In this paper, we present a simple yet effective formulation called Coverage Axis for 3D shape skeletonization. Inspired by the set cover problem, our key idea is to all surface points using as few inside medial balls possible. This inherently induces compact and expressive approximation of Medial Transform (MAT) given shape. Different from previous methods that rely on local error, method allo...

The article deals with the relationship between Laguerre geometry and Minkowski sum. This relationship is used to create new geometry based generally on fundamental objects different to closed balls that formed Laguerre geometry. In the end of the article, there is defined also generalization of medial axis transform to the newly defined spaces and proved its uniqueness. The article continues t...

UNLABELLED BACKGROUND The purpose of this study was to assess the concurrent validity of alternative measures of frontal plane knee alignment, namely the radiographic anatomic axis and two clinical measures in patients complaining of knee malalignment as compared with the mechanical axis on full-length radiograph of lower limbs. METHODS The knee-alignment angle was measured in 100 knees of...

We describe aD algorithm for constructing the skeleton (medial-axis transform) of three-dimensional solids defined in constructive solid geometry.

We propose a novel framework for computing the medial axis transform of 3D shapes while preserving their features via restricted power diagram (RPD). Medial features, including external such as sharp edges and corners input mesh surface internal seams junctions axis, are important shape descriptors both topologically geometrically. However, existing approximation methods fail to capture preserv...

The behavior of the entire medial gastrocnemius (MG) superficial and deep aponeurosis structure was investigated with velocity-encoded phase-contrast, spin-tag, and three-dimensional morphometric magnetic resonance imaging. The displacements and strain of both these aponeuroses, muscle length, and the cross-sectional segment length of the deep aponeurosis were measured during isometric plantarf...

In binary images, the distance transformation (DT) and the geometrical medial axis are classic tools for shape analysis. In the digital geometry literature, recent articles have demonstrated that fast algorithms can be designed without any approximation of the Euclidean metric. The aim of the paper is to first give an overview of separable techniques to compute the distance transformation, the ...

An important question about a ne skeletons is the existence of di erential equations that are related to the A ne Distance and the Area Distance (hence to a ne skeletons) in the same way the Eikonal equation is related to the Euclidean Distance (and the medial axis). We show a surprisingly simple nonlinear second order PDE of Monge-Ampère type that relates to the a ne skeletons (and extends the...

We present an accurate algorithm to compute the internal Voronoi diagram and medial axis of a 3-D polyhedron. It uses exact arithmetic and exact representations for accurate computation of the medial axis. The algorithm works by recursively finding neighboring junctions along the seam curves. To speed up the computation, we have designed specialized algorithms for fast computation with algebrai...

A large family of shape comparison methods is based on a medial axis transform combined with an encoding of the skeleton by a graph. Despite many qualities this encoding of shapes suffers from the non continuity of the medial axis transform. In this paper, we propose to integrate robustness against structural noise inside a graph kernel. This robustness is based on a selection of the paths acco...