Homogeneity Index as Stopping Criterion for Anisotropic Diffusion Filter

Abstract

The Anisotropic Diffusion Filter is an image smoothing method often applied to improve segmentation and classification tasks. Because it is an adaptive and iterative method, one should define some stopping criterion in order to avoid unnecessary computational cost while producing the desired output. However, state-of-the-art methods in this regard consider costly comparative functions computed at each iteration or allowing extra iterations before actually stopping. Therefore, in this paper we propose a new stopping criterion to overcome this difficulty that defines the number of iterations without additional comparisons during the image processing. Our stopping criterion is based on the image homogeneity index and the constants included in the filter definition, which can be calculated before the first iteration. Using three different measures of similarity in grayscale and colorful images from different domains with variation of tonality, our results indicate that the proposed stopping criterion reduces the number of iterations and, simultaneously, maintains the quality of the diffused images. Consequently, our method can be applied to images from different sources, color composition, and levels of noise.