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Partitioned iterated function systems with division and a fractal dependence graph in recognition of 2D shapes

Gdawiec K., Domańska D.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 4

757-767

One of the approaches in pattern recognition is the use of fractal geometry. The property of self-similarity of fractals has been used as a feature in several pattern recognition methods. All fractal recognition methods use global analysis of the shape. In this paper we present some drawbacks of these methods and propose fractal local analysis using partitioned iterated function systems with division. Moreover, we introduce a new fractal recognition method based on a dependence graph obtained from the partitioned iterated function system. The proposed method uses local analysis of the shape, which improves the recognition rate. The effectiveness of our method is shown on two test databases. The first one was created by the authors and the second one is the MPEG7 CE-Shape-1PartB database. The obtained results show that the proposed methodology has led to a significant improvement in the recognition rate.

A study on Partitioned Iterative Function Systems for image compression

Mitra S.K., Murthy C.A., Kundu M.K.

Fundamenta Informaticae

1998

Vol. 34, nr 4

413-428

The technique of image compression using Iterative Function System (IFS) is known as fractal image compression. An extension of IFS theory is called as Partitioned or local Iterative Function System (PIFS) for coding the gray level images. The theory of PIFS appears to be different from that of IFS in the sense of application domain. Assuming the theory of PIFS is the same as that of IFS, several techniques of image compression have been developed. In the present article we have studied the PIFS scheme as a separate one and proposed a mathematical formulation for the existence of its attractor. Moreover the results of a Genetic Algorithm (GA) based PIFS technique is presented. This technique appears to be efficient in the sense of computational cost.