Pattern entropy

Quality metric that is computed from the entropy of all the pixels in the diffraction pattern. The pixels with a value of zero are ignored, so that the pixels removed from the Mask disc operation are ignored (Note the sum starts at 1 instead of 0).

\[Q = -\sum\limits_{i=1}^{255}{P_i\ln{P_i}}\]

where \(P_i\) is the probability of having a pixel with the color i.

This quality index was used by Wright and Nowell [Wright2006] and Tao and Eades [Tao2005]. They summarized this quality index as:

• Related to the compressability of information
• Describe the ‘business’ of an image
  • Low entropy image: Low contrast, large number of pixels with same or similar values
• Similar results than Image quality
• Similar results than Pattern standard deviation

Example on NiCoCrAlY sample