Multiscale Statistical Image Invariants

It is often necessary to evaluate measured features of an image with respect to estimated properties of noise incorporated with the image values. In some cases, differential geometric methods lead to erroneous decisions arising from the assumption of linearity of the noisy feature space. This paper introduces new work in multiscale image statistics, a local framework that supports adaptive measurement of image structure with unknown and often non-stationary noise functions. Furthermore, it presents directional local statistics that enable the local normalization of feature measurement, reducing biases in noise measurement introduced by the underlying image geometry. Such measurements have applications in nonlinear filtering, texture analysis, and image segmentation.