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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...
www.scielo.br/cam Fractal coding based on image local fractal dimension
"... Abstract. Fractal codification of images is based on selfsimilar and selfaffine sets. The codification process consists of construction of an operator which will represent the image to be encoded. If a complicated picture can be represented by an operator then it will be transmitted or stored very ..."
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Abstract. Fractal codification of images is based on selfsimilar and selfaffine sets. The codification process consists of construction of an operator which will represent the image to be encoded. If a complicated picture can be represented by an operator then it will be transmitted or stored very efficiently. Clearly, this has many applications on data compression. The great disadvantage of the automatic form of fractal compression is its encoding time. Most of the time spent in construction of such operator is due on finding the best match between parts of the image to be encoded. However, since the conception of automatic fractal image compression, researches on improvement of the compression time are widespread. This work aims to provide a new idea for decrease the encoding time: a classification of image parts based on their local fractal dimension. The idea is implemented on two steps. First, a preprocessing analysis of the image identify the complexity of each image block computing its dimension. Then, only parts within the same range of complexity are used for testing the better selfaffine pairs, reducing the compression time. The performance of this proposition, is compared with others fractal image compression methods. The points considered are image fidelity, encoding time and amount of compression on the image file.
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...
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...