Discrete Bisector Function and Euclidean Skeleton

Abstract

We propose a new definition and an exact algorithm for the discrete bisector function, which is an important tool for analyzing and filtering Euclidean skeletons. We also introduce a new thinning method which produces homotopic discrete Euclidean skeletons. Unlike previouly proposed approaches, this method is still valid in 3D.

Comparing Sky Shape Skeletons for the Analysis of Visual Dynamics along Routes

“…We have tested four different methods for calculating the skeleton of sky shapes: one developed by Thiel (1994) which is based on the extraction of the distance map, another one developed by Ogniewicz (1993) which uses the Voronoi diagram of the shape boundary, a method developed by Siddiqi et al (2002) which is based on the fire front simulation, and a last one developed by Couprie and Zrour (2005) based on the extraction of the distance map.…”

“…The method developed by Siddiqi et al is very accurate, but the only implementation we had access to was very slow and was not successful for images with more than two shapes or with holes. The method developed by Couprie and Zrour (2005) is the only one which proved to be both accurate and fast.…”

A linear-time algorithm for Euclidean feature transform sets

“…In dimension d > 2, however, the number grows as n (d−2)/2 . It follows that the algorithm of [4] is not linear-time in higher dimensions.…”

“…The paper [4] uses feature transform sets to determine Euclidean skeletons of images. It calls the feature transform set the downstream.…”

“…It calls the feature transform set the downstream. The algorithm of [4] to compute the (extended) downstream uses the Euclidean distance transform and a lookup table for the integral vectors of given lengths. For 2D, the number of integral vectors with a given square length n is approximately constant (the average is π ).…”