Edge Preserving Smoothing in Time Series and Digital Images: From Abstract Principles to Practical Applications

• Antragsteller: Professor Dr. Gerhard Winkler
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2001 bis 2004
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 5333874

In this proposal the focus is on the probabilistic and statistical analysis of discontinuous phenomena in time series and digital images. One aim is a matching and better understanding of methods and algorithms from different fields like engineering, computer science, physics, statistics, or mathematics. We want to establish general principles for discontinuous and related phenomena like jumps, boundaries, modes or regions of monotonicity in order to compare and evaluate the different methods in a common framework and w.r.t. common criteria. This, and the experience gathered from applications to practically relevant (bio-medical) data, will lead to new and more stringent criteria which allow to design new and better methods. The recent methods we have in mind are nonlinear filters and estimators for edge-preserving smoothing and segmentation. Examples of the former are Sigma filters and their cascades, wavelet shrinkage, diffusion filtering and regularization. Probabilistic approaches include Bayesian methods, local M-smoothing, or taut string algorithms. All these methods share robustness in various disguises Applicability will be verified on bio-medical data, for example fMRI data of the human brain or mammograms. This requires the development of software (and standards within the DFG-Schwerpunkt). Validity will be checked in close cooperation with radiologists.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1114: Mathematische Methoden der Zeitreihenanalyse und digitalen Bildverarbeitung
• Beteiligte Person: Professor Dr. Volkmar Liebscher