Automatic continuum analysis of reflectance spectra

A continuum algorithm based on a Segmented Upper Hull method (SUH) is described. An upper hull is performed on segments of a spectrum defined by local minima and maxima. The segments making a complete spectrum are then combined. The definition of the upper hull allows the continuum to be both concave and/or convex, adapting to the shape of the spectrum. The method performs multiple passes on a spectrum by segmenting each local maximum to minimum and performing an upper hull. The algorithm naturally adapts to the widths of absorption features, so that all features are found, including the nature of doublets, triplets, etc. The algorithm is also reasonably fast on common minicomputers so that it might be applied to the large data sets from imaging spectrometers

A fast adaptive convex hull algorithm on two-dimensional processor arrays with a reconfigurable BUS system

A bus system that can change dynamically to suit computational needs is referred to as reconfigurable. We present a fast adaptive convex hull algorithm on a two-dimensional processor array with a reconfigurable bus system (2-D PARBS, for short). Specifically, we show that computing the convex hull of a planar set of n points taken O(log n/log m) time on a 2-D PARBS of size mn x n with 3 less than or equal to m less than or equal to n. Our result implies that the convex hull of n points in the plane can be computed in O(1) time in a 2-D PARBS of size n(exp 1.5) x n

Computing Optimal Kernels in Two Dimensions

Let $P$ be a set of $n$ points in $\mathbb{R}^2$. A subset $C\subseteq P$ is an $\varepsilon$-kernel of $P$ if the projection of the convex hull of $C$ approximates that of $P$ within $(1-\varepsilon)$-factor in every direction. The set $C$ is a weak $\varepsilon$-kernel if its directional width approximates that of $P$ in every direction. We present fast algorithms for computing a minimum-size $\varepsilon$-kernel as well as a weak $\varepsilon$-kernel. We also present a fast algorithm for the Hausdorff variant of this problem. In addition, we introduce the notion of $\varepsilon$-core, a convex polygon lying inside $CH(P)$, prove that it is a good approximation of the optimal $\varepsilon$-kernel, present an efficient algorithm for computing it, and use it to compute an $\varepsilon$-kernel of small size

Building Voronoi Diagrams for Convex Polygons in Linear Expected Time

Let P be a list of points in the plane such that the points of P taken in order form the vertices of a convex polygon. We introduce a simple, linear expected-time algorithm for finding the Voronoi diagram of the points in P. Unlike previous results on expected-time algorithms for Voronoi diagrams, this method does not require any assumptions about the distribution of points. With minor modifications, this method can be used to design fast algorithms for certain problems involving unrestricted sets of points. For example, fast expected-time algorithms can be designed to delete a point from a Voronoi diagram, to build an order k Voronoi diagram for an arbitrary set of points, and to determine the smallest enclosing circle for points at the vertices of a convex hull