A hybrid of fractal image coding and fractal dimension for an efficient retrieval method
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A hybrid of fractal image coding and fractal dimension for an efficient retrieval method Nadia M. G. Al-Saidi1 · Shaimaa S. Al-Bundi2 · Neseif J. Al-Jawari3
Received: 11 June 2016 / Revised: 5 August 2016 / Accepted: 15 August 2016 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016
Abstract Fractal image coding (FIC) based on the inverse problem of an iterated function system plays an essential role in several areas of computer graphics and in many other interesting applications. Through FIC, an image can be transformed to compressed representative parameters and be expressed in a simple geometric way. Dealing with digital images requires storing a large number of images in databases, where searching such databases is time consuming. Therefore, finding a new technique that facilitates this task is a challenge that has received increasing attention from many researchers. In this study, a new method that combines fractal dimension (FD) which is an indicator of image complexity with the FIC scheme is proposed. Classifying images in databases according to their texture by using FD helps reduce the retrieval time of query images. The validity of the proposed method is evaluated using geosciences images. Result shows that the method is computationally attractive. Keywords Fractal encoding · Fractal dimension · Iterated function system · Fractal inverse problem · Collage theorem
Communicated by Cristina Turner.
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Nadia M. G. Al-Saidi [email protected] Shaimaa S. Al-Bundi [email protected] Neseif J. Al-Jawari [email protected]
1
Department of Applied Sciences, University of Technology, Baghdad, Iraq
2
Department of Mathematics, College of Education for pure Sciences, Ibn Al-Haitham, Baghdad University, Baghdad, Iraq
3
Department of Mathematics, College of Sciences, Al-Mustansiriah University, Baghdad, Iraq
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N. M. G. Al-Saidi et al.
1 Introduction Fractals are geometric shapes that exhibit a self-similarity nature at different scales. They were first introduced by Mandelbort (1982). According to him, a complex image can be created by iteratively transforming a set of equation. Barnesly (1988) used this idea and introduced a new technique called iterated function system (IFS) to express any image that is selfsimilar, or has a locality that is self-similar to a set of mathematical equations. This concept was first introduced by Hutchinson (1981). The construction of an operator to represent the lossless technique is based on self-affine sets. Representing images with operators facilitate their efficient transmission or storage. This advantage makes this attractive for use in many applications, such as geographical maps, digital libraries, and management of medical images. The exponential growth in the number of digital images from many sensors, such as; those of NASA, Landsat-7, and commercial satellites, has increased the need for new methods for handling and analyzing such types of data efficiently and effectively. Image retrieval methods are implemented with two appro
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