Fast All Nearest Neighbor Algorithms from Image Processing Perspective

Abstract

In this paper, we solve the k-dimensional all nearest neighbor (kD/spl I.bar/ANN) problem, where k=2 or 3, on a linear array with a reconfigurable pipelined bus system (LARPBS) from image processing perspective. Three scalable O(1) time algorithms are proposed, one for solving the Euclidean distance transform (EDT) problem and the other two for solving the all nearest neighbor (ANN) problem. First, for a two-dimensional (2D) binary image of size N/spl times/N, we devise an algorithm for solving the 2D/spl I.bar/EDT problem using an LARPBS of size N/sup 2+/spl epsiv//, where 0</spl epsiv/=/spl epsi/+/spl delta/=1/2/sup c+1/-1+1/k<1, k and c are constants, and an algorithm for solving the 2D/spl I.bar/ANN problem using an LARPBS of size N/sup 2+/spl epsi//, where 0</spl epsi/=1/2/sup c+1/-1/spl Lt/1. Then, for a three-dimensional (3D) binary image of size N/spl times/N/spl times/N, we devise an algorithm for solving the 3D/spl I.bar/ANN problem using an LARPBS of size N/sup 3+/spl epsiv// based on the computed 2D/spl I.bar/EDT and 2D/spl I.bar/ANN. To the best of our knowledge, all results derived above are the best O(1) time EDT and ANN algorithms on the LARPBS model known.