EDT Method for Multiple Labelled Objects Subject to Tied Distances

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches aligned with real-world applications. The Euclidean distance transform (EDT) has fared well in both cases, providing a sound theoretical basis for a number of applications, such as median axis transform, fractal analysis, skeletonization, and Voronoi diagrams. Despite its wide applicability, the discrete form of the EDT includes interesting properties that have not yet been fully exploited in the literature. In this paper, we are particularly interested in the properties of 1) working with multiple objects/labels; and 2) identifying and counting equidistant pixels/voxels from certain points of interest. In some domains (such as dataset classification, texture, and complexity analysis), the result of applying the EDT transform with different objects, and their respective tied distances, may compromise the performance. In this sense, we propose an efficient modification in the method presented in 1, which leads to a novel approach for computing the distance transform in a space with multiple objects, and for counting equidistant pixels/voxels.