# Geodesic squared exponential kernel for non-rigid shape registration

arXiv: https://arxiv.org/abs/2112.11853 · HTML: https://mlsanity.com/paper/2112.11853/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 22 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [3D Morphable Face Models -- Past, Present and Future](https://mlsanity.com/paper/1909.01815/) (2019)
- [FaceScape: a Large-scale High Quality 3D Face Dataset and Detailed Riggable 3D Face Prediction](https://mlsanity.com/paper/2003.13989/) (2020)
- [Morphable Face Models - An Open Framework](https://mlsanity.com/paper/1709.08398/) (2017)
- [Geodesic Exponential Kernels: When Curvature and Linearity Conflict](https://mlsanity.com/paper/1411.0296/) (2014)
- [Gaussian Process Morphable Models](https://mlsanity.com/paper/1603.07254/) (2016)
- [Human Skin Detection Using RGB, HSV and YCbCr Color Models](https://mlsanity.com/paper/1708.02694/) (2017)

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

- [Geometric Learning with Positively Decomposable Kernels](https://mlsanity.com/paper/2310.13821/) (2023)

## Abstract (arXiv)

This work addresses the problem of non-rigid registration of 3D scans, which is at the core of shape modeling techniques. Firstly, we propose a new kernel based on geodesic distances for the Gaussian Process Morphable Models (GPMMs) framework. The use of geodesic distances into the kernel makes it more adapted to the topological and geometric characteristics of the surface and leads to more realistic deformations around holes and curved areas. Since the kernel possesses hyperparameters we have optimized them for the task of face registration on the FaceWarehouse dataset. We show that the Geodesic squared exponential kernel performs significantly better than state of the art kernels for the task of face registration on all the 20 expressions of the FaceWarehouse dataset. Secondly, we propose a modification of the loss function used in the non-rigid ICP registration algorithm, that allows to weight the correspondences according to the confidence given to them. As a use case, we show that we can make the registration more robust to outliers in the 3D scans, such as non-skin parts.