The skeleton and its associated medial axis give a very compact representation of objects, even in the case of complex shapes and topologies. They are powerful shape descriptors, bridging the gap between low-level and high-level object representations. Surprisingly, skeletons have been used in a relatively small number of applications, and almost every time for very precise and concrete tasks. ...

In the vertebrate embryo, segmentation is built on repetitive structures, named somites, which are formed progressively from the most rostral part of presomitic mesoderm, every 90 minutes in the avian embryo. The discovery of the cyclic expression of several genes, occurring every 90 minutes in each presomitic cell, has shown that there is a molecular clock linked to somitogenesis. We demonstra...

Approximating a given three-dimensional object in order to simplify its handling is a classical topic in computational geometry and related fields. A typical approach is based on incremental approximation algorithms, which start with a small and topologically correct polytope representation (the seed polytope) of a given sample point cloud or input mesh. In addition, a correspondence between th...

Approximating a given three-dimensional object in order to simplify its handling is a classical topic in computational geometry and related fields. A typical approach is based on incremental approximation algorithms, which start with a small and topologically correct polytope representation (the seed polytope) of a given sample point cloud or input mesh. In addition, a correspondence between th...

In this report we give an algorithm to construct an approximate medial axis of a connected domain without any holes, in 2-D, also known as the simply connected domain. The first part of the report concentrates on the algorithm which gives the approximate medial axis of a domain bounded by simple, closed C curve. In the second part of the report we look at a modified version of which looks at do...

In this rst installment of a two-part paper, the underlying theory for an algorithm that computes the Voronoi diagram and medial axis of a planar domain bounded by free-form (polynomial or rational) curve segments is presented. An incremental approach to computing the Voronoi diagram is used, wherein a single boundary segment is added to an existing boundary-segment set at each step. The introd...

In digital geometry, the study of a multiresolution representation of digital objects has been carried out (using an homotopic thinning) [8]. This hierarchical structure does not change the medial axis (i.e. the balls radii) of the shape on the first stage, and provides the medial axis pruning. In this PhD, we would like to develop a hierarchical structure which, as in the continuous case, is f...

This paper presents a new method that combines a medial axis and implicit surfaces in order to reconstruct a 3D solid from an unstructured set of points scattered on the object's surface. The representation produced is based on iso-surfaces generated by skeletons, and is a particularly compact way of deening a smooth free-form solid. The method is based on the minimisation of an energy represen...

Shape restoration for characters in video is challenging because natural scene characters usually suffer from low resolution, complex background and perspective distortion. In this paper, we propose histogram gradient division and reverse gradient orientation in a new way to select Text Pixel Candidates (TPC) for a given input character. We apply a ring radius transform on TPC in different dire...

The cut locus C of a closed set A in the Euclidean space E is defined as the closure of the set containing all points p A which have at least two shortest paths to A. We present a theorem stating that the complement of the cut locus i.e. E\(C ∪A) is the maximal open set in (E\A) where the distance function with respect to the set A is continuously A differentiable. This theorem includes also th...