Two new methods for discriminating textures in images, based on the estimation of texture image lacunarity, are proposed in this paper. The concept of lacunarity was introduced by Mandelbrot and “describes the texture pattern in terms of spatial dispersion of gaps of a specific size” (in other words, a measure of how a pattern fills a space). Methods for estimating lacunarity are usually applied to binary images. Alternative methods have been proposed for dealing with grayscale images, such as differential box counting (DBC).

Backes proposes two methods: the first is based on a local threshold, and the second involves gliding a box over a 3D image representation (x,y,z, where z is the pixel gray level). The paper also proposes an optimized algorithm implementation for the second method. Usually, when lacunarity is applied to binary images, the adoption of a global threshold for binarization is very common. The first proposed method (Lac3) introduces the idea of obtaining a local threshold to account for local texture properties, allowing a simple and fast threshold calculation for the lacunarity estimation method. The second method (Lac4) glides a box over the intensity coordinates (a 3D representation of the grayscale image), computing the “mass distribution” over the image.

The proposed methods, Lac3 and Lac4, were compared with two other methods from the literature, and were found to produce better results for lacunarity estimation and image texture classification. Even though the results seems to be very promising, the tests involved a quite small and specific image dataset (150 patterns grouped into 15 texture samples per class, yielding ten texture classes of images of plant leaves).