# Descriptive Analysis of Image Data - Basic Models

### I. Gurevich, V. Yashina

#### Abstract

The paper is devoted to the foundations, general methodology, the axiomatic and formal structures of the Descriptive Theory for Image Analysis (DTIA) providing a methodology, mathematical and computational techniques for automation of image analysis and estimation (IAE). The main purpose of theoretical apparatus of the DTIA is structuring of the variety of methods, operations and representations being used in IEA. The final goal of the DTIA is automated image mining: a) automated selection of techniques and algorithms for image recognition, estimation, and understanding; b) automated testing of the raw data quality and its suitability for solving the image recognition problem. The DTIA provides mathematical fundamentals for image mining. The axiomatics and formal structures of Descriptive Theory of Image Analysis provide the ways and means to represent and to describe images for its analysis and estimating. The main contributions of axiomatics are Descriptive Image Models: its definitions, classification, properties, interrelations, and conditions of generation.

#### References

- Grenander, U., 1993. General Pattern Theory. A Mathematical Study of Regular Structures, Clarendon Press, Oxford.
- Gurevich, I.B., 1991. Descriptive Technique for Image Description, Representation and Recognition. In Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications in the USSR, Vol.1, No1. -P.50-53.
- Gurevich, I.B., 2005. The Descriptive Approach to Image Analysis. Current State and Prospects. In Proceedings of 14th Scandinavian Conference, SCIA2005. LNCS 3540. - P.214-223.
- Gurevich, I.B., Yashina, V.V., 2003. Descriptive Image Algebras with One Ring. In Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Application, Vol.13, No.4. MAIK “Nauka/Interperiodica”.-P. 579-599.
- Gurevich, I.B., Yashina, V.V., 2005. Generating Descriptive Trees. In Proceedings, 10th International Fall Workshop on Vision, Modeling, and Visualization. Infix.-P.367-374.
- Gurevich, I.B., Yashina, V.V., 2006. Operations of Descriptive Image Algebras with One Ring. In Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications, Vol.16,No.3. Pleiades Publishing, Inc.-P.298-328.
- Ritter, G.X., Wilson, J.N., 2001. Handbook of Computer Vision Algorithms in Image Algebra, CRC Press Inc. 2nd edition.
- Zhuravlev, Yu.I., 1998. An Algebraic Approach to Recognition and Classification Problems. In Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications, Vol.8. MAIK "Nauka/Interperiodica".-P.59-100.

#### Paper Citation

#### in Bibtex Style

@conference{imta08,

author={I. Gurevich and V. Yashina},

title={Descriptive Analysis of Image Data - Basic Models},

booktitle={Proceedings of the 1st International Workshop on Image Mining Theory and Applications IMTA 2008 - Volume 1: IMTA, (VISIGRAPP 2008)},

year={2008},

pages={3-15},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002340000030015},

isbn={978-989-8111-25-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Workshop on Image Mining Theory and Applications IMTA 2008 - Volume 1: IMTA, (VISIGRAPP 2008)

TI - Descriptive Analysis of Image Data - Basic Models

SN - 978-989-8111-25-8

AU - Gurevich I.

AU - Yashina V.

PY - 2008

SP - 3

EP - 15

DO - 10.5220/0002340000030015

#### in Harvard Style

Gurevich I. and Yashina V. (2008). **Descriptive Analysis of Image Data - Basic Models** . In *Proceedings of the 1st International Workshop on Image Mining Theory and Applications IMTA 2008 - Volume 1: IMTA, (VISIGRAPP 2008)* ISBN 978-989-8111-25-8, pages 3-15. DOI: 10.5220/0002340000030015