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An increasing demand of secure data transmission over internet leads to the challenge of implementing a consistent cryptosystem. In 2004, USA navy published the patent which highlights the importance of fractal as an encryption/decryption key in a cryptosystem [1]. Fractal possess butterfly effect i.e. sensitivity to initial condition, due to which small change in input produces a major change in output. This paper summarizes the various recent image encryption techniques in which fractal key is used to encrypt/decrypt followed by substitution, scrambling and diffusion techniques to provide strong cryptosystem. The algorithms covered both private key encryption as well as public key encryption technique in the paper. The analysed algorithms include a set of fractal function such as Mandelbrot set, Julia set, Hilbert curve, 3D fractal, multi-fractal, IFS and chaotic function to generate a complex key used in the encryption process. Corresponding performance of each algorithm is analysed by PSNR test, key space, sensitivity analysis and correlation coefficient value between the adjacent pixels of both images (Original image and encrypted image) which shows significant improvement in performance over the traditional encryption methods.

This paper applies the entropy-based fractal indexing scheme that enables the grid environment for fast indexing and querying. It addresses the issue of fault tolerance and load balancing-based fractal management to make computational grids more effective and reliable. A fractal dimension of a cloud of points gives an estimate of the intrinsic dimensionality of the data in that space. The main drawback of this technique is the long computing time. The main contribution of the suggested work is to investigate the effect of fractal transform by adding R-tree index structure-based entropy to existing grid computing models to obtain a balanced infrastructure with minimal fault. In this regard, the presented work is going to extend the commonly scheduling algorithms that are built based on the physical grid structure to a reduced logical network. The objective of this logical network is to reduce the searching in the grid paths according to arrival time rate and path&rsquo, s bandwidth with respect to load balance and fault tolerance, respectively. Furthermore, an optimization searching technique is utilized to enhance the grid performance by investigating the optimum number of nodes extracted from the logical grid. The experimental results indicated that the proposed model has better execution time, throughput, makespan, latency, load balancing, and success rate.

This paper presented comprehensive study with performance analysis of very recent Wavelet transform based image compression techniques. Image compression is one of the necessities for such communication. The goals of image compression are to minimize the storage requirement and communication bandwidth. Compression is achieved by the removal of redundant data. Discrete Wavelet Transform (DWT) is a recently developed compression technique in image compression. DWT image compression includes decomposition (transform of image), Detail coefficients thresholding, and entropy encoding. This paper mainly describes the transform of an image using DWT and thresholding techniques. In this paper we have taken the standard image Lena of size 256X256 of 8 bit depth and applied DWT (haar). Then two results set are obtained by applying two different techniques of thresholding and then compare the result.Keywords: Discrete Cosine Transform, Wavelet Transform, JPEG Compression and Entropy Encoding

Main objective of the proposed work is to develop an approach for video coding based on Fractal coding using the weighted finite automata (WFA). The proposed work only focuses on reducing the encoding time as this is the basic limitation why the Fractal coding not becomes the practical reality. WFA is used for the coding as it behaves like the Fractal Coding (FC). WFA represents an image based on the idea of fractal that the image has self-similarity in itself. The plane WFA (applied on every frame), and Plane FC (applied on every frame) coding approaches are compared with each other. The experimentations are carried out on the standard uncompressed video databases, namely, Traffic, Paris, Bus, Akiyo, Mobile, Suzie etc. and on the recorded video, namely, Geometry and Circle. Developed approaches are compared on the basis of performance evaluation parameters, namely, encoding time, decoding time, compression ratio, compression percentage, bits per pixel and Peak Signal to Noise Ratio (PSNR). Though the initial number of states is 256 for every frame of all the types of videos, but we got the different number of states for different frames and it is quite obvious due to minimality of constructed WFA for respective frame. Based on the obtained results, it is observed that the number of states is more in videos namely, Traffic, Bus, Paris, Mobile, and Akiyo, therefore the reconstructed video quality is good in comparison with other videos namely, Circle, Suzie, and Geometry.

This paper presents a novel approach to calculate the affine parameters of fractal encoding, in order to reduce its computational complexity. A simple but efficient approximation of the scaling parameter is derived which satisfies all properties necessary to achieve convergence. It allows us to substitute to the costly process of matrix multiplication with a simple division of two numbers. We have also proposed a modified horizontal-vertical (HV) block partitioning scheme, and some new ways to improve the encoding time and decoded quality, over their conventional counterparts. Experiments on standard images show that our approach yields performance similar to the state-of-the-art fractal based image compression methods, in much less time.

In this paper, the ancient Chinese algorithm is applied to derive fractal microgravity forced oscillator’s frequency–amplitude response curves using the two-scale fractal transform derivative. Depending on the fractal parameter values, it is shown that the system restoring forces exhibit hardening or softening behavior. Furthermore, the proposed solution approach is simple, efficient, and accurate for obtaining the approximate steady-state solution of a fractal microgravity nonlinear oscillator with a purely nonlinear power-form restoring force.

The box-counting (BC) method is frequently used as a measure of irregularity and roughness of fractals with self-similarity property due to its simplicity and high reliability. It requires a proper choice of the number of box sizes, corresponding sizes, and size limits to guarantee the accuracy of the fractal dimension estimation. Most of the existing BC methods utilize the geometric-step method, which causes a lack of fitting data points and wasted pixels for images of large size and/or arbitrary size. This paper presents a BC algorithm in combination with a novel sampling method and fractional box-counting method which will allow us to overcome some of limitations evident in the conventional BC method. The new sampling method introduces a partial competition based on the coverage of box sizes and takes more number of box sizes than the geometric-step method. To circumvent the border problem occurring for images of arbitrary size, the fractional box-counting method allows the number of the boxes to be real, rather than integer. To show its feasibility, the proposed method is applied to a set of fractal images of exactly known fractal dimension.

With the rapid development of computer science, problems with digital products piracy and copyright dispute become more serious; therefore, it is an urgent task to find solutions for these problems. In this study, the authors' develop a digital watermarking algorithm based on a fractal encoding method and the discrete cosine transform (DCT). The proposed method combines fractal encoding method and DCT method for double encryptions to improve traditional DCT method. The image is encoded by fractal encoding as the first encryption, and then encoded parameters are used in DCT method as the second encryption. First, the fractal encoding method is adopted to encode a private image with private scales. Encoding parameters are applied as digital watermarking. Then, digital watermarking is added to the original image to reversibly using DCT, which means the authors can extract the private image from the carrier image with private encoding scales. Finally, attacking experiments are carried out on the carrier image by using several attacking methods. Experimental results show that the presented method has higher performance characteristics such as robustness and peak signal to noise ratio than classical methods.

The image compression performance of transform coders highly depends on the energy compaction (EC) capability of transforms. The popular transforms such as discrete cosine transform (DCT) and discrete wavelet transform (DWT) provide decent EC; however, their capability is not enough to deliver good quality image reconstruction for higher compression levels (CLs). In this study, the authors propose a new hybrid transform which is a fusion of wavelet packet transform (WPT) and block-DCT (BDCT) transform to achieve high-quality image compression. This new hybrid WPT-BDCT transform is able to attain higher EC than the existing transforms. Further, the authors have found a new energy compaction index (ECI) to evaluate the energy compactness of the image transforms. The proposed hybrid transform has been extensively evaluated, based on proposed ECI parameter, the visual quality assessment of reconstructed images and with the standard image quality indexes peak-signal-to-noise ratio and structural similarity index measure. It is reported that the proposed hybrid transform provides higher EC and outperforms the transforms namely DCT, DWT, WPT, multi-wavelet transform and existing hybrid transforms for all the CLs.

Objective: To develop a system that aims at optimal storage for voluminous image data sets that are acquired during various events, by generating codebook for image clusters by exploiting the fact that these images are generally multiple shots of similar scenes at frequent intervals. Methods: Images taken during the events on various occasions in organizations are increasing exponentially and pose tremendous challenge in terms of storage and retrieval. The volume, veracity and variety of features present in image data induce complexity in computation. Optimal storage and efficient tagging will ease the retrieval process of these image data. Among various lossy image compression techniques, vector quantization yields desirable compression ratio in many applications and is one of the efficient approaches for image compression. In this research work, vector quantization technique is explored to optimize the storage space required to maintain an archive of event image data set, by generating code book for a cluster of images. Findings: The similarity in the images that are acquired during a short span of time induces redundancy. This fact has been exploited by organizing the image data set into clusters that are similar. For each cluster, vector quantization technique is used to generate code book. The codebook generated has been used to encode the image by creating an index table for each image. The codebook of the cluster and the index table of each image is further used for decoding. The compression ratio and the peak signal to noise ratio of this method are above eighty percent and thirty DB respectively. Applications: The codebook generation technique described in this work could be applied for creating image archives. Archival images are generally voluminous and consume huge storage space. The code book generated for image clusters would reduce the storage requirement. This work also finds its application in transmitting video and image clusters in a network.

The concept of a mapping, which takes its values in an infinite-dimensional functional space, has been studied by the mathematical community since the third decade of the last century. This effort has produced a range of important contributions, many of which have already made their way to applied sciences, where they have been successfully used to facilitate numerous practical applications across various fields. Surprisingly enough, one particular field, which could have benefited from the above contributions to a much greater extent, still relies on finite-dimensional models and approximations, thus missing out on numerous advantages offered through adopting a more general framework. This field is image processing, which is in the focus of this study. In particular, in this paper, we introduce an alternative approach to the analysis of multidimensional imagery data based on the mathematical theory of function-valued mappings. In addition to extending various tools of standard functional calculus, we generalize the notions of Fourier and fractal transforms, followed by their application to processing of multispectral imaging data. Some applications and future extensions of this work are discussed as well. HighlightsWe propose an alternative approach for the analysis of multidimensional images.Fourier transforms of function-valued mappings (FVMs) are defined.We derive an Euler-Lagrange equation for functionals which operate on FVMs.A class of fractal transforms (FTs) for FVMs is defined, allowing fractal coding.We show how an FT on an FVM induces a generalized FT on its Fourier transform.

Transform coding is commonly used in image processing algorithms to provide high compression ratios, often at the expense of processing time and simplicity of the system. We have recently proposed a pixel value prediction scheme in order to exploit adjacent pixel correlation, providing a low-complexity model for image coding. However, the proposed model was unable to reach high compression ratios retaining high quality of reconstructed image at the same time. In this paper we propose a new segmentation algorithm which further utilizes adjacent pixel correlation, provides higher compression ratios and it is based on application of Hadamard transform coding. Additional compression is provided by using vector quantization for a low number of quantization levels and by simplifying generalized Lloyd’s algorithm where the special attention is paid to determination of optimal partitions for vector quantization, making a fixed quantizer. The proposed method is quite simple and experimental results show that it ensures better or similar rate-distortion ratio for very low bit-rates, comparing to the other similar methods that are based on wavelet or curvelet transform coding and support or core vector machine application. Furthermore, the proposed method requires very low processing time since the proposed quantizers are fixed, much less than the required time for the aforementioned methods that we compare with as well as much less than the time required for fractal image coding. In the end, the appropriate discussion is provided comparing the results with a scheme based on linear prediction and dual-mode quantization.

This study aim was to increase the compression ratio and find out how much memory could be saved but also maintaining the quality of the image. The study was quantitative-analytic used samples of simple random sampling. Singular Value Decomposition algorithm (SVD) is a mathematical method to decipher a single matrix by compressing into three smaller matrices of the same size by reducing the data in columns and rows. while Discrete Wavelet Transform (DWT) is excellent in image energy concentrated on a small group of coefficients. It could also provide a combination of information about the frequency and scale resulting in a more accurate image reconstruction. Incorporation of these methods a compression system was lossy compression. The results of the compression process were carried out by compression rate calculation and MSSIM. The results of the study showed that compression system using a combination of SVD –DWT had a good performance. At Threshold_T = 15 and rank criteria _K = 4 generated the compression rate of 15.04% - 39.67%, or an average = 29.35% and MSSIM between 0.99 51,847 to 0.99 94 172 or average = 0.996219 with status almost close to 1, which mean the image of the original image compression and it could not be distinguished visual, it saved memory about 29.81%. It was better than DWT method tested in the same case with the result of the compression rate 28.85%.

The paper presents the possibilities of using the fractal dimension to evaluate the signals in wavelet decomposition process. The tests have been carried out on samples produced by face milling process for the six types of materials. It has been shown that the fractal dimension enables characterize signal irregularities in quantitatively and qualitatively way.

Video compression has become more and more important nowadays along with the increasing application of video sequences and rapidly growing resolution of them. H.264 is a widely applied video coding standard for academic and commercial purposes. And fractal theory is one of the most active branches in modern mathematics, which has shown a great potential in compression. In this paper, this study proposes an improved inter prediction algorithm for video coding based on fractal theory and H.264. This study take the same approach to make intra predictions as H.264 and this study adopt the fractal theory to make inter predictions. Some improvements are introduced in this algorithm. First, luminance and chrominance components are coded separately and the partitions are no longer associated as in H.264. Second, the partition mode for chrominance components has been changed and the block size now rages from $16\times 16$ to $4\times 4$ , which is the same as luminance components. Third, this study introduced adaptive quantization parameter offset, changing the offset for every frame in the quantization process to acquire better reconstructed image. Comparison between the improved algorithm, the original fractal compress algorithm and JM19.0 (The latest H.264/AVC reference software) confirms a slightly increase in Peak Signal-to-Noise Ratio, a significant decrease in bitrate while the time consumed for compression remains less than 60% of that using JM19.0.

At present, a hyperspectral image has a significant advantage in the aspect of application because of its high spectral resolution. However, owing to the limit of communication capacity, a hyperspectral image must be compressed. In this paper, we develop and propose a fractal lossy hyperspectral image compression method based on prediction. First, we exploit spatial correlation by applying predictive lossy compression to obtain a reference band of high quality. Then, the local similarity between the two adjacent bands is used through fractal encoding using a local search algorithm. Next, we encode the fractal parameters and the error and fractal residual is transformed by discrete cosine transform, quantized, and entropy encoded to improve the decoded quality. Through experiments, we demonstrate that the proposed algorithm leads to considerably improved performance in compression compared with the other well-known methods. Finally, we validate whether the compression affects the data in the hyperspectral images through classification. The results indicate that the accuracy of classification obtained for the reconstructed image is marginally less than the accuracy reported for the original data set; however, the loss in accuracy is less than 1% and thus acceptable.

Transform coding plays a very important role in image and video compression. Discrete Cosine Transform (DCT) is used as standard scheme (i.e. JPEG) in lossy image compression. Consequently, integer Discrete Cosine Transform (iDCT) is presented to achieve lossless compression for the compatibility of JPEG. Presently, with the investigation of new and well performed image transform techniques, there is an undeniable need for novel transform coding technologies to improve the compression rates and reduce computational complexity in the field of transform based lossless image compression. Discrete Tchebichef Transform (DTT) is a potentially unexploited orthogonal transform, and has shown a number of valuable properties like energy compaction and recursive computation. It has been preliminarily introduced in lossy image compression and shown the superiority in the compression rates. However, the DTT has not been investigated in lossless image compression. In this paper, we study DTT and matrix factorization theory firstly, and then factorize the N×N DTT matrix into N+1 single-row elementary reversible matrices (SERMs) with minimum rounding errors. On this base, we introduce a novel algorithm, named integer DTT (iDTT), to achieve integer to integer mapping for efficient lossless image compression. A series of experiments are carried out and results show that the proposed iDTT algorithm not only has higher compression ratio than iDCT method, but also is compatible with the widely used JPEG standard. A framework of lossless image compression based on integer DTT is proposed.The compression efficiency of integer DTT is higher than integer DCT.The proposed lossless image compression scheme is compatible with JPEG.Both lossy and lossless image compression can be realized under the proposed scheme.A lossless color transform method based on traditional RGB to YCbCr is presented.

Fractal image compression is an innovative way of image representation by using relationships among the sub-section of image itself. It utilizes the existence of self-symmetry and uses affine contractive transforms. This technique has manifold advantages like, very high compression ratio, high decompression speed, high bit-rate and resolution independence, but high computation time expenses of suitable domain search in coding phase is the major bottleneck of the technique. This paper presents a fast fractal compression scheme based on feature extraction and innovative way of image comparison. In proposed development the complexity of suitable domain search is reduced by transforming the problem from image domain to vector domain. Simulation results confirms that suggested variant leads to a faster system as compared to existing state-of art Fractal Image Compression techniques.

Fractal image coding (FIC) based on the inverse problem of an iterated function system plays an essential role in several areas of computer graphics and in many other interesting applications. Through FIC, an image can be transformed to compressed representative parameters and be expressed in a simple geometric way. Dealing with digital images requires storing a large number of images in databases, where searching such databases is time consuming. Therefore, finding a new technique that facilitates this task is a challenge that has received increasing attention from many researchers. In this study, a new method that combines fractal dimension (FD) which is an indicator of image complexity with the FIC scheme is proposed. Classifying images in databases according to their texture by using FD helps reduce the retrieval time of query images. The validity of the proposed method is evaluated using geosciences images. Result shows that the method is computationally attractive.

This paper investigates image data compression as it is applicable to different fields of image processing, in order to reduce the volume of pictorial data which one may need to store or transmit, The research modifies a method for image data compression based on the two component code, in this coding technique, the image is partitioned into regions of slowly varying intensity. The contours separating the regions are coded by hadamard transform, while the rest image regions are coded by (AMBTC).

A lossy hyperspectral image compression scheme based on intra-band prediction and inter-band fractal is proposed.Intra-band prediction exploiting spatial correlation is applied to I-bands.Inter-band fractal encoding with a local search algorithm is applied to P-bands.SVM classification accuracy for the reconstructed image is slightly higher than that for the original one. Recently, hyperspectral image compression has become an urgent issue for remote sensing applications. A lossy hyperspectral image compression scheme based on intra-band prediction and inter-band fractal encoding is put forward in this paper. The hyperspectral image is firstly partitioned into several groups of bands (GOBs). Intra-band prediction is applied to the first band in each GOB, exploiting spatial correlation, while inter-band fractal encoding with a local search algorithm is applied to the other bands in each GOB, making use of the local similarity between two adjacent bands. The fractal parameters are signed Exp-Golomb entropy encoded. To improve the decoded quality, the prediction error and fractal residual are further transformed, quantized, and entropy encoded. Experimental results illustrate that the proposed scheme can obtain a better compression performance with low complexity compared with other well-known methods. In addition, the effect of compression on SVM (Support Vector Machine) classification is presented. Display Omitted

The DCT-based JPEG image compression technique is a standard for lossy image compression. But the technique is not suitable at high compression ratios. Again, it is resolution dependent. Alternativ...

This paper suggests techniques to enhance coding time which is a problem in traditional fractal compression and to improve fidelity of reconstructed images by determining fractal coefficient through adaptive selection of block approximation formula. First, to reduce coding time, we construct a linear list of domain blocks of which characteristics is given by their luminance and variance and then we control block searching time according to the first permissible threshold value. Next, when employing three-level block partition, if a range block of minimum partition level cannot find a domain block which has a satisfying approximation error, There applied to 24-bpp color image compression and image techniques. The result did not occur a loss in the image quality of the image when using the encoding method, such as almost to the color in the YIQ image compression rate and image quality, such as RGB images and showed good.

In this work a lossless wavelet-fractal image coder is proposed. The process starts by compressing and decompressing the original image using wavelet transformation and fractal coding algorithm. The decompressed image is removed from the original one to obtain a residual image which is coded by using Huffman algorithm. Simulation results show that with the proposed scheme, we achieve an infinite peak signal to noise ratio (PSNR) with higher compression ratio compared to typical lossless method. Moreover, the use of wavelet transform speeds up the fractal compression algorithm by reducing the size of the domain pool. The compression results of several welding radiographic images using the proposed scheme are evaluated quantitatively and compared with the results of Huffman coding algorithm.

image compression is a an active area of research with new promising technique that will work very effectively in areas where we have to deal with a huge size of data .In Fractal compression major challenge is the exhaustive comparison needed in the encoding stage. In this paper a method of iteration free- detail space fractal image compression is proposed, in which time of encoding is reduced without compromising much on the quality of image and this algorithm guarantees a high compression ratio. This is a hybrid algorithm of fractal mathematics and wavelet Transform. When comparing with the existing hybrid techniques the advantage of this proposed method is, only the approximation space undergoes exhaustive comparison and thereby it guarantees higher speed than the existing Hybrid techniques. IFS (Iterated function system) of detail space are calculated using the result of approximation space. Experimental results show that in the proposed method Computational over head is considerably reduced and maintains a good tradeoff between compression ratio and quality of image. Resultant image is resolution independent, which is the one of the properties of fractal image compression. Since this new technique guarantees, high compression ratio and low encoding time, it may work very well in mobile communication, especially in face book application.

With the advent of multimedia technology, video compression has become imperative. The high definition of video required huge amount of storage space and large amount of bandwidth for the transmission of video. The largest part of multimedia is video. There is upsurge in demand of compressed data due to excessive usage of multimedia applications on Internet. Hence in success of multimedia data, video compression and decompression are majorly used. There are already various transform functions such as wavelet transform, DCT transform and fractal transform functions which are used for compression and decompression of video. In all transform function, the fractal transforms function adhere to the rule of block symmetry. It is very proficient process, but the rate of compression is very time-consuming, however, the decompression is very fast. In this paper, we adopted fractal triangular partitioning scheme to compress and decompress the videos. Here in this work for our analysis, we used very short length videos which are of different size. The primary objective of this work is to minimize the encoding time of video and achieve better compression ratio. The process of video compression and decompression methods is simulated in MATLAB software and used some standard parameters for the evaluation of compression and decompression results.

Data processing with multiple domains is an important concept in any platform; it deals with multimedia and textual information. Where textual data processing focuses on a structured or unstructured way of data processing which computes in less time with no compression over the data, multimedia data are processing deals with a processing requirement algorithm where compression is needed. This involve processing of video and their frames and compression in short forms such that the fast processing of storage as well as the access can be performed. There are different ways of performing compression, such as fractal compression, wavelet transform, compressive sensing, contractive transformation and other ways. One way of performing such a compression is working with the high frequency component of multimedia data. One of the most recent topics is fractal transformation which follows the block symmetry and archives high compression ratio. Yet, there are limitations such as working with speed and its cost while performing proper encoding and decoding using fractal compression. Swarm optimization and other related algorithms make it usable along with fractal compression function. In this paper, we review multiple algorithms in the field of fractal-based video compression and swarm intelligence for problems of optimization.

Reducing encoding complexity and improving the tradeoff between quality of image and compression ratio are active areas of research in the field of fractal image compression. In this paper two techniques are proposed to reduce the encoding complexity and to improve the PSNR of the reconstructed image. The first method is the prediction of affine transformation, based on the gradient direction of domain and range block using a Tag Matrix and the second involves calculation of score value based on the maximum value of intensity difference of range and domain block. An important merits of this new method is that encoding time is highly reduced and PSNR is also improved than the existing fractal coding techniques. This technique will be very applicable in situation where we have limited storage space and bandwidth but have to store and transmit enormous amount of data.

This paper presents simpler image compression technique using vector quantization and hybrid wavelet transform. Hybrid wavelet transform is generated using Kronecker product of two different transforms. Image is converted to transform domain using hybrid wavelet transform and very few low frequency coefficients are retained to achieve good compression. Vector quantization is applied on these coefficients to increase compression ratio significantly. VQ algorithms are applied on transformed image and codebooks of minimum possible size 16 and 32 are generated. KFCG and KMCG are faster in execution and beats performance of LBG algorithm. KFCG combined with hybrid wavelet transform gives lowest distortion and acceptable image quality at compression ratio 192.

Image compression evidence has been utilized as an important forensic feature to justify image authenticity. However, some recent studies showed that the compression evidence of block transform-based image coding, e.g., JPEG and JPEG2000, can be effectively erased by adding designed dither noise in the transform domain. In this paper, we demonstrate that it is also feasible to hide the compression evidence of lossy predictive image coding, a class of compression paradigm widely employed in critical scenarios. To tackle the challenging issue of error propagation inherent to predictive coding, we design a prediction-direction preserving strategy, allowing us to add dither noise in the prediction error (PE) domain, while minimizing the incurred distortion. Extensive experimental results are provided to verify the effectiveness of the proposed anti-forensic algorithm for lossy predictive image coding.

Space-frequency filtering and filters based on Fourier images of Gaussian and Morlet wavelets are used to synthesize microstructure images with fractal properties. Ways of analyzing the local fractal properties of structures, based on evaluating the fractal dimension in a small sliding window, are proposed and studied.

Fractal properties of real world objects are commonly examined in digital images. Digital images are discrete representations of objects or scenes and are unavoidably contaminated with noise disturbing the representation of the captured objects. We evaluate the noise dependency of frequently applied algorithms for the calculation of the fractal dimension in digital images. Three mathematically defined fractals (Koch Curve, Sierpinski Gasket, Menger Carpet), representative for low, middle and high values of the fractal dimension, together with an experimentally obtained fractal structure were contaminated with well-defined levels of artificial noise. The Box-Counting Dimension, the Correlation Dimension and the rather unknown Tug-of-War Dimension were calculated for the data sets in order to estimate the fractal dimensionality under the presence of accumulated noise. We found that noise has a significant influence on the computed fractal dimensions (relative increases up to 20%) and that the influence is sensitive to the applied algorithm and the space filling characteristics of the investigated fractal structures. The similarities of the effect of noise on experimental and artificial fractals confirm the reliability of the obtained results.

image compression methods aim to compress color image while ensuring that noise removal compression technique produce the good quality level images. The storage of images is becoming difficult with number of images growing to million and billions. Hence the image compression becoming absolute necessity in computing field. The Discrete Cosine Transform is widely used in image compression technique. Redundant information in an image needs to be eliminated by adopting intelligent method. In the recent research attempts better quality of compression is observed with the use of Discrete Cosine Transform (DCT) and Quantization. In this paper, the proposed system efficient image encoder removes the sinusoidal noise from original image by Butterworth Band Reject Filter (BBRF) algorithm in FDCT color image compression. The objective of this color image compression scheme is efficiently noise removal image, calculate the Compression Ratio(CR), Peak Signal to Noise Ratio (PSNR) Mean Square Error (MSE) by changing the FDCT level and using Fine Inverse Discrete Cosine Transform (F-IDCT) factor while preserving the quality of reconstructed image. Experimentation has been carried out on different image formats successfully. The proposed system achieved a good compression ratio and considerable test application for the quality of the reconstructed color image. KeywordsFIDCT, PSNR, MSE, Sinusoidal Noise, BBRF, Image Compression.

Fractal based technique for compression is one of the popular methods for compression of videos and images. It has generated much interest due to its promise of high compression ratios at good decompression quality and it enjoys the advantage of very fast decompression and resolution independent decoding .But it suffers from highly computationally intensive encoding process which makes it unsuitable for real time applications. Many approaches have been suggested but they do not satisfy the requirement of low encoding time and high quality reconstructed images. In this paper parallel algorithm for fractal image compression using NVIDIA`s GPGPU is proposed. Also novel discrete wavelet transform based feature detection is used to reduce the number of block comparisons. Experimental results show significant reduction in encoding time and quality of reconstructed images is also good compared to other approaches making this technique suitable for real time applications such as image retrieval, image denoising, Image authentication and encryption, satellite and medical imaging.. General Terms Parallel computing, Image compression