The paper describes an algorithm for generating an approximation of the medial axis transform (MAT) for planar objects with free form boundaries. The algorithm generates the MAT by a tracing technique that marches along the object boundary rather than the bisectors of the boundary entities. The level of approximation is controlled by the choice of the step size in the tracing procedure. Criteri...

Fig. 1 The de…nition of isogonal conjugates is based on the following theorem (Fig. 1): Theorem 1. Let ABC be a triangle and P a point in its plane. Then, the re‡ections of the lines AP; BP; CP in the angle bisectors of the angles CAB; ABC; BCA concur at one point. This point is called the isogonal conjugate of the point P with respect to triangle ABC: We denote this point by Q: Note that we wo...

This paper applies the randomized incremental construction (RIC) framework to computing the Hausdorff Voronoi diagram of a family of k clusters of points in the plane. The total number of points is n. The diagram is a generalization of Voronoi diagrams based on the Hausdorff distance function. The combinatorial complexity of the Hausdorff Voronoi diagram is O(n + m), where m is the total number...

We present a novel index for approximate searching in metric spaces based on random bisectors and binary fingerprints. The aim is to deal with scenarios where the main memory available is small. The method was tested on synthetic and real-world metric spaces. Our results show that our scheme outperforms the standard permutant-based index in scenarios where memory is scarce.

We propose a method for detecting facial symmetry axis from frontal face image. The proposed adopts voting procedure like Hough transform that transforms set of edge points into perpendicular bisectors two different selected the set. The initial guess is adjusted accurately by following fine tuning procedure. Experimental results show correctly detects axes real images visually a...

High resolution echelle spectra of PW And (HD 1405) have been taken during eight observing runs from 1999 to 2002. The detailed analysis of the spectra allow us to determine its spectral type (K2V), mean heliocentric radial velocity (V hel = −11.15 km s −1) rotational velocity (v sin i = 22.6 km s −1), and equivalent width of the lithium line λ6707.8 ˚ A (EW (Li I) = 273 m ˚ A). The kinematic (...

Abstract A simple geometric mechanism: ‘the locus of intersections perpendicular bisectors and normal lines’, often arises in many guises nonlinear sciences. In this paper, a new application mechanism is given. Namely, we show that gives answers to all four basic problems on envelopes created by hyperplane families (existence problem, representation equivalence problem definitions, uniqueness p...