In this paper, we give a solution to the problem of conflict-free access of various slices of data in parallel processor for image processing. Image processing operations require a memory system that permits parallel and conflict-free access of rows, columns, forward diagonals, backward diagonals, and blocks of two-dimensional image array for an arbitrary location. Linear skewing schemes are useful methods for those requirements, but these schemes require complex Euclidean division by prime number. On the contrary, nonlinear skewing schemes such as XOR-schemes have more advantages than the linear ones in address generation, but these schemes allow conflict-free access of some array slices in restricted region. In this paper, we propose a new XOR-scheme which allows conflict-free access of arbitrarily located various slices of data for image processing, with a two-fold the number of memory modules than that of processing elements. Further, we propose an efficient data alignment network which consists of log N + 2-stage multistage interconnection network utilizing Omega network.