We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizi...

In this paper we provide a computational approach to the shape of curves which are rational in polar coordinates, i.e. which are defined by means of a parametrization (r(t), θ(t)) where both r(t), θ(t) are rational functions. Our study includes theoretical aspects on the shape of these curves, and algorithmic results which eventually lead to an algorithm for plotting the “interesting parts” of ...

Continuous shape change is represented as curves in the shape space. A method for checking the closeness of these curves to a geodesic is presented. Three large databases of short human motions are considered and shown to be well approximated by geodesics. The motions are thus approximated by two shapes on the geodesic and the rate of progress along the path. An analysis of facial motion data t...

Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and meaningful information about a shape. We have first to separate the curves belonging to features from those caused by noise and then to select the lines, which descri...

Second order Sobolev metrics are a useful tool in the shape analysis of curves. In this paper we combine these metrics with varifoldbased inexact matching to explore a new strategy of computing geodesics between unparametrized curves. We describe the numerical method used for solving the inexact matching problem, apply it to study the shape of mosquito wings and compare our method to curve matc...

In [TSP], level curves of a function , called “the edge strength function,” defined for 2–dimensional shapes, are interpreted as successively smoother versions of the initial shape boundary. The local minima of the absolute gradient along the level curves of are shown to be a robust criterion for determining the shape skeleton. More generally, at an extremal point of along a level curve, the le...

Wepropose a geometric interpretation to the ranking of patent assignees by their h-indices as indicating the relative positions of their rank-citation curves.We thenpropose two shape descriptors characterizing the rank-citation curves over the h-cores and h-tails, respectively. Together with the h-indices, the shape descriptors help verifying the geometric relationship among rank-citation curve...

This paper presents a geometric method for parameterization, matching, and analysis of surface shapes. Surfaces are parameterized and represented by intrinsic coordinate maps derived from the conformal structure of the shape. This parameterization is invariant to rigid transformations of the shape, as well as angle-preserving parameterizations of the surface. Shape matching between coordinate m...

In this paper a new kind of quasi-quartic trigonometric polynomial base functions with two shape parameters λ and μ over the space Ω = span {1, sin t, cos t, sin2t, cos2t, sin3t, cos3t} is presented and the corresponding quasi-quartic trigonometric Bézier curves and surfaces are defined by the introduced base functions. Each curve segment is generated by five consecutive control points. The sha...