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Local detection of defects from image sequences

100%
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.
2
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On the dynamics of equations with infinite delay

75%
Pražák D.
Open Mathematics
|
2006
|
tom 4
|
nr 4
635-647
EN
We consider a system of ordinary differential equations with infinite delay. We study large time dynamics in the phase space of functions with an exponentially decaying weight. The existence of an exponential attractor is proved under the abstract assumption that the right-hand side is Lipschitz continuous. The dimension of the attractor is explicitly estimated.
3
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A necessary and sufficient condition for the existence of an exponential attractor

63%
Pražák D.
Open Mathematics
|
2003
|
tom 1
|
nr 3
411-417
EN
We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.
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