Does Hausdorff Dimension Measure Texture Complexity?

Abstract

It has been suggested by Jürgensen and Staiger [1] that local Hausdorff dimension is representative of local image texture complexity, or “messiness”. If true, this could be a useful local texture feature in computer vision applications such as image segmentation and object classification. In this study we investigate whether the interpretation of Hausdorff dimension as a measure of texture complexity corresponds to reality, that is, human perception of texture complexity. Jürgensen and Staiger consider black and white images described by finite-state and closed ω-languages [1]. The (local) Hausdorff dimension of an ω-language can be computed from its corresponding automaton. Thus, we are interested in the relationship between the Hausdorff dimension of ω-languages which describe black and white texture images and the perceived texture complexity of the image described.

This research was funded in part by NSERC grant RGPIN262027-03 (M. G. Eramian), in part by an NSERC Undergraduate Research Award (M. Drotar) and in part by institutional grants from the University of Saskatchewan.