

Abstract

The size of 3-D data stored around the Web has become bigger. Therefore the development of recognition applications and retrieval systems of 3-D models is important. In this paper we propose a new scheme to measure similarity between 3-D models. The main idea is to reconstruct a 3-D closed curve that represents a 3-D model given by a polygonal mesh, and to extract a signature from this 3-D closed curve using the Fourier series. The proposed descriptor needs CPCA (Continuous Principal Component Analysis) to align 3-D models into a canonical position. The feature vectors constructed using this method, named FSD (Fourier Series Descriptor) are invariants under rigid transformations composed of translation, rotation, flipping and scale; robust to noise and level of detail. A 3-D polygonal mesh model serves as a query for search by shape similarity in a large collection of 3-D models database using an interactive 3-D search engine.