Non-linear scale-space based on fuzzy contrast enhancement: Theoretical results

摘要

This work presents a contrast enhancement operator based on a fuzzy-numerical description of images at the pixel level; this operator is further used to construct a scale-space, whose theoretical and practical properties are reviewed. A very remarkable feature of our scale-space is that, in contrast to many other scale-spaces, it converges to non-trivial stages. Within the study of our scale-space, we present a series of theoretical results that show that the convergence of the scale-space is closely related to the signal's convexity. Specifically, we prove formally that the intensities in convex signals tend to converge to the minimum intensity. As a result, our scale-space increases the contrast in the image and homogenizes images. In addition to theoretical results, we illustrate the scale-space's behaviour in ad-hoc 1D signals and in greyscale images. Finally, to validate the potential application of this theoretical approach, we show that the proposal can be used as a preprocessing that performed before a neural network technique, increasing the accuracy in a classification task. (c) 2021 Elsevier B.V. All rights reserved.