AMAT: Medial Axis Transform for Natural Images

The medial axis transform (MAT) is a powerful shape abstraction that has been successfully used in shape editing, matching and retrieval. Despite its long history, the MAT has not found widespread use in tasks involving natural images, due to the lack of a generalization that accommodates color and texture. In this paper we introduce Appearance-MAT (AMAT), by framing the MAT of natural images 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 established BSDS500 database. We also measure the quality of reconstructed images from the same dataset, 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 is available at https://github.com/tsogkas/amat.