FRACTAL DIMENSION PRESERVATION BY GABOR FILTERS IN IMAGE PROCESSING

Gabor filters are parametric functions that are located in both the spatial and frequency domains, they are used in digital signal processing and have been combined with the fractal dimension in the biometric recognition of the iris of the eye and oil exploration to identify the layers that form a soil structure. In this work, we present an example of a Gabor filter that does not preserve fractal dimension, which affects the efficiency of the methods of recognition. In this sense, S. Albeverio, M. Pratsiovytyi, and G. Torbin provide a study on the functions that preserve the fractal dimension and show that those that have a decomposable domain such that they have the property of being bi-Lipschitz on each element of the decomposition, then they will preserve the dimension, however, in this investigation, it is proven that the Gabor filter is not a function of this kind. Therefore, as a main result, the conditions on the parameters are provided for the Gabor filters to preserve it.