The convolution of the image with this mask along the three axes produces the three components of the gradient vector at each voxel. Two versions of the orientation histogram are then possible: Each gradient vector calculated is assigned to the appropriate bin of the histogram according to the method described in Section 2, and the bin value is incremented by the magnitude of the gradient vector. Alternatively, the bin of the orientation histogram may be accumulated by 1 every time a vector is assigned to it, irrespective of the magnitude of that vector. The latter approach was proved more robust when the weakest 5-7% of the gradient values were trimmed off when the orientation histogram was created, because such gradient vectors have very poorly defined orientations. This is the approach adopted in all experiments with real data presented in Section 6.
Examples of the resultant orientation histograms of the two approaches for the same volume of a CT vertebral image are shown in Fig. 3. The difference in the two appearances reflects the bone structure of the spinal cord, which had strong edges in four dominant orientations. These edges dominate the orientation histogram when the gradient magnitudes are added. However, their role is diminished when only gradient vectors are counted, as they are fewer in number than average and weak textural gradients. For this reason, the approach of ignoring the actual gradient magnitudes is considered more appropriate for describing microtextures.
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