# AMAT: Medial Axis Transform for Natural Images

## TL;DR

This paper introduces AMAT, a novel medial axis transform for natural images that encodes local scale and appearance, enabling accurate shape decomposition and image reconstruction with minimal data.

## Contribution

The paper extends medial point detection to color images with local scales, introduces an invertible encoding for image reconstruction, and develops a clustering scheme for shape decomposition.

## Key findings

- State-of-the-art medial point detection performance.
- High-quality image reconstruction with only 10% of pixels.
- Good generalization across multiple datasets.

## Abstract

We introduce Appearance-MAT (AMAT), a generalization of the medial axis transform for natural images, that is framed as a weighted geometric set cover problem. We make the following contributions: i) we extend previous medial point detection methods for color images, by associating each medial point with a local scale; ii) inspired by the invertibility property of the binary MAT, we also associate each medial point with a local encoding that allows us to invert the AMAT, reconstructing the input image; iii) we describe a clustering scheme that takes advantage of the additional scale and appearance information to group individual points into medial branches, providing a shape decomposition of the underlying image regions. In our experiments, we show state-of-the-art performance in medial point detection on Berkeley Medial AXes (BMAX500), a new dataset of medial axes based on the BSDS500 database, and good generalization on the SK506 and WH-SYMMAX datasets. We also measure the quality of reconstructed images from BMAX500, obtained by inverting their computed AMAT. Our approach delivers significantly better reconstruction quality with respect to three baselines, using just 10% of the image pixels. Our code and annotations are available at https://github.com/tsogkas/amat .