title: Unstable operators in image processing.
abstract: Digital image processing is a powerful tool in biomedical applications and is used for image enhancement, segmentation or classification. Unfortunately, some of the processes in image analysis are unstable operators. Even small perturbations in the image data can cause significant errors in the result. The corresponding practical algorithms are sensitive to deviations in the input data and the behaviour is similar to linear systems with ill conditioned matrices. This property is related to the so called ill posed problems. We review the framework of ill posed problems and regularization in image analysis. We examine a few examples related to biomedical imaging: segmentation by thresholding, edge detection, length estimation, orientation.
authors.affiliation: University of Applied Sciences, Rgensburg.
authors.forename: Dietwald
authors.initials: D
authors.lastname: Schuster
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000295:instrumentation*; D008962:Models, Theoretical; D010363:Pattern Recognition, Automated; D012815:Signal Processing, Computer-Assisted / Q000295:instrumentation*; D012984:Software