Image analysis and spatial statistics

• Antragstellerinnen / Antragsteller: Dr. Markus Kiderlen; Professorin Dr. Eva B. Vedel Jensen
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2011 bis 2018
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 173504944

The goal of this project is to develop methods of extracting geometric characteristics and features from physical data in a quantitative, robust and efficient manner. The six subprojects cover image analyis and statistical aspects of several topics of the planned Research Unit. For digital input, a combination of image analysis on the one hand and geometric concepts from mathematical morphology, discrete, stochastic and integral geometry on the other hand have to be combined to obtain efficient algorithms. In addition to the design of algorithms for Minkowski functionals and tensor valuations, focus is put on comparison of competing approaches and specifications of necessary regularity assumptions on the underlying structures. Besides digital data, we also treat continuous input in the design based situation, where inference for tensor valuations (or derived quantities) is based on lower dimensional central sections. Methods from classical local stereology including variance reducing sampling designs have to be transferred and analysed. Concerning the model based approach, we first aim at developing a new (measure-valued) estimator of the radius distribution of a stationary planar Boolean model. Second, we will study statistical inference for random field models based on local morphological measurements, exemplified by the analysis of the H.E.S.S. sky maps. In view of the importance of tensor valuations in the present application, we also consider the shape-from-tensors problem of recovering (approximating) a set from (finitely) many of its tensor valuations

• DFG-Verfahren: Forschungsgruppen
• Teilprojekt zu: FOR 1548: Geometry and Physics of Spatial Random Systems
• Internationaler Bezug: Dänemark