Fast computation of all pairs of geodesic distances

TL;DR

This paper introduces new methods for efficiently computing all pairs of geodesic distances in images by exploiting redundancy, significantly reducing computational operations compared to existing approaches.

Contribution

The authors propose a novel approach that selects source points based on minimal distances, improving computational efficiency by up to 32-50% over previous methods.

Findings

Improved method reduces operations by up to 32% compared to existing methods.

Further reduction of up to 50% over naive approaches.

Demonstrates significant efficiency gains in geodesic distance computations.

Abstract

Computing an array of all pairs of geodesic distances between the pixels of an image is time consuming. In the sequel, we introduce new methods exploiting the redundancy of geodesic propagations and compare them to an existing one. We show that our method in which the source point of geodesic propagations is chosen according to its minimum number of distances to the other points, improves the previous method up to 32% and the naive method up to 50% in terms of reduction of the number of operations.