Blur and disorder

Blurring is not the only way to selectively remove fine spatial detail from an image. An alternative is to scramble pixels locally over areas defined by the desired blur circle. We refer to such scrambled images as "locally disorderly". Such images have many potentially interesting applications. In this contribution we discuss a formal framework for such locally disorderly images. It boils down to a number of intricately intertwined scale spaces, one of which is the ordinary linear scale space for the image. The formalism is constructed on the basis of an operational definition of local histograms of arbitrary bin width and arbitrary support.