Pictures as Complex Systems

When we try to process images — restore, analyze, or understand them — we can approach the problem by viewing the image as a complex system of units, combined by certain rules of regularity. The choice of units is by no means straightforward. Initially, it may appear that a natural choice would be the picture elements (pixels), say black and white, or gray scale, or color, etc. A closer scrutiny, however, reveals this approach to be too superficial and that we must use more intrinsic, more informative, units that lead to the construction of random geometries, several instances of which we study herein.