Modal function transformation for isometric 3D shape representation

Isometric deformations complicate 3D shape representation and recognition. Therefore, proper modeling is in need. In this paper, we propose a novel modal function transformation framework for shape information abstraction. Key to our approach is to generalize the notion of pairwise shape matching by comparing their modal functions. By choosing intrinsic embedding basis (e.g. eigenfunction of Laplace-Beltrami Operator (LBO)) properly on each shape, we get a compact function space that is suitable for informative inference. To characterize the interior shape structure, a special inner function is devised. Then, the largest spectra of the inner functions are adopted as our modal feature. On this basis, we discuss the properties of the modal feature. For performance evaluation, non-rigid object recognition experiments are carried out on several popular shape matching benchmarks. The final results show that the proposed approach works well with significant accuracy improvement against the LBO based methods. Besides, the performance of our method is comparable with state-of-the-art results. Graphical abstractDisplay Omitted HighlightsA new modal function transformation (MFT) framework is proposed for non-rigid 3D shape representation and retrieval.Different implementations of the MFT framework are studied and discussed.We report state-of-the-art performance for isometric shape retrieval.The proposed MFT approach is robust to noise.