Description of 3D-shape using a complex function on the sphere

We propose a novel feature vector suitable for searching collections of 3D-objects by shape similarity. In this search a polygonal mesh model serves as a query. For each model feature vectors are automatically extracted and stored. Shape similarity between 3D-objects in the search space is determined by finding and ranking nearest neighbors in the feature vector space. Ranked objects are retrieved for inspection, selection, and processing. The feature vector is obtained by forming a complex function on the sphere. Afterwards, we apply the Fast Fourier Transform (FFT) on the sphere and obtain Fourier coefficients for spherical harmonics. The absolute values of the coefficients form the feature vector. Retrieval efficiency of the new approach is evaluated by constructing precision/recall diagrams and using two different 3D-model databases. We compared the approach with two methods based on real functions on the sphere. Our empirical comparison showed that the complex feature vector performed best. We also prepared a Web-based retrieval system for testing methods discussed in this paper.