Discrete bisector function and Euclidean skeleton in 2D and 3D

Abstract

International audienceWe 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 algorithm which produces homotopic discrete Euclidean skeletons. These algorithms, which are valid both in 2D and 3D, are integrated in a skeletonization method which is based on exact transformations, allows the filtering of skeletons, and is computationally efficient

An introduction to simple sets

“…In discrete grids (Z 2 , Z 3 , or Z 4 ), such transformations can be defined and efficiently implemented thanks to the notion of simple point (Kong and Rosenfeld (1989); Bertrand (1994); Couprie and Bertrand (2009)): intuitively, a point of an object is called simple if it can be deleted from this object without altering its topology. A typical topology-preserving transformation based on simple points deletion, that we call guided homotopic thinning (Davies and Plummer (1981); Couprie et al (2007)), may be described as follows. The input data consists of a set X of points in the grid (called object), and a subset K ⊂ X (called constraint set).…”

Automated, Accurate and Fast Segmentation of 4D Cardiac MR Images

“…The idea is to reduce this set while both preserving its topology and respecting facts (a) and (b). To this aim, we use a constrained ultimate homotopic skeleton [12]. Roughly speaking, an ultimate homotopic skeleton of a set X constrained by a set C, has the same topology as X, contains C, and cannot be reduced (by point removal) while keeping these two invariants.…”

Collection of informatics proposals from 2007

“…Implement a new "exact medial axis" algorithm (Couprie et al 2007, Saúde et al 2006) for creating a 3-D skeleton, based on Remy and Thiel (2005). This will avoid having to choose along which axis a skeletal slice-stack should be constructed, avoid skeletal artifacts such as those arising from folds lying along a slice, increase accuracy and reduce inconsistencies across acquisitions and orientations, and result in much faster processing times.…”