Sum entropy t8 = - Y^ Cx + y(fc) log{Cx + y(fc)} (48)

fc=0 K1

Difference entropy t9 = - ^^ cx-y(*) log{cx_y(*)} (49)

Each of the texture metrics t: through t9 can be obtained for each of the four 6 values at the selected distance d. While this orientation dependence may be desired in some cases, if a texture metric that addresses all directions is needed, the four co-occurrence matrices can be averaged and metrics can be derived from this multi-orientation matrix. Three co-occurrence matrix measures are illustrated with Fig. 13 and Table 1.

Co-occurrence matrix measures have been used for non-invasive analysis of tumors in dermatology [45], for quantification of texture in echographic images [46], for classification of heart diseases in echocardiography [47], for discrimination of prostatic tissues [48], for analyzing ultrasonic liver images [49], for quantification of tissue texture surrounding microcalcifications in mammograms [50], and for analyzing tissue texture in ultrasonic images of the breast [51]. An approach for detecting the texture periodicity using the cooccurrence matrix also has been suggested [52].

The use of co-occurrence matrices for texture analysis in 2D explained here can be extended to the quantification of texture in 3D as described in Chapter 15.

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