Morphological conditional estimates of image complexity and information content

We propose new morphological conditional estimates of image complexity and information content as well as morphological mutual information. These morphological estimates take into account both the number and the shape of image tessellation (mosaic) regions. We provide such a region shape account via joint use of mosaic image shape models based on the morphological image analysis (MIA) proposed by Yu. Pyt’ev and morphological thickness maps from the mathematical morphology (MM) introduced by J. Serra. Mathematical properties of morphological thickness maps are explored w.r.t. properties of structured elements, and corresponding properties of the proposed morphological image complexity and information content are proved. Some experimental results on image shape comparison in terms of shape complexity and information are reported. Open access images from a Kimia99 database are utilized for these experiments.

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IMAGE AND SHAPE COMPARISON VIA MORPHOLOGICAL CORRELATION

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xliv-2-w1-2021-207-2021 ◽

2021 ◽

Vol XLIV-2/W1-2021 ◽

pp. 207-211

Author(s):

Y. V. Vizilter ◽

S. Y. Zheltov ◽

M. A. Lebedev

Keyword(s):

Image Analysis ◽

Correlation Coefficient ◽

Image Matching ◽

Shape Matching ◽

Image Correlation ◽

Shape Comparison ◽

Shape Models ◽

Morphological Image Analysis ◽

Morphological Image ◽

Morphological Correlation

Abstract. A lot of image matching applications require image comparison to be invariant relative to intensity values variations. The Pyt’ev theory for Morphological Image Analysis (MIA) was developed based on image-to-shape matching with mosaic shape models. Within the framework of this theory, the problem of shape-to-shape comparison was previously considered too. The most sophisticated and weakest part of MIA theory is the comparison of mosaic shapes with some arbitrary restrictions described by graphs or relations. In this paper we consider the possible options for comparing images and shapes using morphological projection and morphological correlation. Our contribution is a new scheme of morphological shape-to-image projection and, correspondingly, the new morphological correlation coefficient (MCC) for shape-to-image correlation with restricted mosaic models. We also refine the expressions for shape-to-shape comparison.

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MORPHOLOGICAL IMAGE ANALYSIS BASED ON ATTRIBUTE AND RELATIONAL REPRESENTATIONS OF MOSAIC IMAGE MODELS

Vestnik komp iuternykh i informatsionnykh tekhnologii ◽

10.14489/vkit.2021.06.pp.019-028 ◽

2021 ◽

pp. 19-28

Author(s):

Yu. V. Vizilter ◽

O. V. Vygolov ◽

S. Yu. Zheltov ◽

A. V. Morzhin

Keyword(s):

Image Analysis ◽

Morphological Analysis ◽

Image Model ◽

Morphological Operators ◽

Mosaic Image ◽

Morphological Image Analysis ◽

Morphological Operator ◽

Image Models ◽

Morphological Image ◽

Functional Attribute

A unified scheme for morphological analysis based on attribute and relational representations of mosaic image models is proposed. We consider 4 main types of model representation: functional-attribute (2D feature map), functional-relational (4D relational map), structure-resource-attribute (an area list with resources and attributes), and structure-resource-relational (a graph, which nodes correspond to regions and edges – to relations and both having resource attributes). In this case, the forms of representation of the model are equivalent to each other, in the sense that they contain the same information, there is a one-to-one correspondence between them, and the formulas for the transition from one representation to another can be written out explicitly. In this scheme, the construction of specific morphological operator for some complete image model presumes the separation of this model into two parts: the guiding (modifying) part, which determines the transformation algorithm, and the guided (modifiable) part to be transformed. These two parts of the model can intersect, therefore cannot be called “variable” and “constant” components. As a basic sample, we consider the halftone Pyt’ev morphology. We explore the specifics of different-sort models, introduce the mutual models and propose different tools for creation of model-based morphological operators. Further, various other morphological systems can be described and explored using the proposed generalized approach.

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Comparison of statistical properties for various morphological filters based on mosaic image shape models

Computer Optics ◽

10.18287/2412-6179-co-842 ◽

2021 ◽

Vol 45 (3) ◽

pp. 449-460

Author(s):

Y.V. Vizilter ◽

O.V. Vygolov ◽

S.Y. Zheltov

Keyword(s):

Qualitative Difference ◽

Statistical Properties ◽

Morphological Filters ◽

Linear Filters ◽

Shape Models ◽

Image Shape ◽

Shape Simplification ◽

Shape Complexity ◽

The Relationship ◽

Morphological Correlation

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.

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