# Wavelet-based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis

arXiv: https://arxiv.org/abs/2007.11632 · HTML: https://mlsanity.com/paper/2007.11632/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2020.

## Built on by (most cited first, 8 of 8)

- [DPFM: Deep Partial Functional Maps](https://mlsanity.com/paper/2110.09994/) (2021)
- [TIDE: Time Derivative Diffusion for Deep Learning on Graphs](https://mlsanity.com/paper/2212.02483/) (2022)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Beyond Complete Shapes: A Benchmark for Quantitative Evaluation of 3D Shape Surface Matching Algorithms](https://mlsanity.com/paper/2411.03511/) (2024)
- [Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities](https://mlsanity.com/paper/2604.01274/) (2026)
- [Learning Canonical Embedding for Non-rigid Shape Matching](https://mlsanity.com/paper/2110.02994/) (2021)
- [Joint Symmetry Detection and Shape Matching for Non-Rigid Point Cloud](https://mlsanity.com/paper/2112.02713/) (2021)
- [Extracting a functional representation from a dictionary for non-rigid shape matching](https://mlsanity.com/paper/2305.10332/) (2023)

## Abstract (arXiv)

In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well-established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multiscale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that it leads to a family of functions that inherit many attractive properties of the heat kernel (e.g., a local support, ability to recover isometries from a single point, efficient computation). Due to its natural ability to encode high-frequency details on a shape, the proposed method reconstructs and transfers δ-functions more accurately than the Laplace-Beltrami eigenfunction basis and other related bases. Finally, we apply our method to the challenging problems of partial and large-scale shape matching. An extensive comparison to the state-of-the-art shows that it is comparable in performance, while both simpler and much faster than competing approaches.