Fractal Coding Research Articles

CONCEPT RETRIEVAL BASED ON A COMBINATION OF FRACTAL CODING, FUZZY RULE BASED SYSTEM AND SVM

Most information retrieval systems make indirect use of human knowledge in their retrieval process. The new method we present here aims to efficiently use human knowledge directly in combination with fractal coding and support vector machine (SVM) for clustering. As illustrated in this paper, this approach is particularly applicable to soccer concept retrieval from video databases. The first phase consists of extracting suitable features and key frames from video shots. Then, using a fractal coding, soccer shots are retrieved, and using a fuzzy rule base containing the experiences of experts, shots that do not include significant soccer events are removed. Finally, the last phase uses SVM to classify results coming from the fuzzy system. The results of the classification phase are accompanied by a textual description and enables retrieval through text based query. Experimental results show proper classification and satisfying retrieval process.

Combining Fractal Coding and Orthogonal Linear Transforms

Many desirable properties make fractals a powerful mathematic model applied in several image processing and pattern recognition tasks: image coding, segmentation, feature extraction, and indexing, just to cite some of them. Unfortunately, they are based on a strong asymmetric scheme, consequently suffering from very high coding times. On the other side, linear transforms are quite time balanced, allowing them to be usefully exploited in realtime applications, but they do not provide comparable performances with respect to the image quality for high bit rates. In this paper, we investigate different levels of embedding orthogonal linear transforms in the fractal coding scheme. Experimental results show a clear improved quality for compression ratios up to 15 : 1.

A multi-purpose digital image watermarking using fractal block coding

In this paper, a new multi-purpose watermarking technique is presented which satisfies both verification and authentication purposes simultaneously by embedding a binary watermark into the image. The proposed method uses a special type of fractal block coding with a local search region with contrast scaling and mean of range block as its parameters. It also utilizes Fuzzy C-Mean clustering to specify the watermark bits. To overcome the high computational complexity of fractal coding, a new simple coding method is also presented which improves the robustness of the watermarking and decreases the run time of fractal block coding in the watermarking procedure. To measure the fragility and robustness of the method to signal distortions such as JPEG compression, median filter, and additive noise, some experiments were employed. The experimental results showed that the proposed method has provided a sensitive authentication and a reliable verification.

Prediction on decoded image quality for fractal image coding

A new decoded image quality prediction algorithm for fractal image coding was proposed.According to the results of many experiments,there exists an approximately exponential discipline between the average collage error and the PSNR of decoded image quality.The collage error of each range block was computed in the fractal encoding process and the PSNR of decoded image quality was predicted according to the average collage error.The experimental results show that for different sizes of range blocks and fast fractal image encoding,the proposed algorithm can obtain satisfying prediction results of decoded image quality.

An Effective chaos-based image watermarking scheme using fractal coding

Abstract The image watermarking technology is a technique of embedding hidden data in an original image. In this paper, a new watermarking method for embedding watermark bits based on Chaos-Fractal Coding is given. A chaotic signal is defined as being deterministic, pseudo periodic and presenting sensitivity to initial conditions. Combining a chaos system with Fractal Coding plays an important role in the security, invisibility and capacity of the proposed scheme. The main idea of the new proposed algorithm for coding is to determine a set of selective blocks for steady embedding. Simulation results show that the CFC algorithm (Chaos-Fractal Coding) has a confident capacity. The embedding technique that proposed in this paper is quite general, and can be applied to the extracting scheme with demanded changes.

Efficient Fractal Image Coding using Fast Fourier Transform

The fractal coding is a novel technique for image compression. Though the technique has many attractive features, the large encoding time makes it unsuitable for real time applications. In this paper, an efficient algorithm for fractal encoding which operates on entire domain image instead of overlapping domain blocks is presented.The algorithm drastically reduces the encoding time as compared to classical full search method. The reduction in encoding time is mainly due to use of modified crosscorrelation based similarity measure. The implemented algorithm employs exhaustive search of domain blocks and their isometry transformations to investigate their similarity with every range block. The application of Fast Fourier Transform in similarity measure calculation speeds up the encoding process. The proposed eight isometry transformations of a domain block exploit the properties of Discrete Fourier Transform to minimize the number of Fast Fourier Transform calculations. The experimental studies on the proposed algorithm demonstrate that the encoding time is reduced drastically with average speedup factor of 538 with respect to the classical full search method with comparable values of Peak Signal To Noise Ratio.

Research and Implementation of Fast Image Fractal Coding Algorithm

Image is one of the most important carriers for communication in our life, and it’s the utmost medium containing information. As all we known, the data quantity of digital image is so large that it should be compressed for high-speed transmission and store. So image encoding has become one of the key technologies on which the digital society depends.

A novel fast fractal super resolution technique

A novel supe-resolution method is proposed to construct a higher resolution image from a low resolution image using fractal coding. This super-resolution method utilizes a special type of orthogonal fractal coding method in which the fractal affine transform is determined by the range block mean and contrast scaling. The proposed non-adaptive fractal super-resolution procedure uses a fixed domain block and a fixed contrast scaling factor. Thus, no additional information must be stored for the fractal coding. Because the mean of each range block of the decoding series in the orthogonal fractal decoding is invariant, a higher resolution image consists of range blocks can be reconstructed from a low resolution image consisting of range block means. Experimental results are presented to show the impact of this method in terms of image quality and its computational requirements.

Facial image recognition based on fractal image encoding

Fractal image encoding uses self-similarity to encode an image. Utilizing this feature, a new method of facial image recognition based on fractal image encoding is examined. Fractal image encoding can approximate any given image by capturing intrinsic self-similarity within the image. This method has some invariance to rotation, scaling, translation, and luminance. The method encodes an image of record through the use of an encoding dictionary composed of images in a face image database. The fractal codes are then placed in a file, and the fractal codes are iterated multiple times to obtain decoding images. By comparing the peak signal-to-noise ratio of the image of record to all the decoding images, the image in the image database whose decoding image minimizes this norm is the recognized image. By experiment, the recognition performance achieved by this new method posted an average recognition rate of 94.54 percent on the publicly available database of faces hosted by the Cambridge University Computer Laboratory Digital Technology Group, when facial images at a side profile orientation are within 15 degrees of a full frontal image.

Real time fractal image coder based on characteristic vector matching

Fractal coding algorithm has many applications including image compression. In this paper a classification scheme is presented which allows the hardware implementation of the fractal coder. High speed and low power consumption are the goal of the suggested design. The introduced method is based on binary classification of domain and range blocks. The proposed technique increases the processing speed and reduces the power consumption while the qualities of the reconstructed images are comparable with those of the available software techniques. In order to show the functionality of the proposed algorithm, the architecture was implemented on a FPGA chip. The application of the proposed hardware is shown in image compression. The resulted compression ratios, PSNR error, gate count, compression speed and power consumption are compared with the existing designs. Other applications of the proposed design are feasible in certain fields such as mass–volume database coding and also in video coder’s block matching schemes.

A FAST FRACTAL CODING IN APPLICATION OF IMAGE RETRIEVAL

Aiming at content-based image retrieval (CBIR) in fractal domain, this paper puts forward a fast fractal encoding method to extract image features, which is based on a novel non-searching and adaptive quadtree division. As a result, it enhances fractal coding speed sharply, only needs 0.0485 seconds on average for a 256 × 256 image and is approximately 70 times faster than algorithm in addition to good reconstructed image quality. Furthermore, this paper improves image matching algorithm, consequently enhancing the accuracy of query results. In addition, we present a method to further accelerate image retrieval based on the analysis to fractal codes distance and number. Experimental results show that our proposed method is performs highly in retrieval speed and feasible in retrieval accuracy.

A FAST FRACTAL ENCODING METHOD BASED ON FRACTAL DIMENSION

In this paper a fast fractal coding method based on fractal dimension is proposed. Image texture is an important content in image analysis and processing which can be used to describe the extent of irregular surface. The fractal dimension in fractal theory can be used to describe the image texture, and it is the same with the human visual system. The higher the fractal dimension, the rougher the surface of the corresponding graph, and vice versa. Therefore in this paper a fast fractal encoding method based on fractal dimension is proposed. During the encoding process, using the fractal dimension of the image, all blocks of the given image first are defined into three classes. Then each range block searches the best match in the corresponding class. The method is based on differential box counting which is chosen specifically for texture analysis. Since the searching space is reduced and the classification operation is simple and computationally efficient, the encoding speed is improved and the quality of the decoded image is preserved. Experiments show that compared with the full search method, the proposed method greatly reduced the encoding time, obtained a rather good retrieved image, and achieved the stable speedup ratio.

A New Fast Fractal Modeling Approach for the Detection of Microcalcifications in Mammograms

In this paper, a novel fast method for modeling mammograms by deterministic fractal coding approach to detect the presence of microcalcifications, which are early signs of breast cancer, is presented. The modeled mammogram obtained using fractal encoding method is visually similar to the original image containing microcalcifications, and therefore, when it is taken out from the original mammogram, the presence of microcalcifications can be enhanced. The limitation of fractal image modeling is the tremendous time required for encoding. In the present work, instead of searching for a matching domain in the entire domain pool of the image, three methods based on mean and variance, dynamic range of the image blocks, and mass center features are used. This reduced the encoding time by a factor of 3, 89, and 13, respectively, in the three methods with respect to the conventional fractal image coding method with quad tree partitioning. The mammograms obtained from The Mammographic Image Analysis Society database (ground truth available) gave a total detection score of 87.6%, 87.6%, 90.5%, and 87.6%, for the conventional and the proposed three methods, respectively.

A Necessary and Sufficient Contractivity Condition for the Fractal Transform Operator

This paper revisits the concept of fractal image coding and the contractivity conditions of the fractal transform operator. All such existing conditions are only sufficient. This paper formulates a necessary and sufficient condition for the contractivity of the fractal transform operator associated to a fractal code. Furthermore, analytical results on the convergence of the fractal image decoding will be derived.

2nd Issue of Real-Time Image Processing

The first quarter of 2007 started as an active season for the real-time image processing community. The annual SPIE Conference on Real-Time Image Processing, which was held in San Jose, CA, highlighted recent developments in this growing branch of image processing. As one of the few regular events with its focus matching that of JRTIP, one witnessed the growth in applications of real-time image and video processing. The conference served as an effective instrument to foster the dissemination of recent results and to leverage the cohesion of the real time image processing community. The preparations for the next SPIE Conference on Real-Time Image Processing in 2008 are already progressing and its call-for-papers is included at the end of this issue. In 2007, JRTIP is going to seek involvement of more scientists in the field of real-time image and video processing. After 1 year of operation, the editors-in-chief have started to recruit additional associate editors to enlarge the expertise base of the editorial board, to solicit manuscript submissions from potential authors, and to make the reviewing process more efficient. Interested colleagues should contact the editors-in-chief expressing their Associate Editor candidature in support of one or more fields within the focus of JRTIP. In addition, they wish to encourage researchers to act as guest editors for special issues on any real-time image or video processing related topics of interest to them. It is possible to schedule two special issues in 2007, provided that a draft call-for-papers is sent to the editors-in-chief as soon as possible. The third issue of JRTIP presents four articles, two are survey papers and two are original research papers. These articles address different real-time image processing perspectives ranging from algorithmic to hardware issues. The first survey paper deals with the real-time filtering in 2D and 3D using ordered statistics that are supported by a rich set of experimental results derived from several algorithmic variations. Performance measurements are used to demonstrate the effect of noise suppression and preservation of fine image structures and to show the DSP implementation of denoising filters. The second survey paper introduces a non-invasive analysis of dynamic processes in living cells using microscopic computer vision techniques for understanding the interactions between cellular and molecular functional units and for providing novel insights into the cell biology. The third article is an original research paper covering a machine vision application involving vision-based position sensing for aerial refueling of unmanned aerial vehicles in real-time. A full image processing chain is investigated and tested in a MATLAB/Simulink soft real-time environment as well as in a Linux/RTAI hard real-time environment. The feasibility of the real-time implementation is shown using off-the-shelf commercial hardware. The fourth article is another original research paper describing a hardware architecture for real-time fractal coding for image compression. The introduced parallel hardware architecture contains units for domain M. F. Carlsohn (&) Ingenieurberatung fur Computer Vision und Bildkommunikation, Am Heiddamm 36g, 28355 Bremen, Germany e-mail: matthias.carlsohn@t-online.de

Randomness-Based Fractal Coding of Maneuvering Affordance with Applications to Interactive as-is Mapping

Randomness-Based Fractal Coding of Maneuvering Affordance with Applications to Interactive as-is Mapping

Fractal-based methods in imaging

Through a procedure called the LIFSM algorithm, based on the Collage Theorem, it is possible to represent an image by a set of data, known as a fractal code, from which we may construct an approximation of the image. This algorithm is largely based upon the idea of matching larger portions of an image, called “parent blocks,” to smaller portions called “child blocks” in order to minimize a quantity known as the “collage distance.” We modify the LIFSM algorithm through the consideration of “near-optimal pairings.” We develop the theory, discuss applications and present examples in image denoising, image reconstruction, and edge detection.

IFS imaging beyond compression

Historically, most research in fractal image coding focused on its compression capabilities, seeking to obtain the best domain–range block matching with the minimal amount of fractal code. In the course of these investigations, it was implicitly known, yet perhaps not fully investigated, that a number of domain image subblocks will approximate a given range image subblock almost as well as the optimal domain subblock selected by collage coding. Recently we have presented a simple mathematical model of image self-similarity and a series of computer experiments that examine the self-similarity of natural images under contractive affine greyscale maps [S. Alexander, E. Vrscay, S. Tsurumi, A simple, general model for the affine self-similarity of images, in: A. Campilho, M. Karnel (Eds.), ICIAR, in: Lecture Notes in Computer Science, vol. 5112, Springer-Verlag, 2008, pp. 192–203; S. Alexander, Multiscale methods in image modelling and image processing, Ph.D. thesis, Dept. of Applied Mathematics, University of Waterloo, 2005]. We demonstrated that typical natural images have large numbers of such maps that closely approximate all areas (i.e. range subblock) of the image. In the present work, some implications of this are explored. A novel IFS-type ‘fractal operator’ with overlapping maps (IFSOM) is presented. Application of this technique in a multiscale manner is demonstrated to have denoising performance comparable to current state-of-the-art methods. Extensions of this preliminary work are discussed.

Digital Watermarking Based on Fractal Image Coding Using Discrete Wavelet Transformation

In this paper, we propose a new digital watermarking method using fractal image coding and discrete wavelet transformation (DWT). We decompose an original image into low frequency band LL1 and LL2 using DWT. In fractal image coding, LL1 and LL2 are used for the range block area and domain block area, respectively. The watermark information is embedded into the address information of the range block. As the watermark is embedded into LL1, the robustness against JPEG compression is improved. Moreover, the quality of the watermarked image is improved, in spite of embedding the watermark into LL1, because the fractal image coding is applied only to the candidate range blocks for embedding. Experimental results prove the effectiveness of the proposed method.

Slow Motion and Zoom in HD Digital Videos Using Fractals

Slow motion replay and spatial zooming are special effects used in digital video rendering. At present, most techniques to perform digital spatial zoom and slow motion are based on interpolation for both enlarging the size of the original pictures and generating additional intermediate frames. Mainly, interpolation is done either by linear or cubic spline functions or by motion estimation/compensation which both can be applied pixel by pixel, or by partitioning frames into blocks. Purpose of this paper is to present an alternative technique combining fractals theory and wavelet decomposition to achieve spatial zoom and slow motion replay of HD digital color video sequences. Fast scene change detection, active scene detection, wavelet subband analysis, and color fractal coding based on Earth Mover's Distance (EMD) measure are used to reduce computational load and to improve visual quality. Experiments show that the proposed scheme achieves better results in terms of overall visual quality compared to the state-of-the-art techniques.