Ramanathan Muthuganapathy

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We present an algorithm for generating the Voronoi cells for a set of rational C<sup>1</sup>-continuous planar closed curves, which is precise up to machine precision. Initially, bisectors for pairs of curves, (<i>C(t), C<sup>i</sup>(r))</i>, are generated symbolically and represented as implicit forms in the <i>tr</i>-parameter space. Then, the bisectors(More)
Analysis of mesh models is gaining prominence as it has wide range of applications from engineering to medicine. In this paper, we present a method for analyzing meshes through the abstraction of its prominent cross-sections (PCS). An algorithm that can robustly yield prominent cross-section at any point on the mesh that approximates the local sweep has(More)
Content based image retrieval (CBIR), a techniquewhich uses visual contents to search images from the large scale image databases, is an active area of research for the past decade. It is increasingly evident that an image retrieval system has to be domain specific. In this paper, we present an algorithm for retrieving images with respect to a database(More)
The problem of computing the minimum enclosing sphere (MES) of a point set is a classical problem in Computational Geometry. As an LP-type problem, its expected running time on the average is linear in the number of points. In this paper, we generalize this approach to compute the minimum enclosing sphere of free-form hypersurfaces, in arbitrary dimensions.(More)
We present an algorithm for generating Voronoi cells for a set of planar piecewise C1-continuous closed rational curves, which is precise up to machine precision. The algorithm starts with the symbolically generated bisectors for pairs of C1-continuous curve segments (C(t),Ci(r)). The bisectors are represented implicitly in the tr-parameter space. Then,(More)
Given a finite set of points S ⊆ R, we define a proximity graph called as shape-hull graph(SHG(S)) that contains all Gabriel edges and a few non-Gabriel edges of Delaunay triangulation of S. For any S, SHG(S) is topologically regular with its boundary (referred to as shape-hull(SH)) homeomorphic to a simple closed curve. We introduce the concept of(More)
In this paper, we present a fully automatic Delaunay based sculpting algorithm for approximating the shape of a finite set of points S in R2. The algorithm generates a relaxed Gabriel graph (RGG) that consists of most of the Gabriel edges and a few non-Gabriel edges induced by the Delaunay triangulation. Holes are characterized through a structural pattern(More)
We present a method to extract the contour of geometric objects embedded in binary digital images using techniques in computational geometry. Rather than directly dealing with pixels as in traditional contour extraction methods, we process on object point set extracted from the image. The proposed algorithm works in four phases: point extraction, Euclidean(More)