From the Slit-Island Method to the Ising model: Analysis of irregular grayscale objects

Przemysław Mazurek; Dorota Oszutowska-Mazurek

International Journal of Applied Mathematics and Computer Science (2014)

  • Volume: 24, Issue: 1, page 49-63
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Przemysław Mazurek, and Dorota Oszutowska-Mazurek. "From the Slit-Island Method to the Ising model: Analysis of irregular grayscale objects." International Journal of Applied Mathematics and Computer Science 24.1 (2014): 49-63. <http://eudml.org/doc/271912>.

@article{PrzemysławMazurek2014,
abstract = {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.},
author = {Przemysław Mazurek, Dorota Oszutowska-Mazurek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {slit island method; area-perimeter method; Ising model; image analysis; cervical cancer; slit island method (SIM)},
language = {eng},
number = {1},
pages = {49-63},
title = {From the Slit-Island Method to the Ising model: Analysis of irregular grayscale objects},
url = {http://eudml.org/doc/271912},
volume = {24},
year = {2014},
}

TY - JOUR
AU - Przemysław Mazurek
AU - Dorota Oszutowska-Mazurek
TI - From the Slit-Island Method to the Ising model: Analysis of irregular grayscale objects
JO - International Journal of Applied Mathematics and Computer Science
PY - 2014
VL - 24
IS - 1
SP - 49
EP - 63
AB - 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.
LA - eng
KW - slit island method; area-perimeter method; Ising model; image analysis; cervical cancer; slit island method (SIM)
UR - http://eudml.org/doc/271912
ER -

References

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