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Local detection of defects from image sequences

Ewaryst RafajłowiczMarek WnukWojciech Rafajłowicz — 2008

International Journal of Applied Mathematics and Computer Science

Our aim is to discuss three approaches to the detection of defects in continuous production processes, which are based on local methods of processing image sequences. These approaches are motivated by and applicable to images of hot metals or other surfaces, which are uniform at a macroscopic level, when defects are not present. The first of them is based on the estimation of fractal dimensions of image cross-sections. The second and third approaches are compositions of known techniques, which are...

Nonlinear image processing and filtering: A unified approach based on vertically weighted regression

Ewaryst RafajłowiczMirosław PawlakAngsar Steland — 2008

International Journal of Applied Mathematics and Computer Science

A class of nonparametric smoothing kernel methods for image processing and filtering that possess edge-preserving properties is examined. The proposed approach is a nonlinearly modified version of the classical nonparametric regression estimates utilizing the concept of vertical weighting. The method unifies a number of known nonlinear image filtering and denoising algorithms such as bilateral and steering kernel filters. It is shown that vertically weighted filters can be realized by a structure...

A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics

Ewaryst RafajłowiczKrystyn StyczeńWojciech Rafajłowicz — 2012

International Journal of Applied Mathematics and Computer Science

Our aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is selected and tested.

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