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A range/domain approximation errorbased approach for fractal image compression
 IEEE Trans. Image Process
, 2006
"... Abstract—Fractals can be an effective approach for several applications other than image coding and transmission: database indexing, texture mapping, and even pattern recognition problems such as writer authentication. However, fractalbased algorithms are strongly asymmetric because, in spite of ..."
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Abstract—Fractals can be an effective approach for several applications other than image coding and transmission: database indexing, texture mapping, and even pattern recognition problems such as writer authentication. However, fractalbased algorithms are strongly asymmetric because, in spite of the linearity of the decoding phase, the coding process is much more time consuming. Many different solutions have been proposed for this problem, but there is not yet a standard for fractal coding. This paper proposes a method to reduce the complexity of the image coding phase by classifying the blocks according to an approximation error measure. It is formally shown that postponing range\slash domain comparisons with respect to a preset block, it is possible to reduce drastically the amount of operations needed to encode each range. The proposed method has been compared with three other fractal coding methods, showing under which circumstances it performs better in terms of both bit rate and/or computing time. Index Terms—Classification, feature vector, fractal image compression. I.
Fractal coding based on image local fractal dimension
 Computational and Applied Mathematics Journal
, 2005
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Fast Code Enhancement With Local Search For Fractal Image Compression
 Proc. IEEE Int. Conf. on Image Processing
, 2000
"... Optimal fractal coding consists of finding in a finite set of contractive affine mappings one whose unique fixed point is closest to the original image. Optimal fractal coding is an NPhard combinatorial optimization problem. Conventional coding is based on a greedy suboptimal algorithm known as col ..."
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Optimal fractal coding consists of finding in a finite set of contractive affine mappings one whose unique fixed point is closest to the original image. Optimal fractal coding is an NPhard combinatorial optimization problem. Conventional coding is based on a greedy suboptimal algorithm known as collage coding. In a previous study, we proposed a local search algorithm that significantly improves on collage coding. However, the algorithm, which requires the computation of many fixed points, is computationally expensive. In this paper, we provide techniques that drastically reduce the time complexity of the algorithm. 1. INTRODUCTION The ratedistortion results of the best fractal coders are inferior to those of the stateoftheart in image compression [14]. However, the potential of fractal image compression has not been fully exploited because current fractal schemes do not find optimal codes. In fractal image compression, the code is a representation of a contractive affine mapping...
Distortion Minimization with Fast Local Search for Fractal Image Compression
, 2000
"... this paper, we provide techniques that drastically ..."
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On the Inverse Problem of Fractal Compression
"... . The inverse problem of fractal compression amounts to determining a contractive operator such that the corresponding xed point approximates a given target function. The standard method based on the collage coding strategy is known to represent a suboptimal method. Why does one not search for optim ..."
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. The inverse problem of fractal compression amounts to determining a contractive operator such that the corresponding xed point approximates a given target function. The standard method based on the collage coding strategy is known to represent a suboptimal method. Why does one not search for optimal fractal codes? We will prove that optimal fractal coding, when considered as a discrete optimization problem, constitutes an NPhard problem, i.e., it cannot be solved in a practical amount of time. Nevertheless, when the fractal code parameters are allowed to vary continuously, we show that one is able to improve on collage coding by netuning some of the fractal code parameters with the help of dierentiable methods. The dierentiability of the attractor as a function of its luminance parameters is established. We also comment on the approximating behavior of collage coding, state a lower bound for the optimal attractor error, and outline an annealing scheme for improved fractal codin...
ENHANCED FRACTAL IMAGE CODING (FIC) WITH COLLAGE AND RECONSTRUCTION RESIDUALS
, 2006
"... Abstract. In this paper, two new paradigms are proposed with fractal collage and reconstruction residuals to enhance FIC. In the first new paradigm, FIC is optimized using the reconstruction residuals. In the second paradigm, the selected collage residuals are used to correct the iterated function s ..."
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Abstract. In this paper, two new paradigms are proposed with fractal collage and reconstruction residuals to enhance FIC. In the first new paradigm, FIC is optimized using the reconstruction residuals. In the second paradigm, the selected collage residuals are used to correct the iterated function system (IFS) of FIC, and an effective technique for coding the selected collage residuals is applied based on DCT and embedded bitplane coding. In the first paradigm, the reconstruction quality is improved without increasing the bit rate. Using the second paradigm, we can improve the reconstruction quality with a little bit (about 0.01 bpp) increase in bit rate. Experimental results show that the proposed paradigms achieve better performance than JPEG at lower bit rate and similar performance at higher bit rate.
Fractal Image Compression
 Proc. 1st Seminar on Information Technology and its Applications (ITA'91
, 1991
"... Standard graphics systems encode pictures by assigning an address and colour attribute for each point of the object resulting in a long list of addresses and attributes. Fractal geometry enables a newer class of geometrical shapes to be used to encode whole objects, thus image compression is achieve ..."
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Standard graphics systems encode pictures by assigning an address and colour attribute for each point of the object resulting in a long list of addresses and attributes. Fractal geometry enables a newer class of geometrical shapes to be used to encode whole objects, thus image compression is achieved. Compression ratios of 10,000:1 have been claimed by researchers 1 in this field. The fractal equations describing these shapes are very simple equations. Specifically, iterated function system (IFS) codes are investigated. The difficult inverse problem of finding a suitable IFS code whose fractal image is to represent the real image and hence achieve compression is investigated through the use of: a) a library of IFS codes and complex moments, b) the method of simulated annealing, for solving nonlinear equations of many parameters. Image Compression Image compression is reducing the number of bits required to represent an image in such a way that either an exact replica of the image (lossless compression) or an approximate replica (lossy compression) of the image can be retrieved. 1 M.F. BARNSLEY, A.D. SLOAN, "A better way to compress images", BYTE, Jan 1988, p.215223. Proc. 1 st Seminar on Information Technology and its Applications (ITA `91), Markfield Conf. Centre, Leicester, U.K., 29 Sept., 1991. 1 Canonical Representation of Digital Images A digital picture consists of an n m array of integer numbers or picture elements (pels), see Fig.1. n m pixels pixels Fig.1 Canonical Representation of Digital Images. If it takes B bits to encode each pel, then: n m B bits are required to represent the picture digitally. Thus for a 512 512 raster with 8 bits/pel: 512 512 8 = 2,097,152 bits. (A large number!) Reasons for Compressing Images 1) To reduce the speed...
SEE PROFILE
, 2010
"... On the accuracy of hiding information metrics: Counterfeit protection for education and important certificates Article in International journal of physical sciences · September 2010 ..."
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On the accuracy of hiding information metrics: Counterfeit protection for education and important certificates Article in International journal of physical sciences · September 2010