An address generator, for an N-dimensional pseudo-Hilbert scan in a hyper-rectangular, parallelepiped region

Abstract

The Hilbert curve is a one-to-one mapping between N-dimensional (N-D) space and 1-D space. The Hilbert curve has been applied to image processing as a scanning technique (Hilbert scan). Applications to multi-dimensional image processing are also studied. In this application. We use the N-D Hilbert scan which maps N-D data to 1-D data along the N-D Hilbert curve. However, the N-D Hilbert scan is the application limited to data in a hyper-cube region. In this paper, we present a novel algorithm for generating N-D pseudo-Hilbert curves in a hyper-rectangular parallelepiped region. Our algorithm is suitable for real-time processing and is easy to implement in hardware, since it is a simple and non-recursive computation using look-up tables.