The popularity of medial axis in shape modeling and analysis comes from several of its well known fundamental properties. For example, medial axis captures the connectivity of the domain, has a lower dimension than the space itself, and is closely related to the distance function constructed over the same domain. We formally define the new concept of a medial zone of an n-dimensional semi-analy...

After habituation of looking at an object that repeatedly approached and receded through 50 cm along the medial axis, infants of about 18 weeks of age were presented with both the same moving object and one of a different size falling within the same range of visual angles as those projected during habituation. The starting point for movement varied widely from trial to trial to "desensitize" s...

The main question we address is: What is the minimal information required to generate closed, nonintersecting planar boundaries? For this paper, we restrict “shape” to this meaning. More precisely, we examine whether the medial axis, together with dynamics, can serve as a language to design shapes and to effect shape changes, e.g., for modeling, to generate a morph sequence, etc. We represent t...

Path planning for walking characters in complicated virtual environments is a fundamental task in simulations and games. A navigation mesh is a data structure that allows efficient path planning. The Explicit Corridor Map (ECM) is a navigation mesh based on the medial axis. It enables path planning for disk-shaped characters of any radius. In this paper, we formally extend the medial axis (and ...

Two challenges for taxonomists are proper identification of specimens to known species and extracting information from specimens to diagnose new species. Both tasks are complicated by the very large numbers of known and unknown species and the dwindling numbers of qualified taxonomists to identify/diagnose them all. Automated species identification is a tool that can assist taxonomists facing t...

In this short chapter, we introduce some of the objects that will be used throughout the thesis: the distance functions, projection functions and medial axes. We survey some known result concerning the local regularity of medial axis (eg. Hausdorff dimension, rectifiability), a few of which come from the semi-concavity of the distance function. The compilation of these results complements the s...

We present a new, continuously defined three-dimensional medial shape representation based on subdivision surfaces. The shape is modeled via its medial axis, and the associated boundary is computed directly from this axis at every point. Our model is parameterized over a fixed domain, so comparison among different shapes is possible. It is the first such model to support branch curves, which al...

We propose an Euclidean medial axis filtering method which generates subsets of the Euclidean medial axis, where filtering rate is controlled by one parameter. The method is inspired by Miklos’, Giesen’s and Pauly’s scale axis method which preserves important features of an input object from shape understanding point of view even if they are at different scales. Our method overcomes the most im...

BACKGROUND In total knee arthroplasty, it is better to use more than one reference point for correct alignment of the components. By measuring the distances of Achilles tendon (AT) and other conventional landmarks from the mechanical axis in magnetic resonance imaging (MRI) of the ankle, we aimed to demonstrate that, as a novel landmark which can help for correct alignment in the coronal plane,...