# Local Geometry Inclusive Global Shape Representation

arXiv: https://arxiv.org/abs/1707.06699 · HTML: https://mlsanity.com/paper/1707.06699/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2017.

## Built on by (most cited first, 1 of 1)

- [Modeling Aesthetic Preferences in 3D Shapes: A Large-Scale Paired Comparison Study Across Object Categories](https://mlsanity.com/paper/2505.12373/) (2025)

## Abstract (arXiv)

Knowledge of shape geometry plays a pivotal role in many shape analysis applications. In this paper we introduce a local geometry-inclusive global representation of 3D shapes based on computation of the shortest quasi-geodesic paths between all possible pairs of points on the 3D shape manifold. In the proposed representation, the normal curvature along the quasi-geodesic paths between any two points on the shape surface is preserved. We employ the eigenspectrum of the proposed global representation to address the problems of determination of region-based correspondence between isometric shapes and characterization of self-symmetry in the absence of prior knowledge in the form of user-defined correspondence maps. We further utilize the commutative property of the resulting shape descriptor to extract stable regions between isometric shapes that differ from one another by a high degree of isometry transformation. We also propose various shape characterization metrics in terms of the eigenvector decomposition of the shape descriptor spectrum to quantify the correspondence and self-symmetry of 3D shapes. The performance of the proposed 3D shape descriptor is experimentally compared with the performance of other relevant state-of-the-art 3D shape descriptors.