Construction of the nearest neighbor embracing graph of a point set

This paper gives optimal algorithms for the construction of the Nearest Neighbor Embracing Graph (NNE-graph) of a given set of points V of size n in the k-dimensional space (k-D) for k = (2, 3). The NNE-graph provides another way of connecting points in a communication network, which has lower expected degree at each point and shorter total length of connections than Delaunay graph. In fact, the NNE-graph can also be used as a tool to test whether a point set is randomly generated or has some particular properties. We show in 2-D that the NNE-graph can be constructed in optimal O(n2) time in the worst case. We also present an O(n log n + nd) algorithm, where d is the Ω(log n)th largest degree in the output NNE-graph. The algorithm is optimal when d = O(log n). The algorithm is also sensitive to the structure of the NNE-graph, for instance when d = g · (log n), the number of edges in NNE-graph is bounded by O(gn log n) for 1 ≤ g ≤ n/log n. We finally propose an O(n log n + nd log d*) algorithm for the problem in 3-D, where d and d* are the Ω(log n/log log n)th largest vertex degree and the largest vertex degree in the NNE-graph, respectively. The algorithm is optimal when the largest vertex degree of the NNE-graph d* is O(log n/log log n). © Springer-Verlag Berlin Heidelberg 2004.link_to_subscribed_fulltex

Use of a spatial light modulator as an adaptable phase mask for wavefront coding

A wavefront-coded imaging system employing a spatial light modulator (SLM) for the agile implementation of phase masks is presented. The SLM is a liquid crystal display that can be modulated to implement cubic phase masks of variable coding strength. These phase masks produce broad point spread functions insensitive to defocus aberration and are used in combination with post-detection digital image processing to extend the depth-of-field of an imaging system. A detailed description of the calibration process of the SLM in phase mode is presented together with experimental results which include wavefront-coded modulation transfer functions and increased depth-of-field images. The most interesting feature is the versatility provided by the imaging system, as compared to conventional (fixed phase mask) designs, and the agility in which it is done