Multidimensional and multiscale Higuchi dimension for the analysis of colorectal histological images

Fracta1 techniques are widely explored to quantity and recognize texture patterns in digital images. Among the different types of fractal techniques, one that stands out is the Higuchi fractal dimension. The Higuchi fractal dimension allows determining how much space is filled in a two-dimensional image through the projection of the image in 1D signals. This property provides the possibility to calculate the Higuchi fractal dimension of specific regions of an image. The main drawback of this technique is that it does not allow the analysis of color images. In this work, a new Higuchi fractal dimension model is presented with the inclusion of multidimensional and multiscale strategies to expand the traditional Higuchi dimension for texture analysis in color images. The multidimensional approach was applied considering each pixel of the color image as an n-dimensional vector. The multiscale strategy was defined using different scales of observation. The proposed model was applied to a set of 151 colorectal histological images to test its ability to quantity and separate the benign and malignant groups from colorectal cancer. The performance of the proposed model was compared with that provided by consolidated fractal dimension techniques. The results obtained are promising and indicate that the proposal contributes significantly to the literature focused on the quantification and recognition of texture patterns with fractal techniques.