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Comparison of statistical properties for various morphological filters based on mosaic image shape models
Y.V. Vizilter 1, O.V. Vygolov 1, S.Y. Zheltov 1

State Research Institute of Aviation Systems (GosNIIAS), Moscow

 PDF, 890 kB

DOI: 10.18287/2412-6179-CO-842

Pages: 449-460.

Full text of article: Russian language.

Abstract:
We consider the statistical properties of different mosaic filters. We demonstrate that in Pitiev's morphology, the measure of shape complexity is directly related to the shape simplicity measure based on morphological correlation coefficient (MCC). Based on MCC, we introduce the normalized morphological simplification index (NMSI). Using NMSI, we show that the simpler the mosaic shape, the more shape simplification is provided by the corresponding Pyt'ev projector. For the examples of mean and median mosaic filters, we address the problem of different operator comparison. In this context we introduce the concept of statistically simplifying morphological operators. Morphological correlation of mosaic shape and diffusion mosaic operator is considered. We prove that the NMSI for the diffusion mosaic operator is not related to the complexity for the corresponding diffusion shape kernel. Thus, a principal qualitative difference in the relationship between relational and operator models for diffuse and projective mosaic linear filters is demonstrated.

Keywords:
morphological image analysis, diffusion morphology, morphological correlation, morphological operators, shape complexity.

Citation:
Vizilter YV, Vygolov OV, Zheltov SY. Comparison of statistical properties for various morphological filters based on mosaic image shape models. Computer Optics 2021; 45(3): 449-460. DOI: 10.18287/2412-6179-CO-842.

Acknowledgements:
This work was supported by a grant from the Russian Science Foundation No. 16-11-00082.

References:

  1. Pytev YuP, Chulichkov AI. Methods for morphological analysis of images [In Rusian]. Moscow: "Fizmatlit" Publisher; 2010.
  2. Vizilter YuV, Vygolov OV, Zheltov SYu, Morgin AV. Morphological analysis based on attribute and relational representations of mosaic image models [In Russian]. Vestnik Komp'iuternykh i Informatsionnykh Tekhnologii 2021 (In Print).
  3. Vizilter YuV, Geltov SYu. Mathematical morphologies based on non-complicating e-filters [In Russian]. All-Russian conference MMRO-17: Collection of reports 2015.
  4. Vizilter YuV, Rubis AYu. Morphological comparison of images by complexity [In Russian]. All-Russian conference MMRO-17: Collection of reports 2015: 70.
  5. Vizilter YuV, Rubis AYu. Metric image shape space [In Russian]. Intellectualization of information processing (IOI-9) 2012: 406-409.
  6. Vizilter YuV, Rubis AYu, Gorbatsevich VS. Relational models of image shapes and shape comparison space [In Russian]. Intellectualization of information processing (IOI-9) 2012: 410-413.
  7. Vizilter YV, Zheltov SY. Geometrical correlation and matching of 2D image shapes. ISPRS Annals 2012: I-3: 191-196. DOI: 10.5194/isprsannals-I-3-191-2012.
  8. Vizilter YuV, Gorbatsevich VS, Rubis AYu, Zheltov SYu. Shape-based image matching using heat kernels and diffusion maps. Int Arch Photogramm Remote Sens Spat Inf Sci 2014; XL-3: 357-364.
  9. Vizilter YuV, Gorbatsevich VS, Rubis AYu, Vygolov OV. Image shape matching using diffusion morphology and diffusion correlation. Computer Optics 2015; 39(2): 265-274. DOI: 10.18287/0134-2452-2015-39-2-265-274.

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