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Image based analysis of complex microstructures of engineering materials

100%
Wejrzanowski T., Spychalski W., Różniatowski K., Kurzydłowski K.
International Journal of Applied Mathematics and Computer Science
|
2008
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tom 18
|
nr 1
33-39
EN
The paper presents various methods for quantitative description of material structures. The main focus is on direct methods of description based on image analysis. In particular, techniques for the estimation of the size, shape and spatial distribution of structural elements observed by different microscopic techniques are described. The application of these methods for the characterization of the structures of engineering materials is demonstrated on a stainless steel used in petrochemical installations. It is shown that the methods applied are useful for the assessment of service degradation of materials.
2
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From the Slit-Island Method to the Ising model: Analysis of irregular grayscale objects

88%
Mazurek P., Oszutowska-Mazurek D.
International Journal of Applied Mathematics and Computer Science
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2014
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tom 24
|
nr 1
49-63
EN
The Slit Island Method (SIM) is a technique for the estimation of the fractal dimension of an object by determining the area-perimeter relations for successive slits. The SIM could be applied for image analysis of irregular grayscale objects and their classification using the fractal dimension. It is known that this technique is not functional in some cases. It is emphasized in this paper that for specific objects a negative or an infinite fractal dimension could be obtained. The transformation of the input image data from unipolar to bipolar gives a possibility of reformulated image analysis using the Ising model context. The polynomial approximation of the obtained area-perimeter curve allows object classification. The proposed technique is applied to the images of cervical cell nuclei (Papanicolaou smears) for the preclassification of the correct and atypical cells.
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Redescending M-estimators in regression analysis, cluster analysis and image analysis

75%
Müller C.
Discussiones Mathematicae Probability and Statistics
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2004
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tom 24
|
nr 1
59-75
EN
We give a review on the properties and applications of M-estimators with redescending score function. For regression analysis, some of these redescending M-estimators can attain the maximum breakdown point which is possible in this setup. Moreover, some of them are the solutions of the problem of maximizing the efficiency under bounded influence function when the regression coefficient and the scale parameter are estimated simultaneously. Hence redescending M-estimators satisfy several outlier robustness properties. However, there is a problem in calculating the redescending M-estimators in regression. While in the location-scale case, for example, the Cauchy estimator has only one local extremum this is not the case in regression. In regression there are several local minima reflecting several substructures in the data. This is the reason that the redescending M-estimators can be used to detect substructures in data, i.e. they can be used in cluster analysis. If the starting point of the iteration to calculate the estimator is coming from the substructure then the closest minimum corresponds to this substructure. This property can be used to construct an edge and corner preserving smoother for noisy images so that there are applications in image analysis as well.
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