Summary form only given. The vast majority of signal processing research studies linear operations on vectors of samples from one-, two-, or higher dimensional signals. While linear operators can be very successful at exploiting many types of relationships among signal samples, they are ineffective for processing a very common form of uncertainty in images and video: location uncertainty. The locations of edges in images sketch 1-D contours which constitute an important part of the information in most images. Thisarticle shows how signals imbedded in location uncertainty of image contours induce a nonlinear manifold structure to the probability of images. Due to this nonlinear manifold structure to the space of images, no linear decomposition of images (e.g. transforms, wavelets, etc.) can fully exploit the dependencies within images. Based on these observations, we point to new directions for developing improved image processing tools.
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