Look-Up Tables for Medial Axis on Squared Euclidean Distance Transform

Abstract

International audienceMedial Axis (MA), also known as Centres of Maximal Disks, is a useful representation of a shape for image description and analysis. MA can be computed on a distance transform, where each point is labelled to its distance to the background. Recent algorithms allow to compute Squared Euclidean Distance Transform (SEDT) in linear time in any dimension. While these algorithms provide exact measures, the only known method to characterize MA on SEDT, using local tests and Look-Up Tables, is limited to 2D and small distance values [5]. We have proposed in [14] an algorithm which computes the look-up table and the neighbourhood to be tested in the case of chamfer distances. In this paper, we adapt our algorithm for SEDT in arbitrary dimension and show that results have completely different properties

Discrete 2D and 3D euclidean medial axis in higher resolution

“…Many algorithms found in the literature only compute approximations of the Euclidean distance transform (e.g., [12]) or medial axis (e.g., [13] Euclidean distance maps (in Z n , for any nÞ was proposed only in 1994 [14], and optimal versions of that algorithm have appeared in 1996 [15], see also [16]. Efficient algorithms to compute exact Euclidean medial axes were not known before 2003 [17,18]. Also in 2003 a linear-time algorithm was proposed [19,20] to compute a reduced medial axis, which allows for an exact reconstruction of the original object.…”

Exact medial axis with euclidean distance

“…We present in this article (which is an extended version of Ref. [16]) an adaptation of Ref. [15], which efficiently computes the LUT for SEDT in any dimension.…”

Euclidean Skeletons of 3D Data Sets in Linear Time by the Integer Medial Axis Transform

“…We first examine the definition of the medial axis [3], see also [5][6][7]16]. Actually, we present three possible formalizations: CMD, RMA, and IMA.…”

“…For x ∈ Z d , the inscribed integer disk M (x) is the intersection D(x, r)∩Z d , where D(x, r) is its inscribed disk. The set CMD (centers of maximal disks) consists of the points x ∈ Z d for which M (x) is not contained in any M (y) with y = x, see also [7,16]. As is presumably well known, it is not true that CMD ⊆ RMA ∩ Z d .…”

“…Our method does not aim at a minimal skeleton useful for image compression with exact reconstruction, but at a computation of connected skeletons directly from the Euclidean feature transform, thus avoiding the costly and complicated phase of removing centers of not-quite-maximal disks by the techniques of [16]. We establish a number of mathematical properties of the IMA and point out some relations to Blum's real medial axis (RMA) and to the CMD skeleton.…”