Haralick’s texture measurements (IEEE Transactions vol. SMC-3, no. 6, pp 610-621, 1973) can vary depending on the angle between the reference pixel and its neighboring pixel. That is, the value of a particular texture measurement can change depending on whether you take the neighboring pixel to be the pixel positioned to the right (at the 0 degree angle), or at a diagonal (45 or 135 degrees), or above (at 90 degrees) relative to the reference pixel.
Haralick dealt with this problem by calculating a new measurement for each orientation (0, 45, 90, and 135 degree angles), and so, for example, calculated four different values of the ‘angular second moment’ texture measurement for a single object. In contrast, CellProfiler calculates only a single value for any particular texture measurement. How does CP do this? Does CP assume that the orientation between reference and neighbor pixels to be 0 degrees, for instance? Or does CP average the four separate values for the different orientations?