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. First, for a two-dimensional (2D) binary image of size N × N , we devise an algorithm for solving the 2D_ANN problem using a LARPBS of size N 2 + ϵ , where 0 < ϵ ⪡ 1 . Then, for a three-dimensional (3D) binary image of size N × N × N , we devise an algorithm for solving the 3D_ANN problem using a LARPBS of size N 3 + ɛ , where 0 < ɛ < 1 . To the best of our knowledge, all results derived above are the best O ( 1 ) time 2D_ANN and 3D_ANN algorithms on the LARPBS model known.