P = (M — d/v^2)(N — d/\/l) for 6 = 45° and 6 = 135°
The value of P' given by ^¡j hij can also be accumulated during computation of H(d, 6).
The co-occurrence matrix C(d, 6) is made of elements cij = hij/P namely the probability of having pixel pairs with values i and j in locations that exhibit the selected relative position. The size of the co-occurrence matrix that depends on the number of gray levels in the image can be inconveniently large in many cases. For example, a 10-bit image would yield a 1024 x 1024 co-occurrence matrix, the storage and computational load of which may be too large for many applications. Often, the pixel values of the image are mapped to new values
which weighs each element cij with the gray level difference i — j that produced it. In this manner, larger transitions are emphasized, and this metric becomes sensitive to the local contrast of the inhomogeneity. The inertia metric will have low values for homogeneous regions, and high values for inhomo-geneous regions with high contrast. A metric that penalizes the regions with higher contrast is the inverse difference moment:
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