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

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Rafajłowicz E., Pawlak M., Steland A.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom 18
|
nr 1
49-61
EN
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 of three interconnected radial basis function (RBF) networks. We also assess the performance of the algorithm by studying industrial images.
2
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Local detection of defects from image sequences

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Rafajłowicz E., Wnuk M., Rafajłowicz W.
International Journal of Applied Mathematics and Computer Science
|
2008
|
tom 18
|
nr 4
581-592
EN
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 selected and tuned to our goal. We discuss their advantages and disadvantages, since they provide different information on defects. The results of their testing on 12 industrial images are also summarized.
3
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A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics

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Rafajłowicz E., Styczeń K., Rafajłowicz W.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
nr 2
313-326
EN
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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