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Figure 2.5: Fractal dimension from box-counting response. (a) Original image. (b) Fractal dimension response with neighborhoods of 10 x 10.

method for calculating the fractal dimension the mean difference of intensities is calculated for different scales (each scale given by the euclidian distance between two pixels), and the slope of the regression line between log E(\I (p1) — I(p2)\) and ^J(x2 — x1) + (y2 — y1) gives the Hurst parameter.

Triangular Prism Surface Area Method. The triangular prism surface area (TPSA) algorithm considers an approximation of the "area" of the fractal structure using triangular prisms. If a rectangular neighborhood is defined by its vertices A, B, C, and D, the area of this neighborhood is calculated by tessellating the surface with four triangles defined for each consecutive vertex and the center of the neighborhood.

The area of all triangles for every central pixel is summed up to the entire area for different scales. The double logarithmic Richardson-Mandelbrot plot should again yield a linear line whose slope is used to determine the TPSA dimension. Figure 2.5 shows the fractal dimension value of each pixel of an IVUS image considering the fractal dimension of a neighborhood around the pixel. The size of the neighborhood is 10 x 10. The response of this technique seems to take into account the border information of the structures in the image.

2.2.1.4 Local Binary Patterns

Local binary patterns [28] are a feature extraction operator used for detecting "uniform" local binary patterns at circular neighborhoods of any quantization of

Figure 2.6: Typical neighbors: (Top left) P = 4, R = 1.0; (top right) P = 8, R = 1.0; (bottom left) P = 12, R = 1.5; (bottom right) P = 16, R = 2.0.

the angular space and at any spatial resolution. The operator is derived based on a circularly symmetric neighbor set of P members on a circle of radius R. It is denoted by LBPPR Parameter P controls the quantization of the angular space, and R determines the spatial resolution of the operator. Figure 2.6 shows typical neighborhood sets. To achieve gray-scale invariance, the gray value of the center pixel (gc) is subtracted from the gray values of the circularly symmetric neighborhood gp (p = 0, 1,..., P — 1) and assigned a value of 1 if the difference is positive and 0 if negative.

0 otherwise

By assigning a binomial factor 2p for each value obtained, we transform the neighborhood into a single value. This value is the LBPR,P :

To achieve rotation invariance the pattern set is rotated as many times as necessary to achieve a maximal number of the most significant bits, starting always from the same pixel. The last stage of the operator consists on keeping the information of "uniform" patterns while filtering the rest. This is achieved using a transition count function U. U is afunction that counts the number of transitions

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