A Feature-preserved Canonical Form for Non-rigid 3D Meshes Zhouhui Lian 1,2 and Afzal Godil 1 1 National Institute of Standards and Technology, Gaithersburg, USA 2 Beihang University, Beijing, China Abstract Measuring the dissimilarity between non-rigid objects is a challenging problem in 3D shape retrieval. One poten- tial solution is to construct the models’ 3D canonical forms (i.e., isometry-invariant representations in 3D Euclidean space) on which any rigid shape matching algorithm can be applied. However, existing methods, which are typically based on embedding procedures, result in greatly distorted canonical forms, and thus could not provide satisfactory performance to distinguish non-rigid models. In this paper, we present a feature-preserved canonical form for non-rigid 3D meshes. The basic idea is to natu- rally deform original models against corresponding initial canonical forms calculated by Multidimensional Scaling (MDS). Specifically, objects are first segmented into near- rigid subparts, and then, through properly-designed rota- tions and translations, original subparts are transformed into poses that correspond well with their positions and di- rections on MDS canonical forms. Final results are ob- tained by solving some nonlinear minimization problems for optimal alignments and smoothing boundaries between subparts. Experiments on a widely utilized non-rigid 3D shape benchmark not only verify the advantages of our al- gorithm against existing approaches, but also demonstrate that, with the help of the proposed canonical form, we can obtain significantly better retrieval accuracy compared to the state-of-the-art. 1. Introduction With the ever increasing accumulation of 3D models, how to accurately and efficiently search these data has be- come an important problem in computer graphics, mechan- ical CAD, computer vision, pattern recognition and many other fields [26][31]. One of most challenging issues in this problem is the calculation of dissimilarity between non- rigid objects that are commonly seen in our surroundings (e.g., Fig. 1(a)). In order to compare these non-rigid 3D models quickly and effectively, it is often desired that the shapes can be represented by some discriminative signa- Figure 1. Non-rigid models (a) and their canonical forms obtained using Least Square MDS (b) and our method (c), respectively. tures which are invariant or approximately invariant under various isometric transformations (i.e., rigid-body transfor- mations, non-rigid bending and articulation). While a large number of retrieval methods for rigid 3D shapes have been proposed in the last few years, there has been considerably less work for non-rigid models. In general, existing non-rigid 3D shape retrieval methods can be roughly classified into algorithms using local features, isometry-invariant global geometric properties, topological structures, direct shape matching, or canonical forms. Al- though these algorithms are all guaranteed to be isometry- invariant, they are still not well suited for practical appli- cations in non-rigid 3D shape retrieval. This is mainly due to the fact that they are either computationally expensive or poor in discrimination. Further discussions are provided in section 2. Perhaps, the utilization of canonical forms (un- less otherwise specified, canonical form mentioned in this paper means the canonical form in 3D Euclidean Space) is potentially the most effective way to address the problem 1