Abstract:

Compensated convex transforms enjoy tight-approximation and locality properties that can be exploited to develop multi-scale, parametrised methods  for identifying singularities in functions. These tools can then be used, via a numerical implementation, to detect features in images or data, remove noise from images, identify intersections between surfaces, etc, and thus produce new geometric techniques for image processing, feature extraction and geometric interrogation.  Advantages of such an approach include the use of blind global methods that are Hausdorff-stable under perturbation and different sampling techniques, and are also multi-scale, providing scales for features that allow users to select which size of feature they wish to detect. This is joint work with Kewei Zhang, Nottingham, and Antonio Orlando, Tucumán, Argentina.