Project Details
Projekt
Image analysis and spatial statistics
Subject Area
Mathematics
Term
from 2011 to 2018
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 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 Programme
Research Units
Subproject of
FOR 1548:
Geometry and Physics of Spatial Random Systems
International Connection
Denmark
