Fast All Nearest Neighbor Algorithms from Image Processing Perspective

In this paper, we solve the k-dimensional all nearest neighbor (kD_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 x N, we devise an algorithm for solving the 2D_EDT problem using an LARPBS of size N^{2+ε} , where 0 < ε = ∊ + δ = frac{1}{{2^{c + 1} - 1}} + frac{1}{k} < 1, k and c are constants, and an algorithm for solving the 2D_ANN problem using an LARPBS of size N^{2+ε} , where 0 < ∊ = frac{1}{{2^{c + 1} - 1}} ≪ 1. Then, for a three-dimensional (3D) binary image of size N x N x N, we devise an algorithm for solving the 3D_ANN problem using an LARPBS of size N^{3+ε} based on the computed 2D_EDT and 2D_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.