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 di sorderly. Such images have many potentially interesting applications. In th is contribution we discuss a formal framework for such locally disorderly i mages. It boils down to a number of intricately intertwined scale spaces, o ne of which is the ordinary linear scale space for the image. The formalism is constructed on the basis of an operational definition of local histogra ms of arbitrary bin width and arbitrary support. (C) 2000 Academic Press.