Abstract
The geometric properties of descriptors derived from the diusion geometry family have many valuable
properties for shape analysis. These descriptors, also known as diusion distances, use the eigenvalues
and eigenfunctions of the Laplace-Beltrami operator to construct invariant metrics about the
shape. Although they are invariant to many transformations, non-rigid deformations still modify the
shape spectrum. In this paper, we propose a shape descriptor framework based on a Lagrangian formulation
of dynamics on the surface of the object. We show how our framework can be applied to
non-rigid shape retrieval, once it benefits from the analysis and the automatic identification of shape
joints, using a curvature-based scheme to identify these regions. We also propose modifications to
the Improved Wave Kernel Signature in order to keep descriptors more stable against non-rigid deformations.
We compare our spectral components with the classic ones and our spectral framework with
state-of-the-art non-rigid signatures on traditional benchmarks, showing that our shape spectra is more
stable and discriminative and clearly outperforms other descriptors in the SHREC’10, SHREC’11 and
SHREC’17 benchmarks.
properties for shape analysis. These descriptors, also known as diusion distances, use the eigenvalues
and eigenfunctions of the Laplace-Beltrami operator to construct invariant metrics about the
shape. Although they are invariant to many transformations, non-rigid deformations still modify the
shape spectrum. In this paper, we propose a shape descriptor framework based on a Lagrangian formulation
of dynamics on the surface of the object. We show how our framework can be applied to
non-rigid shape retrieval, once it benefits from the analysis and the automatic identification of shape
joints, using a curvature-based scheme to identify these regions. We also propose modifications to
the Improved Wave Kernel Signature in order to keep descriptors more stable against non-rigid deformations.
We compare our spectral components with the classic ones and our spectral framework with
state-of-the-art non-rigid signatures on traditional benchmarks, showing that our shape spectra is more
stable and discriminative and clearly outperforms other descriptors in the SHREC’10, SHREC’11 and
SHREC’17 benchmarks.
| Original language | English |
|---|---|
| Number of pages | 13 |
| Journal | Computer Vision and Image Understanding |
| Early online date | 17 Apr 2018 |
| DOIs | |
| Publication status | E-pub ahead of print - 17 Apr 2018 |