Image Visualization and Restoration by Curvature Motions
Seminar Room 1, Newton Institute
The role of curvatures in visual perception goes back to '54 and is due to Attneave. It can be argued on neurological grounds that human brain could not possible use all the information provided by states of simulation. But information that stimulates the retina, is located at regions where color changes abruptly (contours), and furthermore at angles and peaks of curvature. Yet, a direct computation of curvatures on a raw image is impossible. We show in this presentation how curvatures can be accurately estimated, at subpixel resolution, by a direct computation on level lines after their independent smoothing. This view towards shape analysis requires a representation of an image in terms of its level lines. At the same time, it involves short time smoothing (in occurrence Curve Shortening or Af?ne Shortening) simultaneously for level lines and images.
In this setting, we found an explicit connection between the geometric approach for Curve / Af?ne Shortening and the viscosity approach for the Mean / Af?ne Curvature Motion, based on a complete image processing pipeline, that we term Level Lines (Af?ne) Shortening, shortly LL(A)S. We show that LL(A)S provides an accurate visualization tool of image curvatures, that we call an Image Curvature Microscope. As an application we give some illustrative examples of image visualization and restoration: noise, JPEG artifacts, and aliasing will be shown to be nicely smoothed out by the subpixel curvature motion.