Fractal lacunarity of trabecular bone and magnetic resonance imaging: New perspectives for osteoporotic fracture risk assessment

Figure 2 Representation of sigmoid function for different choices of parameters k, σ. A: Sigmoid graph obtained by varying values of parameter k; B: Graph obtained by varying values of parameter σ. This new pre-processing step prescribes to consider image J, in place of image I, where the pixels are defined as follows: J(i, j) = 1/1 + esp(-k (I(I,j) - σ), i = 1,2,…M, j = 1,2,…N, and k, σ > 0 are two given parameters. Note that the procedure goes toward a complete binarization by increasing parameter k, related to sigmoid rectangularization.