The medial axis transform provides an alternative representation of geometric models that has many useful properties for analysis modelling. Applications include decomposition of general solids into subregions for mapped meshing, identification of slender regions for dimensional reduction and recognition of small features for suppression. A set of operations for idealisation of the analysis dom...

We describe a region-based shape representation that might be particularly useful from a biological perspective because it promotes the localization of objects, and object parts relative to each other. The proposed medial-point representation is similar to medial-axis type representations, but it is more compact. The medial points are those points along the medial axis that are equidistant from...

We present dense medial descriptors, a new technique which generalizes the well-known medial axes to encode and manipulate whole 2D grayvalue images, rather than binary shapes. To compute our descriptors, we first reduce an image to a set of threshold-sets in luminance space. Next, we compute a simplified representation of each threshold-set using a noise-resistant medial axis transform. Finall...

A method to triangulate the medial axis [1] is modified. In the new method the coping surfaces of a thin-wall object are used for insidedness but ignored for footpoints, yielding the mid-surface, not the medial axis. Three distinct contour-followers are employed. After a brief, manual tagging of the coping surfaces, the method is automatic. It computes a triangulation to arbitrary precision and...

Consider a dense sampling S of the smooth boundary of a planar shape O. We show that the medial axis of the union of Voronoi balls centered at Voronoi vertices inside O has a particularly simple structure: it is the union of all Voronoi vertices inside O and the Voronoi edges connecting them. Therefore, the medial axis of the union of these inner balls can be computed more efficiently and robus...

The basic, still unanswered question about visual object representation is this: what specific information is encoded by neural signals? Theorists have long predicted that neurons would encode medial axis or skeletal object shape, yet recent studies reveal instead neural coding of boundary or surface shape. Here, we addressed this theoretical/experimental disconnect, using adaptive shape sampli...

We present a new fairing method for planar curves, which is particularly well suited for the regularization of the medial axis of a planar domain. It is based on the concept of total variation regularization. The original boundary (given as a closed B-spline curve or several such curves for multiply connected domains) is approximated by another curve that possesses a smaller number of curvature...

We present a very simple computational model for planar shape decomposition that naturally captures most of the rules and salience measures suggested by psychophysical studies, including the minima and short-cut rules, convexity, and symmetry. It is based on a medial axis representation in ways that have not been explored before and sheds more light into the connection between existing rules li...

We propose a method to compute the algebraically correct medial axis for simply connected planar domains which are given by boundary representations composed of rational circular arcs. The algorithmic approach is based on the Divide-&-Conquer paradigm, as used in [2]. However, we show how to avoid inaccuracies in the medial axis computations arising from a non-algebraic biarc construction of th...

In this article, we study the (d − 1)-volume and the covering numbers of the medial axis of a compact subset of R. In general, this volume is infinite; however, the (d− 1)-volume and covering numbers of a filtered medial axis (the μ-medial axis) that is at distance greater than ε from the compact set can be explicitely bounded. The behaviour of the bound we obtain with respect to μ, ε and the c...