# The Weighted Euler Characteristic Transform for Image Shape Classification

arXiv: https://arxiv.org/abs/2307.13940 · HTML: https://mlsanity.com/paper/2307.13940/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jul 2023.

## Built on by (most cited first, 3 of 3)

- [LEAP: Local ECT-Based Learnable Positional Encodings for Graphs](https://mlsanity.com/paper/2510.00757/) (2025)
- [The Morse Transform for Discrete Shape Analysis](https://mlsanity.com/paper/2503.04507/) (2025)
- [Tensor Computation of Euler Characteristic Functions and Transforms](https://mlsanity.com/paper/2511.03909/) (2025)

## Abstract (arXiv)

The weighted Euler characteristic transform (WECT) is a new tool for extracting shape information from data equipped with a weight function. Image data may benefit from the WECT where the intensity of the pixels are used to define the weight function. In this work, an empirical assessment of the WECT's ability to distinguish shapes on images with different pixel intensity distributions is considered, along with visualization techniques to improve the intuition and understanding of what is captured by the WECT. Additionally, the expected weighted Euler characteristic and the expected WECT are derived.