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.
This work introduces a novel tool for interactive, real-time affine transformations of two dimensional IFS fractals. The tool uses some of the nice properties of the barycentric coordinates that are assigned to the po...This work introduces a novel tool for interactive, real-time affine transformations of two dimensional IFS fractals. The tool uses some of the nice properties of the barycentric coordinates that are assigned to the points that constitute the image ofa fractal, and thus enables any affine transformation of the affine basis, done by click-and-drag, to be immediately followed by the same affine transformation of the fractal. The barycentric coordinates can be relative to an arbitrary affine basis of ~2, but in order to have a better control over the fractal, a kind of minimal simplex that contains the fractal attractor is used.展开更多
Based on explanation of wavelet fractal compression method, the significance of introducing wavelet decomposition into conventional fractal compression method is deeply investigated from the point of theoretical and p...Based on explanation of wavelet fractal compression method, the significance of introducing wavelet decomposition into conventional fractal compression method is deeply investigated from the point of theoretical and practical view. The result of study can be regarded as valuable guidelines for taking advantages of wavelet transform to develop more effective image compression algorithm.展开更多
This paper presents a universal scheme （also called blind scheme） based on fractal compression and affinity propagation （AP） clustering to distinguish stego-images from cover grayscale images, which is a very chal...This paper presents a universal scheme （also called blind scheme） based on fractal compression and affinity propagation （AP） clustering to distinguish stego-images from cover grayscale images, which is a very challenging problem in steganalysis. Since fractal codes represent the ＂self-similarity＂ features of natural images, we adopt the statistical moment of fractal codes as the image features. We first build an image set to store the statistical features without hidden messages, of natural images with and and then apply the AP clustering technique to group this set. The experimental result shows that the proposed scheme performs better than Fridrich＇s traditional method.展开更多
Starting with a fractal-based image-compression algorithm based on wavelet transformation for hyperspectral images, the authors were able to obtain more spectral bands with the help of of hyperspectral remote sensing....Starting with a fractal-based image-compression algorithm based on wavelet transformation for hyperspectral images, the authors were able to obtain more spectral bands with the help of of hyperspectral remote sensing. Because large amounts of data and limited bandwidth complicate the storage and transmission of data measured by TB-level bits, it is important to compress image data acquired by hyperspectral sensors such as MODIS, PHI, and OMIS; otherwise, conventional lossless compression algorithms cannot reach adequate compression ratios. Other loss-compression methods can reach high compression ratios but lack good image fidelity, especially for hyperspectral image data. Among the third generation of image compression algorithms, fractal image compression based on wavelet transformation is superior to traditional compression methods,because it has high compression ratios and good image fidelity, and requires less computing time. To keep the spectral dimension invariable, the authors compared the results of two compression algorithms based on the storage-file structures of BSQ and of BIP, and improved the HV and Quadtree partitioning and domain-range matching algorithms in order to accelerate their encode/decode efficiency. The authors' Hyperspectral Image Process and Analysis System (HIPAS) software used a VC++6.0 integrated development environment (IDE), with which good experimental results were obtained. Possible modifications of the algorithm and limitations of the method are also discussed.展开更多
By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we exten...By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we extend this method to determine the Hurst exponents of some irregular self-affine fractal patterns. Experimental results show that optical fractional Fourier transform is a practical method for analyzing the self-affine fractal patterns.展开更多
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
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This work introduces a novel tool for interactive, real-time affine transformations of two dimensional IFS fractals. The tool uses some of the nice properties of the barycentric coordinates that are assigned to the points that constitute the image ofa fractal, and thus enables any affine transformation of the affine basis, done by click-and-drag, to be immediately followed by the same affine transformation of the fractal. The barycentric coordinates can be relative to an arbitrary affine basis of ~2, but in order to have a better control over the fractal, a kind of minimal simplex that contains the fractal attractor is used.
基金This project is supported by the National Natural Science Foundation of China (No. 69774030) Foundation for University Key Teacher by the Ministry of Education.
文摘Based on explanation of wavelet fractal compression method, the significance of introducing wavelet decomposition into conventional fractal compression method is deeply investigated from the point of theoretical and practical view. The result of study can be regarded as valuable guidelines for taking advantages of wavelet transform to develop more effective image compression algorithm.
基金supported by the National Natural Science Foundation of China under Grant No. 61070208the Postdoctor Foundation from North Electronic Systems Engineering Corporation
文摘This paper presents a universal scheme （also called blind scheme） based on fractal compression and affinity propagation （AP） clustering to distinguish stego-images from cover grayscale images, which is a very challenging problem in steganalysis. Since fractal codes represent the ＂self-similarity＂ features of natural images, we adopt the statistical moment of fractal codes as the image features. We first build an image set to store the statistical features without hidden messages, of natural images with and and then apply the AP clustering technique to group this set. The experimental result shows that the proposed scheme performs better than Fridrich＇s traditional method.
文摘Starting with a fractal-based image-compression algorithm based on wavelet transformation for hyperspectral images, the authors were able to obtain more spectral bands with the help of of hyperspectral remote sensing. Because large amounts of data and limited bandwidth complicate the storage and transmission of data measured by TB-level bits, it is important to compress image data acquired by hyperspectral sensors such as MODIS, PHI, and OMIS; otherwise, conventional lossless compression algorithms cannot reach adequate compression ratios. Other loss-compression methods can reach high compression ratios but lack good image fidelity, especially for hyperspectral image data. Among the third generation of image compression algorithms, fractal image compression based on wavelet transformation is superior to traditional compression methods,because it has high compression ratios and good image fidelity, and requires less computing time. To keep the spectral dimension invariable, the authors compared the results of two compression algorithms based on the storage-file structures of BSQ and of BIP, and improved the HV and Quadtree partitioning and domain-range matching algorithms in order to accelerate their encode/decode efficiency. The authors' Hyperspectral Image Process and Analysis System (HIPAS) software used a VC++6.0 integrated development environment (IDE), with which good experimental results were obtained. Possible modifications of the algorithm and limitations of the method are also discussed.
文摘By means of experimental technique of optical fractional Fourier transform, we have determined the Hurst exponent of a regular self-affine fractal pattern to demonstrate the feasibility of this approach. Then we extend this method to determine the Hurst exponents of some irregular self-affine fractal patterns. Experimental results show that optical fractional Fourier transform is a practical method for analyzing the self-affine fractal patterns.
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.
