## №2, 2019

# DEVELOPMENT OF THE FUZZY REPRESENTATION OF A DIGITAL IMAGE BASED ON A FRACTAL MODEL

The objective of the work is to improve the quality of digital image processing in vision systems by developing new features based on the use of fractal theory in conjunction with fuzzy logic and the theory of fuzzy sets. To develop a system of new features, a new model of digital image is needed. It is proposed to modify the fractal model by using a fuzzy distance in it as a measure of similarity of the image areas. This allows you to expand the hierarchy of representations of the source image, thereby increasing the amount of useful information about the original image. The modification of fractal attributes' system is proposed by using the membership function as the main metric, which allows using fuzzy logic in the formation of characteristic values. The proposed new model and a new system of features based on the use of fuzzy measures and membership functions will allow developing new image processing algorithms that differ from the existing possibility of using fuzzy conclusions and results (pp.36-41).

**Keywords:**

*images processing, recognition, multiscale analysis, nanostructures.*

**DOI**: 10.25045/jpit.v10.i2.06

- Mario I. Chacon M. Fuzzy Logic for Image Processing: Definition and Applications of a Fuzzy Image Processing Scheme // Advanced Fuzzy Logic Technologies in Industrial Applications, 2006, pp.101–113.
- Tamalika Chaira. Fuzzy Measures in Image Processing // Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, 2008, pp.587–606.
- Chi Z., Yan H., Pham T. Fuzzy algorithms: With Applications to Image Processing and Pattern Recognition / Singapore, New Jersey, London, Hong Kong: Word Scientific, 1998, 225 p.
- Bing-Yuan Cao, Fuzzy Cluster Analysis and Fuzzy Recognition // Optimal Models and Methods with Fuzzy Quantities Studies in Fuzziness and Soft Computing, 2010, vol.248, pp.117–137.
- Zhiznyakov A.L., Privezentsev D.G., Zakharov A.A. Using fractal features of digital images for the detection of surface defects // Pattern Recognition and Image Analysis (Advances in Mathematical Theory and Applications), 2015, vol.25, no.1, pp.122–131.
- Privezentsev D.G., Zhiznyakov A.L. Use of characteristic image segments in tasks of digital image processing / 2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP), 2015, pp.659–660.
- Zhiznyakov A.L., Privezentsev D.G., Pugin E.V. Use of fractal signs of digital images for detection of surface defects / CriMiCo 2014 - 2014 24th International Crimean Conference Microwave and Telecommunication Technology Conference Proceedings, 2014, pp.391–392.