Optimal Separable Algorithms to Compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension

TL;DR

This paper introduces time-optimal algorithms for reverse Euclidean distance transformation and medial axis extraction in arbitrary dimensions, enhancing shape analysis tools for binary images.

Contribution

It presents novel algorithms that are optimal in time complexity for reverse Euclidean DT and medial axis extraction in any dimension, with a filtering process for shape quality control.

Findings

Algorithms are proven to be time optimal in arbitrary dimensions.

The methods enable reversible shape reconstruction from distance transforms.

A filtering process improves the quality of medial axis extraction.

Abstract

In binary images, the distance transformation (DT) and the geometrical skeleton extraction are classic tools for shape analysis. In this paper, we present time optimal algorithms to solve the reverse Euclidean distance transformation and the reversible medial axis extraction problems for $d$-dimensional images. We also present a $d$-dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape.