ON THE USE OF SPACE-FILLING CURVES IN CHANGING IMAGE DIMENSIONALITY

Abstract

The paper describes a new generalized approach (idea) to solving the image dimensionality change problem. The proposed idea employs continuous space-filling curves (Hilbert, Peano, etc.), characterized by self-similar and self-avoiding geometrical construction. These curves, being applied to multi-dimensional images in the role of image scan trajectories, determine relatively high smoothness of generated one-dimensional image analogues. To illustrate practical applicability and usefulness of the developed approach, some interesting task-oriented digital image processing techniques are discussed in brief, namely: hyperbolic image filtering in spaces of different dimensionality and efficient encoding of multi-dimensional “silhouette” images in the one-dimensional space.