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Relevant bibliographies by topics / Fractal image coding

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Academic literature on the topic 'Fractal image coding'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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Journal articles on the topic "Fractal image coding"

1

LIAN, SHIGUO, XI CHEN, and DENGPAN YE. "SECURE FRACTAL IMAGE CODING BASED ON FRACTAL PARAMETER ENCRYPTION." Fractals 17, no. 02 (June 2009): 149–60. http://dx.doi.org/10.1142/s0218348x09004405.

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In recent work, various fractal image coding methods are reported, which adopt the self-similarity of images to compress the size of images. However, till now, no solutions for the security of fractal encoded images have been provided. In this paper, a secure fractal image coding scheme is proposed and evaluated, which encrypts some of the fractal parameters during fractal encoding, and thus, produces the encrypted and encoded image. The encrypted image can only be recovered by the correct key. To maintain security and efficiency, only the suitable parameters are selected and encrypted through investigating the properties of various fractal parameters, including parameter space, parameter distribution and parameter sensitivity. The encryption process does not change the file format, keeps secure in perception, and costs little time or computational resources. These properties make it suitable for secure image encoding or transmission.

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Barthel, Kai Uwe. "Entropy Constrained Fractal Image Coding." Fractals 05, supp01 (April 1997): 17–26. http://dx.doi.org/10.1142/s0218348x97000607.

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In this paper we present an entropy constrained fractal coding scheme. In order to get high compression rates, previous fractal coders used hierarchical coding schemes with variable range block sizes. Our scheme uses constant range block sizes, but the complexity of the fractal transformations is adapted to the image contents. The entropy of the fractal code can be significantly reduced by introducing geometrical codebooks of variable size and a variable order luminance transformation. We propose a luminance transformation consisting of a unification of fractal and transform coding. With this transformation both inter- and intra- block redundancy of an image can be exploited to get higher coding gain. The coding results obtained with our new scheme are superior compared to conventional fractal and transform coding schemes.

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LU, JIAN, JIAPENG TIAN, CHEN XU, and YURU ZOU. "A DICTIONARY LEARNING APPROACH FOR FRACTAL IMAGE CODING." Fractals 27, no. 02 (March 2019): 1950020. http://dx.doi.org/10.1142/s0218348x19500208.

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In recent years, sparse representations of images have shown to be efficient approaches for image recovery. Following this idea, this paper investigates incorporating a dictionary learning approach into fractal image coding, which leads to a new model containing three terms: a patch-based sparse representation prior over a learned dictionary, a quadratic term measuring the closeness of the underlying image to a fractal image, and a data-fidelity term capturing the statistics of Gaussian noise. After the dictionary is learned, the resulting optimization problem with fractal coding can be solved effectively. The new method can not only efficiently recover noisy images, but also admirably achieve fractal image noiseless coding/compression. Experimental results suggest that in terms of visual quality, peak-signal-to-noise ratio, structural similarity index and mean absolute error, the proposed method significantly outperforms the state-of-the-art methods.

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Chen, Yuanxu, Yupin Luo, and Dongcheng Hu. "Image superresolution using fractal coding." Optical Engineering 47, no. 1 (2008): 017007. http://dx.doi.org/10.1117/1.2835453.

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Jacquin, A. E. "Fractal image coding: a review." Proceedings of the IEEE 81, no. 10 (1993): 1451–65. http://dx.doi.org/10.1109/5.241507.

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Ida, T., and Y. Sambonsugi. "Image segmentation using fractal coding." IEEE Transactions on Circuits and Systems for Video Technology 5, no. 6 (1995): 567–70. http://dx.doi.org/10.1109/76.477072.

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Khaitu, Shree Ram, and Sanjeeb Prasad Panday. "Fractal Image Compression Using Canonical Huffman Coding." Journal of the Institute of Engineering 15, no. 1 (February 16, 2020): 91–105. http://dx.doi.org/10.3126/jie.v15i1.27718.

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Image Compression techniques have become a very important subject with the rapid growth of multimedia application. The main motivations behind the image compression are for the efficient and lossless transmission as well as for storage of digital data. Image Compression techniques are of two types; Lossless and Lossy compression techniques. Lossy compression techniques are applied for the natural images as minor loss of the data are acceptable. Entropy encoding is the lossless compression scheme that is independent with particular features of the media as it has its own unique codes and symbols. Huffman coding is an entropy coding approach for efficient transmission of data. This paper highlights the fractal image compression method based on the fractal features and searching and finding the best replacement blocks for the original image. Canonical Huffman coding which provides good fractal compression than arithmetic coding is used in this paper. The result obtained depicts that Canonical Huffman coding based fractal compression technique increases the speed of the compression and has better PNSR as well as better compression ratio than standard Huffman coding.

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YUEN, CHING-HUNG, and KWOK-WO WONG. "CRYPTANALYSIS ON SECURE FRACTAL IMAGE CODING BASED ON FRACTAL PARAMETER ENCRYPTION." Fractals 20, no. 01 (March 2012): 41–51. http://dx.doi.org/10.1142/s0218348x12500041.

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The vulnerabilities of the selective encryption scheme for fractal image coding proposed by Lian et al.1 are identified. By comparing multiple cipher-images of the same plain-image encrypted with different keys, the positions of unencrypted parameters in each encoded block are located. This allows the adversary to recover the encrypted depth of the quadtree by observing the length of each matched domain block. With this depth information and the unencrypted parameters, the adversary is able to reconstruct an intelligent image. Experimental results show that some standard test images can be successfully decoded and recognized by replacing the encrypted contrast scaling factor and brightness offset with specific values. Some remedial approaches are suggested to enhance the security of the scheme.

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Dalui, Indrani, SurajitGoon, and Avisek Chatterjee. "A NEW APPROACH OF FRACTAL COMPRESSION USING COLOR IMAGE." International Journal of Engineering Technologies and Management Research 6, no. 6 (March 25, 2020): 74–71. http://dx.doi.org/10.29121/ijetmr.v6.i6.2019.395.

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Fractal image compression depends on self-similarity, where one segment of a image is like the other one segment of a similar picture. Fractal coding is constantly connected to grey level images. The simplest technique to encode a color image by gray- scale fractal image coding algorithm is to part the RGB color image into three Channels - red, green and blue, and compress them independently by regarding each color segment as a specific gray-scale image. The colorimetric association of RGB color pictures is examined through the calculation of the relationship essential of their three-dimensional histogram. For normal color images, as a typical conduct, the connection necessary is found to pursue a power law, with a non- integer exponent type of a given image. This conduct recognizes a fractal or multiscale self-comparable sharing of the colors contained, in average characteristic pictures. This finding of a conceivable fractal structure in the colorimetric association of regular images complement other fractal properties recently saw in their spatial association. Such fractal colorimetric properties might be useful to the characterization and demonstrating of natural images, and may add to advance in vision. The outcomes got demonstrate that the fractal-based compression for the color image fills in similarly with respect to the color image.

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Götting, Detlef, Achim Ibenthal, and Rolf-Rainer Grigat. "Fractal Image Coding and Magnification Using Invariant Features." Fractals 05, supp01 (April 1997): 65–74. http://dx.doi.org/10.1142/s0218348x97000644.

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Fractal image coding has significant potential for the compression of still and moving images and also for scaling up images. The objective of our investigations was twofold. First, compression ratios of factor 60 and more for still images have been achieved, yielding a better quality of the decoded picture material than standard methods like JPEG. Second, image enlargement up to factors of 16 per dimension has been realized by means of fractal zoom, leading to natural and sharp representation of the scaled image content. Quality improvements were achieved due to the introduction of an extended luminance transform. In order to reduce the computational complexity of the encoding process, a new class of simple and suited invariant features is proposed, facilitating the search in the multidimensional space spanned by image domains and affine transforms.

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Dissertations / Theses on the topic "Fractal image coding"

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Ali, Maaruf. "Fractal image coding techniques and their applications." Thesis, King's College London (University of London), 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265858.

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Ebrahimpour-Komleh, Hossein. "Fractal techniques for face recognition." Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16289/1/Hossein_Ebrahimpour-Komleh_Thesis.pdf.

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Fractals are popular because of their ability to create complex images using only several simple codes. This is possible by capturing image redundancy and presenting the image in compressed form using the self similarity feature. For many years fractals were used for image compression. In the last few years they have also been used for face recognition. In this research we present new fractal methods for recognition, especially human face recognition. This research introduces three new methods for using fractals for face recognition, the use of fractal codes directly as features, Fractal image-set coding and Subfractals. In the first part, the mathematical principle behind the application of fractal image codes for recognition is investigated. An image Xf can be represented as Xf = A x Xf + B which A and B are fractal parameters of image Xf . Different fractal codes can be presented for any arbitrary image. With the defnition of a fractal transformation, T(X) = A(X - Xf ) + Xf , we can define the relationship between any image produced in the fractal decoding process starting with any arbitrary image X0 as Xn = Tn(X) = An(X - Xf ) + Xf . We show that some choices for A or B lead to faster convergence to the final image. Fractal image-set coding is based on the fact that a fractal code of an arbitrary gray-scale image can be divided in two parts - geometrical parameters and luminance parameters. Because the fractal codes for an image are not unique, we can change the set of fractal parameters without significant change in the quality of the reconstructed image. Fractal image-set coding keeps geometrical parameters the same for all images in the database. Differences between images are captured in the non-geometrical or luminance parameters - which are faster to compute. For recognition purposes, the fractal code of a query image is applied to all the images in the training set for one iteration. The distance between an image and the result after one iteration is used to define a similarity measure between this image and the query image. The fractal code of an image is a set of contractive mappings each of which transfer a domain block to its corresponding range block. The distribution of selected domain blocks for range blocks in an image depends on the content of image and the fractal encoding algorithm used for coding. A small variation in a part of the input image may change the contents of the range and domain blocks in the fractal encoding process, resulting in a change in the transformation parameters in the same part or even other parts of the image. A subfractal is a set of fractal codes related to range blocks of a part of the image. These codes are calculated to be independent of other codes of the other parts of the same image. In this case the domain blocks nominated for each range block must be located in the same part of the image which the range blocks come from. The proposed fractal techniques were applied to face recognition using the MIT and XM2VTS face databases. Accuracies of 95% were obtained with up to 156 images.

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Ebrahimpour-Komleh, Hossein. "Fractal techniques for face recognition." Queensland University of Technology, 2006. http://eprints.qut.edu.au/16289/.

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Fractals are popular because of their ability to create complex images using only several simple codes. This is possible by capturing image redundancy and presenting the image in compressed form using the self similarity feature. For many years fractals were used for image compression. In the last few years they have also been used for face recognition. In this research we present new fractal methods for recognition, especially human face recognition. This research introduces three new methods for using fractals for face recognition, the use of fractal codes directly as features, Fractal image-set coding and Subfractals. In the first part, the mathematical principle behind the application of fractal image codes for recognition is investigated. An image Xf can be represented as Xf = A x Xf + B which A and B are fractal parameters of image Xf . Different fractal codes can be presented for any arbitrary image. With the defnition of a fractal transformation, T(X) = A(X - Xf ) + Xf , we can define the relationship between any image produced in the fractal decoding process starting with any arbitrary image X0 as Xn = Tn(X) = An(X - Xf ) + Xf . We show that some choices for A or B lead to faster convergence to the final image. Fractal image-set coding is based on the fact that a fractal code of an arbitrary gray-scale image can be divided in two parts - geometrical parameters and luminance parameters. Because the fractal codes for an image are not unique, we can change the set of fractal parameters without significant change in the quality of the reconstructed image. Fractal image-set coding keeps geometrical parameters the same for all images in the database. Differences between images are captured in the non-geometrical or luminance parameters - which are faster to compute. For recognition purposes, the fractal code of a query image is applied to all the images in the training set for one iteration. The distance between an image and the result after one iteration is used to define a similarity measure between this image and the query image. The fractal code of an image is a set of contractive mappings each of which transfer a domain block to its corresponding range block. The distribution of selected domain blocks for range blocks in an image depends on the content of image and the fractal encoding algorithm used for coding. A small variation in a part of the input image may change the contents of the range and domain blocks in the fractal encoding process, resulting in a change in the transformation parameters in the same part or even other parts of the image. A subfractal is a set of fractal codes related to range blocks of a part of the image. These codes are calculated to be independent of other codes of the other parts of the same image. In this case the domain blocks nominated for each range block must be located in the same part of the image which the range blocks come from. The proposed fractal techniques were applied to face recognition using the MIT and XM2VTS face databases. Accuracies of 95% were obtained with up to 156 images.

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Cesbron, Fred́eŕique Chantal. "Multiresolution fractal coding of still images." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/15508.

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USUI, Shin'ichi, Masayuki TANIMOTO, Toshiaki FUJII, Tadahiko KIMOTO, and Hiroshi OHYAMA. "Fractal Image Coding Based on Classified Range Regions." Institute of Electronics, Information and Communication Engineers, 1998. http://hdl.handle.net/2237/14996.

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Tan, Teewoon. "HUMAN FACE RECOGNITION BASED ON FRACTAL IMAGE CODING." University of Sydney. Electrical and Information Engineering, 2004. http://hdl.handle.net/2123/586.

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Human face recognition is an important area in the field of biometrics. It has been an active area of research for several decades, but still remains a challenging problem because of the complexity of the human face. In this thesis we describe fully automatic solutions that can locate faces and then perform identification and verification. We present a solution for face localisation using eye locations. We derive an efficient representation for the decision hyperplane of linear and nonlinear Support Vector Machines (SVMs). For this we introduce the novel concept of $\rho$ and $\eta$ prototypes. The standard formulation for the decision hyperplane is reformulated and expressed in terms of the two prototypes. Different kernels are treated separately to achieve further classification efficiency and to facilitate its adaptation to operate with the fast Fourier transform to achieve fast eye detection. Using the eye locations, we extract and normalise the face for size and in-plane rotations. Our method produces a more efficient representation of the SVM decision hyperplane than the well-known reduced set methods. As a result, our eye detection subsystem is faster and more accurate. The use of fractals and fractal image coding for object recognition has been proposed and used by others. Fractal codes have been used as features for recognition, but we need to take into account the distance between codes, and to ensure the continuity of the parameters of the code. We use a method based on fractal image coding for recognition, which we call the Fractal Neighbour Distance (FND). The FND relies on the Euclidean metric and the uniqueness of the attractor of a fractal code. An advantage of using the FND over fractal codes as features is that we do not have to worry about the uniqueness of, and distance between, codes. We only require the uniqueness of the attractor, which is already an implied property of a properly generated fractal code. Similar methods to the FND have been proposed by others, but what distinguishes our work from the rest is that we investigate the FND in greater detail and use our findings to improve the recognition rate. Our investigations reveal that the FND has some inherent invariance to translation, scale, rotation and changes to illumination. These invariances are image dependent and are affected by fractal encoding parameters. The parameters that have the greatest effect on recognition accuracy are the contrast scaling factor, luminance shift factor and the type of range block partitioning. The contrast scaling factor affect the convergence and eventual convergence rate of a fractal decoding process. We propose a novel method of controlling the convergence rate by altering the contrast scaling factor in a controlled manner, which has not been possible before. This helped us improve the recognition rate because under certain conditions better results are achievable from using a slower rate of convergence. We also investigate the effects of varying the luminance shift factor, and examine three different types of range block partitioning schemes. They are Quad-tree, HV and uniform partitioning. We performed experiments using various face datasets, and the results show that our method indeed performs better than many accepted methods such as eigenfaces. The experiments also show that the FND based classifier increases the separation between classes. The standard FND is further improved by incorporating the use of localised weights. A local search algorithm is introduced to find a best matching local feature using this locally weighted FND. The scores from a set of these locally weighted FND operations are then combined to obtain a global score, which is used as a measure of the similarity between two face images. Each local FND operation possesses the distortion invariant properties described above. Combined with the search procedure, the method has the potential to be invariant to a larger class of non-linear distortions. We also present a set of locally weighted FNDs that concentrate around the upper part of the face encompassing the eyes and nose. This design was motivated by the fact that the region around the eyes has more information for discrimination. Better performance is achieved by using different sets of weights for identification and verification. For facial verification, performance is further improved by using normalised scores and client specific thresholding. In this case, our results are competitive with current state-of-the-art methods, and in some cases outperform all those to which they were compared. For facial identification, under some conditions the weighted FND performs better than the standard FND. However, the weighted FND still has its short comings when some datasets are used, where its performance is not much better than the standard FND. To alleviate this problem we introduce a voting scheme that operates with normalised versions of the weighted FND. Although there are no improvements at lower matching ranks using this method, there are significant improvements for larger matching ranks. Our methods offer advantages over some well-accepted approaches such as eigenfaces, neural networks and those that use statistical learning theory. Some of the advantages are: new faces can be enrolled without re-training involving the whole database; faces can be removed from the database without the need for re-training; there are inherent invariances to face distortions; it is relatively simple to implement; and it is not model-based so there are no model parameters that need to be tweaked.

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Bal, Shamit. "Image compression with denoised reduced-search fractal block coding." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq23210.pdf.

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Piché, Daniel G. "Complex Bases, Number Systems and Their Application to Fractal-Wavelet Image Coding." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1057.

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This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wavelet decomposition. To acknowledge this situation, a class of extensions of functions is developed. These are shown to be consistent with the Mallat algorithm. A formal definition of local IFS on wavelet trees (LIFSW) is constructed for MRA associated with number systems, along with an application to the inverse problem. From these investigations, a series of algorithms emerge, namely the Mallat algorithm using addressing in number systems, an algorithm for extending functions and a method for constructing LIFSW operators in higher dimensions. Applications to image coding are given and ideas for further study are also proposed. Background material is included to assist readers less familiar with the varied topics considered. In addition, an appendix provides a more detailed exposition of the fundamentals of IFS theory.

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Pich??, Daniel G. "Complex Bases, Number Systems and Their Application to Fractal-Wavelet Image Coding." Thesis, University of Waterloo, 2002. http://hdl.handle.net/10012/1057.

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This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wavelet decomposition. To acknowledge this situation, a class of extensions of functions is developed. These are shown to be consistent with the Mallat algorithm. A formal definition of local IFS on wavelet trees (LIFSW) is constructed for MRA associated with number systems, along with an application to the inverse problem. From these investigations, a series of algorithms emerge, namely the Mallat algorithm using addressing in number systems, an algorithm for extending functions and a method for constructing LIFSW operators in higher dimensions. Applications to image coding are given and ideas for further study are also proposed. Background material is included to assist readers less familiar with the varied topics considered. In addition, an appendix provides a more detailed exposition of the fundamentals of IFS theory.

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Alexander, Simon. "Two- and Three-Dimensional Coding Schemes for Wavelet and Fractal-Wavelet Image Compression." Thesis, University of Waterloo, 2001. http://hdl.handle.net/10012/1180.

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This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression. Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation. Two methods of approximating functions are discussed: Iterated function systems (IFS) and wavelet-based approximations. IFS methods approximate a function by the fixed point of an iterated operator, using consequences of the Banach contraction mapping principle. Natural images under a wavelet basis have characteristic coefficient magnitude decays which may be used to aid approximation. The relationship between quantization, modelling, and encoding in a compression scheme is examined. Context based adaptive arithmetic coding is described. This encoding method is used in the coding schemes developed. A coder with explicit separation of the modelling and encoding roles is presented: an embedded wavelet bitplane coder based on hierarchical context in the wavelet coefficient trees. Fractal (spatial IFSM) and fractal-wavelet (coefficient tree), or IFSW, coders are discussed. A second coder is proposed, merging the IFSW approaches with the embedded bitplane coder. Performance of the coders, and applications to two- and three-dimensional images are discussed. Applications include two-dimensional still images in greyscale and colour, and three-dimensional streams (video).

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Book chapters on the topic "Fractal image coding"

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Jin, Guohua, Qiang Wang, and Sheng Bi. "Hybrid Fractal Image Coding." In Lecture Notes in Electrical Engineering, 254–61. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6504-1_32.

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Dudbridge, F. "Least-Squares Block Coding by Fractal Functions." In Fractal Image Compression, 229–41. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-2472-3_12.

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Gharavi-Alkhansari, Mohammad, and Thomas S. Huang. "Fractal-Based Image and Video Coding." In Video Coding, 265–303. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-1337-3_7.

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Baharav, Z., D. Malah, and E. Karnin. "Hierarchical Interpretation of Fractal Image Coding and Its Applications." In Fractal Image Compression, 91–117. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-2472-3_5.

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Lin, H., and A. N. Venetsanopoulos. "Fast fractal image coding using pyramids." In Image Analysis and Processing, 649–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60298-4_327.

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Zhang, David, Xiaobo Li, and Zhiyong Liu. "Partial Fractal Model for Hybird Image Coding." In Data Management and Internet Computing for Image/Pattern Analysis, 77–95. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-1-4615-1527-2_5.

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Kwiatkowski, Jan, Wieslawa Kwiatkowska, Krzysztof Kawa, and Piotr Kania. "Using Fractal Coding in Medical Image Magnification." In Parallel Processing and Applied Mathematics, 517–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-48086-2_57.

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Guo, Hui, Jie He, Caixu Xu, and Dongling Li. "Image Retrieval Algorithm Based on Fractal Coding." In Machine Learning and Intelligent Communications, 254–69. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-04409-0_24.

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Amin, Sobia, Richa Gupta, and Deepti Mehrotra. "Analytical Review on Image Compression Using Fractal Image Coding." In Advances in Intelligent Systems and Computing, 309–21. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5699-4_30.

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Asati, Ranjita, M. M. Raghuwanshi, and Kavita R. Singh. "Fractal Image Coding-Based Image Compression Using Multithreaded Parallelization." In Information and Communication Technology for Competitive Strategies (ICTCS 2021), 559–69. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-0095-2_53.

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Conference papers on the topic "Fractal image coding"

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Shuenn-Shyang Wang and Wei-Kai Liao. "Weighted fractal image coding." In 2007 IEEE International Conference on Systems, Man and Cybernetics. IEEE, 2007. http://dx.doi.org/10.1109/icsmc.2007.4413578.

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Zhang, Zhengbing, Yaoting Zhu, Guang-Xi Zhu, Hanqiang Cao, and Donghui Xue. "Hybrid fractal image coding method." In Visual Communications and Image Processing '96, edited by Rashid Ansari and Mark J. T. Smith. SPIE, 1996. http://dx.doi.org/10.1117/12.233209.

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Titkov, Bronislav, Anatoli Tikhotskij, Alexandr Myboroda, and Helmut Buley. "Structure-based fractal image coding." In Advanced Imaging and Network Technologies, edited by Naohisa Ohta. SPIE, 1996. http://dx.doi.org/10.1117/12.251329.

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Wang, Jianji, Yuehu Liu, Ping Wei, Zhiqiang Tian, Yaochen Li, and Nanning Zheng. "Fractal image coding using SSIM." In 2011 18th IEEE International Conference on Image Processing (ICIP 2011). IEEE, 2011. http://dx.doi.org/10.1109/icip.2011.6116131.

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Liu, Xiaoping, Jiaxiong Peng, Mingyue Ding, and Ji Zhou. "Image matching based on fractal image coding." In International Conference on Intelligent Manufacturing, edited by Shuzi Yang, Ji Zhou, and Cheng-Gang Li. SPIE, 1995. http://dx.doi.org/10.1117/12.217452.

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Zhang, Zhiming, and Sile Yu. "Wavelet-fractal coding of image sequence." In Multispectral Image Processing and Pattern Recognition, edited by Jun Tian, Tieniu Tan, and Liangpei Zhang. SPIE, 2001. http://dx.doi.org/10.1117/12.442911.

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Sloan, Alan D. "Low-bit-rate fractal image coding." In SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, edited by Friedrich O. Huck and Richard D. Juday. SPIE, 1994. http://dx.doi.org/10.1117/12.179287.

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Alvarado-Nava, Oscar, Hilda Maria Chable Martinez, and Eduardo Rodriguez-Martinez. "GPGPU implementation of fractal image coding." In 2014 International Work Conference on Bio-inspired Intelligence (IWOBI). IEEE, 2014. http://dx.doi.org/10.1109/iwobi.2014.6913947.

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Shiping Zhu and Juqiang Chen. "Research on fractal image coding methods." In 2012 International Conference on Computer Science and Information Processing (CSIP). IEEE, 2012. http://dx.doi.org/10.1109/csip.2012.6309034.

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Fu, Ping, Shigang Wang, and Su Yan. "Error-control-based fractal coding algorithm." In Multispectral Image Processing and Pattern Recognition, edited by Jun Tian, Tieniu Tan, and Liangpei Zhang. SPIE, 2001. http://dx.doi.org/10.1117/12.442913.

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