Edges identification based on the derivative filters and fractal dimension

Abstract

The purpose of this paper is to offer a comparative study on the fractal dimension (D) used to differentiate edges in brain images processed using first-order derivative filters (Prewitt, Roberts) and second-order derivative filters (Laplacian and Laplacian of Gaussian). PDw (proton density) and T2w (T2-weighted type) brain images of healthy patients and patients diagnosed with metastatic bronchogenic carcinoma (MBC) are used. Experimental results showed that second-order derivative filters clearly separate healthy controls from diseased patients while the first-order derivative filters create false edges that affect the fractal dimension (D) values. The Kullback-Leibler divergence (DKL) determines that the probability distribution of the "real" fractal measurements, specific to healthy patients is different from the probability distribution of the "arbitrary" fractal dimensions, specific to patients with MBC. The highest value to the distance DKL is for Prewitt filter.  The value of distance DKL is close to zero for Laplacian, LoG and Roberts filters.