Mathematical theory of medial axis transform

Groupwise Medial Axis Transform

Medial Axis Transform (MAT) is one of the promising tools used for the shape recognition and it poses the advantages like space and complexity reduction, ease of processing for shape recognition. MAT representation of shapes uses object centred co-ordinate system that represents bending, elongation and thickness. But MAT of the objects is very much sensitive to small perturbations of its bounda...

Mathematical Theory of Medial

The medial axis of a plane domain is deened to be the set of the centers of the maximal inscribed disks. It is essentially the cut loci of the inward unit normal bundle of the boundary. We prove that if a plane domain has nite number of boundary curves each of which consists of nite number of real analytic pieces, then the medial axis is a connected geometric graph in R 2 with nitely many verti...

Stability Analysis of Medial Axis Transform

One-Sided Stability of Medial Axis Transform

Two-dimensional offsets and medial axis transform

We present a mathematical theory of the two-dimensional offset curves from the viewpoint of medial axis transform. We explore the local geometry of the offset curve in relation with the medial axis transform, culminating in the classification of points on the offset curve. We then study the domain decomposition from the viewpoint of offsets, and in particular introduce the concept of monotonic ...