Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, th...Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.展开更多
We present lower and upper bounds for the box dimension of the graphs of certain nonaffine fractal interpolation functions by generalizing the results that hold for the affine case.
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the...Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.展开更多
Research and application of fractal theory in landscape design has greatly enriched the concepts and techniques of garden creation,and pushed forward landscape design closer to the natural world.By elaborating interna...Research and application of fractal theory in landscape design has greatly enriched the concepts and techniques of garden creation,and pushed forward landscape design closer to the natural world.By elaborating internal connection between fractal theory and landscape design,this paper uses iterative function system of the fractal theory and matlab to draw fractal trees.Two designed experiments demonstrate that the fractal theory can be employed to realize the vivid drawing of natural landscapes with the support of limited data.Therefore,fractal theory is a practical tool used to draw vivid natural landscapes efficiently.展开更多
In this paper, image compression and decompression are realized on a personal computer based on fractal theory. The algorithm is effectiveas as the reconstructed image is similar to the original. In the algorithm, the...In this paper, image compression and decompression are realized on a personal computer based on fractal theory. The algorithm is effectiveas as the reconstructed image is similar to the original. In the algorithm, the formulas for contrast scaling and luminance shift are simplified,and the Hausdorff distance is replaced by the Euclidean distance. Thus, the calculation load is reduced. The formula for compression ratio is presented for an ideal situation, from which one can analyze how the different factors influence image compression ratio.展开更多
This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its corresponding mathematical equations which are essential in fractal image construction.
Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the origina...Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the original function. These univariate properties are then used to investigate complete bicubic fractal splines over a rectangle Bicubic fractal splines are invariant in all scales and they generalize classical bicubic splines. Finally, for an original function , upper bounds of the error for the complete bicubic fractal splines and derivatives are deduced. The effect of equal and non-equal scaling vectors on complete bicubic fractal splines were illustrated with suitably chosen examples.展开更多
Some shortcomings of common fractal image coding methods are studied , then they are corrected with a new method. The new method is improved further in DCT domain. Coding results show the advantage of the new method.
Traditionally, fractal image compression suffers from lengthy encoding time in measure ofhours. In this paper, combined with characteristlcs of human visual system, a flexible classification technique is proposed. Thi...Traditionally, fractal image compression suffers from lengthy encoding time in measure ofhours. In this paper, combined with characteristlcs of human visual system, a flexible classification technique is proposed. This yields a corresponding adaptive algorithm which can cut down the encoding timeinto second's magnitude. Experiment results suggest that the algorithm can balance the overall encodingperformance efficiently, that is, with a higher speed and a better PSNR gain.展开更多
Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affin...Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.展开更多
Fast algorithms for reducing encoding complexity of fractal image coding have recently been an important research topic. Search of the best matched domain block is the most computation intensive part of the fractal en...Fast algorithms for reducing encoding complexity of fractal image coding have recently been an important research topic. Search of the best matched domain block is the most computation intensive part of the fractal encoding process. In this paper, a fast fractal approximation coding scheme implemented on a personal computer based on matching in range block's neighbours is presented.Experimental results show that the proposed algorithm is very simple in implementation, fast in encoding time and high in compression ratio while PSNR is almost the same as compared with Barnsley's fractal block coding .展开更多
The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system （IFS）...The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system （IFS） are incomplete. Then the representations of generalized product of IFS are discussed based on the theory of the product of fractal. Furthermore, the dimensional relations between the product of fractal and its semi-product are obtained. The dimensional relations of self-similar set are discussed. Finally, the examples for rendering fractal graphs are given. These results posses potentials in image compression and pattern recognition.展开更多
Using the forward-backward martingale decomposition and the martingale limit theorems, we establish the functional law of iterated logarithm for an additive functional (At) of a reversible Markov process, under the mi...Using the forward-backward martingale decomposition and the martingale limit theorems, we establish the functional law of iterated logarithm for an additive functional (At) of a reversible Markov process, under the minimal condition that σ~2(A)= tim BA_t~2/t exists in R. We extend also t →∞ the previous remarkable functional central limit theorem of Kipnis and Varadhan.展开更多
文摘Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.
文摘We present lower and upper bounds for the box dimension of the graphs of certain nonaffine fractal interpolation functions by generalizing the results that hold for the affine case.
文摘Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.
基金Supported by National University Student Innovation Program of Beijing Forestry University~~
文摘Research and application of fractal theory in landscape design has greatly enriched the concepts and techniques of garden creation,and pushed forward landscape design closer to the natural world.By elaborating internal connection between fractal theory and landscape design,this paper uses iterative function system of the fractal theory and matlab to draw fractal trees.Two designed experiments demonstrate that the fractal theory can be employed to realize the vivid drawing of natural landscapes with the support of limited data.Therefore,fractal theory is a practical tool used to draw vivid natural landscapes efficiently.
文摘In this paper, image compression and decompression are realized on a personal computer based on fractal theory. The algorithm is effectiveas as the reconstructed image is similar to the original. In the algorithm, the formulas for contrast scaling and luminance shift are simplified,and the Hausdorff distance is replaced by the Euclidean distance. Thus, the calculation load is reduced. The formula for compression ratio is presented for an ideal situation, from which one can analyze how the different factors influence image compression ratio.
文摘This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its corresponding mathematical equations which are essential in fractal image construction.
文摘Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the original function. These univariate properties are then used to investigate complete bicubic fractal splines over a rectangle Bicubic fractal splines are invariant in all scales and they generalize classical bicubic splines. Finally, for an original function , upper bounds of the error for the complete bicubic fractal splines and derivatives are deduced. The effect of equal and non-equal scaling vectors on complete bicubic fractal splines were illustrated with suitably chosen examples.
文摘Some shortcomings of common fractal image coding methods are studied , then they are corrected with a new method. The new method is improved further in DCT domain. Coding results show the advantage of the new method.
文摘Traditionally, fractal image compression suffers from lengthy encoding time in measure ofhours. In this paper, combined with characteristlcs of human visual system, a flexible classification technique is proposed. This yields a corresponding adaptive algorithm which can cut down the encoding timeinto second's magnitude. Experiment results suggest that the algorithm can balance the overall encodingperformance efficiently, that is, with a higher speed and a better PSNR gain.
基金supported by the National Natural Science Foundation of China (Grant Nos.60972004 and 60402004)
文摘Employing the properties of the affine mappings, a very novel fractal model scheme based on the iterative function system is proposed. We obtain the vertical scaling factors by a set of the middle points in each affine transform, solving the difficulty in determining the vertical scaling factors, one of the most difficult challenges faced by the fractal interpolation. The proposed method is carried out by interpolating the known attractor and the real discrete sequences from seismic data. The results show that a great accuracy in reconstruction of the known attractor and seismic profile is found, leading to a significant improvement over other fractal interpolation schemes.
文摘Fast algorithms for reducing encoding complexity of fractal image coding have recently been an important research topic. Search of the best matched domain block is the most computation intensive part of the fractal encoding process. In this paper, a fast fractal approximation coding scheme implemented on a personal computer based on matching in range block's neighbours is presented.Experimental results show that the proposed algorithm is very simple in implementation, fast in encoding time and high in compression ratio while PSNR is almost the same as compared with Barnsley's fractal block coding .
基金supported by National Natural Science Foundation of China (50575026, 50275013), National High-Tech. R&D Program for CIMS (2001AA412011).
文摘The definition of generalized product of fractal is first put forward for the research on the relations between original fractal and its product of fractal when the transformations of iteration function system （IFS） are incomplete. Then the representations of generalized product of IFS are discussed based on the theory of the product of fractal. Furthermore, the dimensional relations between the product of fractal and its semi-product are obtained. The dimensional relations of self-similar set are discussed. Finally, the examples for rendering fractal graphs are given. These results posses potentials in image compression and pattern recognition.
基金the National Natural Sciences Foundation of China the Foundation of Y.D. Fok.
文摘Using the forward-backward martingale decomposition and the martingale limit theorems, we establish the functional law of iterated logarithm for an additive functional (At) of a reversible Markov process, under the minimal condition that σ~2(A)= tim BA_t~2/t exists in R. We extend also t →∞ the previous remarkable functional central limit theorem of Kipnis and Varadhan.
