In this paper, we present a novel approach to compute 3D canonical forms which is useful for non-rigid 3D shape retrieval. We resort to using the feature space to get a compact representation of points in a small-dimensional Euclidean space. Our aim is to improve the classical Multi-Dimensional Scaling MDS algorithm to avoid the super-quadratic computational complexity. To this end, we compute the canonical form of the local geodesic distance matrix between pairs of a small subset of vertices in local feature patches. To preserve local shape details, we drive the mesh deformation by the local weighted commute time. When used as a spatial relationship between local features, the invariant properties of the Biharmonic distance improve the final results.

We evaluate the performance of our method by using two different measures: the compactness measure and the Haussdorf distance.


3D canonical forms Multidimensional scaling 3D non-rigid shape Biharmonic distance 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.FSMUniversity of MonastirMonastirTunisia
  2. 2.ENITEl-Manar UniversityTunisTunisia

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