Iterated Function System Codes Research Articles

RANCANGAN MOTIF KAIN POLA GARIS SIMETRIS MODEL FRAKTAL DENGAN EMPAT DAN LIMA KOMPONEN COLLAGE GARIS DAN PERSEGI-EMPAT

The motif pattern of cloths can be designed in fractal form based on Collage components composition by means of the iterated function system (IFS) encoding algorithm to encode the design position into a code and decoding algorithm to decode the code and to display the fractal object. In this paper, two kinds of Collage component composition in straight lines and self-similarity feature are discussed. The first model consists of four lines and one square shape of Collage component. The second model consists of three lines and one square shape of Collage component. The composition is made in a such way, that there are several closed planes to be colored later. The IFS code generated by the IFS encoding algorithm is normalized to ensure that the straight lines are crossed to one or two neighbor lines in the right position and the self-similarity feature is also fitted to fill the void and integrated with the lines

EVOKED POTENTIAL PRIMITIVES OF RAT MOTOR CORTEX SIGNAL ANALYSIS BASED ON ITERATED FUNCTION SYSTEMS

The function of the brain has been the focus of neuroscience studies for nearly half a century. The studies found that the evoked potential signals of the motor cortex are the main source to command action. An action signal is composed of several signal primitives that are mainly generated by the motor cortex. It was found that signal primitives of the motor cortex can be produced by several fixed rules and a group of codes called iterated function systems (IFS) code. The goal of our research is to find the relationships between the signal primitives of the motor cortex and actions. We recorded the action signals of the rat motor cortex using 8-channel micro-electrodes and used independent component analysis (ICA) to find the independent source signals called signal primitives. Then, the IFS algorithm was used to find the signal primitive codes, which is the IFS code. The experimental results showed that the source signals of actions produce the IFS rules and a set of codes by the IFS algorithm and conversely, using the IFS rules and the set of codes can reconstruct the source signals. Every 20-character length of action signals will generate unique 6-character IFS codes, meaning that the action signals can be replaced with IFS codes to achieve the compression. We found that the IFS rules and codes can be used to represent different cortex commands which have distinct IFS codes that can be used to classify the movements of rat. The classification result reached 78.75% for rough movement and nearly 50% for subtle movement, where the rough movement is that the rat performs two motions and the subtle movement is three motions. This result shows that the motor cortex command can consist of distinct signal primitives and the huge file size of the motor cortex command is reduced three times by the IFS algorithm.

Intrinsic parallel random iteration algorithm for fractal image decoding based on iterated function system code

A parallelized random iteration algorithm that is explicit in the iterated function system (IFS) code is proposed to speed up the decoding of fractal images. In a conventional random iteration algorithm, the fractal image is serially decoded and may generate undesirable transient points. The proposed intrinsic parallel random iteration (IPRI) algorithm determines only one initial point and can avoid the transient points. Moreover, the contractive affine transformations (CATs) denoted by the IFS code can operate in parallel and simultaneously generate subimages. The parallel capability is basically proportional to the number of CATs. Two generalized methods of the proposed IPRI algorithm are provided to solve the nonuniformity problem due to the unequal probabilities among CATs. Finally, the proposed IPRI algorithm can cooperate with a previous parallel decoding algorithm to obtain higher parallel capability. Simulation results demonstrate the validity of the proposed IPRI algorithm.

Similarity-based image retrieval system using partitioned iterated function system codes

We propose a new image retrieval system using partitioned iterated function system (PIFS) codes. In PIFS encoding, a compression code contains mapping information between similar regions in the same image. This mapping information can be treated as vectors, and representative vectors can be generated using them. Representative vectors describe the features of the image. Hence, the similarity between images is directly calculable from representative vectors. This similarity is applicable to image retrieval. In this article, we explain this scheme and demonstrate its efficiency experimentally.

Image based rendering of iterated function systems

A fast method to generate fractal imagery is presented. Iterated function systems (IFS) are based on repeatedly copying transformed images. We show that this can be directly translated into standard graphics operations: Each image is generated by texture mapping and blending copies of the previous image. Animations of dynamic IFS codes are generated at 50 frames/s on a notebook PC, using commodity graphics hardware. Various extensions and variations are presented.

Arbitrary affine transformation and their composition effects for two-dimensional fractal sets

Fractal sets can be generated by the iterated function system (IFS) codes using the contractive affine transformation. This paper presents various geometric affine transformations and their composition effects for two-dimensional (2-D) fractal sets. Here, the geometric transformations include translation, rotation, shearing, dilation/contraction, and reflection. First, a hierarchical fixed point-searching algorithm is proposed to determine the original coordinates of a 2-D fractal set directly from its IFS code. Then, the IFS code is modified according to the desired transformation. Instead of post processing the generated result, arbitrary affine transformation on the original fractal set can be directly obtained. On the other hand, the composite geometric transformations for 2-D fractal sets are also available. Finally, a complicated image frame can be synthesized by multiple 2-D fractal sets.

Similarity-based image retrieval system using partitioned iterated function system codes

Similarity-based image retrieval system using partitioned iterated function system codes

Random-iteration algorithm-based optical parallel architecture for fractal-image decoding by use of iterated-function system codes

An optical parallel architecture for the random-iteration algorithm to decode a fractal image by use of iterated-function system (IFS) codes is proposed. The code value is first converted into transmittance in film or a spatial light modulator in the optical part of the system. With an optical-to-electrical converter, electrical-to-optical converter, and some electronic circuits for addition and delay, we can perform the contractive affine transformation (CAT) denoted in IFS codes. In the proposed decoding architecture all CAT's generate points (image pixels) in parallel, and these points then are joined for display purposes. Therefore the decoding speed is improved greatly compared with existing serial-decoding architectures. In addition, an error and stability analysis that considers nonperfect elements is presented for the proposed optical system. Finally, simulation results are given to validate the proposed architecture.

Fractal characteristics of the martensitic transformation in a Fe - 29% Ni - 0.16% C alloy

A fractal model of the martensitic transformation (MT) in a Fe - 29% Ni - 0.16% C alloy is proposed on the basis of metallographic observations. It is an uneven fractal that can better describe the microstructure observed in the experiments. The uneven fractal can be produced by an iterated function system (IFS). The IFS code, consisting of two affine maps, is given to calculate the fractal dimension. Finally, we also propose a partition process to simulate the dynamic process of the MT.

Fractal image coding system based on an adaptive side-coupling quadtree structure

A new fractal-based image compression system, based on a so-called Adaptive Side-Coupling Quadtree (ASCQ) structure, is proposed. The proposed system consists of three processes: a preprocessing, a compression and a decompression process. In the compression process, the original image is represented by an ASCQ structure. The set of Iterated Function System (IFS) codes, which is usually derived in the encoding process, can be calculated directly from this tree structure. Using these IFS codes, an image which is similar to the original one can be reconstructed. Unlike traditional methods, which have separate domain and range pools, the proposed ASCQ structure simultaneously contains the domain pool and range pool. Since the proposed ASCQ is an adaptive structure, the number of IFS codes will be variant depending on their corresponding original images. Experimental results show that the ASCQ structure is indeed an efficient structure for the fractal-based image compression system.

A parallel decoding algorithm for IFS codes without transient behavior

Iterated function systems (IFSs) have received great attention in encoding and decoding fractal images. Barnsley (1988) has shown that IFSs for image compression can achieve a very high compression ratio for a single image. However, the major drawback of such a technique is the large computation load required to both encode and decode a fractal image. We provide a novel algorithm to decode IFS codes. The main features of this algorithm are that it is very suitable for parallel implementation and has no transient behavior. Also, from the decoding process of this method we can understand the encoding procedure explicitly. One example is illustrated to demonstrate the quality of its performance.

An optical decoding architecture for the random iteration algorithm of iterated function system codes

A novel optical architecture based on the random iteration algorithm to decode iterated function system (IFS) codes is presented. The optical part of this system performs the affine transformations of IFS. The code values in the affine transformations of IFS are first translated into the modulation voltages of the electro-optic modulators (EOMS), with a specific probability. Then, the multiplication and addition operations can easily be performed. With the O/E and A/D converters, the light intensity is converted into an electrical signal to address a specific pixel at the display device. A fractal image is then progressively decoded pixel by pixel and superimposed on the display device. The computer simulation and some experimental results for the proposed architecture are provided for verification. The decoding speed is fast, the image quality is high, and the resolution of the generated fractals depends on the resolution of the display device itself.

Fractal image compression

Image compression techniques based on fractals have been developed in the last few years and may promise better compression performance. Fractal image compression techniques are being developed due to the recognition that fractals can describe natural scenes better than shapes of traditional geometry. This paper describes principle and common techniques of fractal image compression. Mathematical foundations for fract image compression techniques are presented first. Then three main fractal image compression techniques are discussed. The first and most important technique is based on iterated function systems (IFS): images are compressed into compact IFS codes at encoding stage, and fractal images are generated to approximate the original image at the decoding stage. The second technique is segment-based coding: images are segmented according to the fractal dimension and these segments are coded efficiently using properties of the human visual system. The third technique is yardstick coding which is similar to DPCM and subsampling with subsequent interpolation. But it was inspired by the fractal geometry on measuring the length of a curve using a yardstick.