Activation Functions Effect on Fractal Coding Using Neural Networks

Activation functions play an essential role in converting the output of the artificial neural network into nonlinear results,since without this nonlinearity,the results of the network will be less accurate.Nonlinearity is the mission of all nonlinear functions,except for polynomials.The activation function must be dif-ferentiable for backpropagation learning.This study’s objective is to determine the best activation functions for the approximation of each fractal image.Different results have been attained using Matlab and Visual Basic programs,which indi-cate that the bounded function is more helpful than other functions.The non-lin-earity of the activation function is important when using neural networks for coding fractal images because the coefficients of the Iterated Function System are different according to the different types of fractals.The most commonly cho-sen activation function is the sigmoidal function,which produces a positive value.Other functions,such as tansh or arctan,whose values can be positive or negative depending on the network input,tend to train neural networks faster.The coding speed of the fractal image is different depending on the appropriate activation function chosen for each fractal shape.In this paper,we have provided the appro-priate activation functions for each type of system of iterated functions that help the network to identify the transactions of the system.

Efficient Quadtree based Fractal Image Coding Scheme in Wavelet Transform Domain *

This paper presents an efficient quadtree based fractal image coding scheme in wavelet transform domain based on the wavelet based theory of fractal image compression introduced by Davis. In the scheme, zerotrees of wavelet coefficients are used to reduce the number of domain blocks, which leads to lower bit cost required to represent the location information of fractal coding, and overall entropy constrained optimization is performed for the decision trees as well as for the sets of scalar quantizers and self quantizers of wavelet subtrees. Experiment results show that at the low bit rates, the proposed scheme gives about 1 dB improvement in PSNR over the reported results.

Chaos-based encryption for fractal image coding

A chaos-based cryptosystem for fractal image coding is proposed. The Renyi chaotic map is employed to determine the order of processing the range blocks and to generate the keystream for masking the encoded sequence. Compared with the standard approach of fraetal image coding followed by the Advanced Encryption Standard, our scheme offers a higher sensitivity to both plaintext and ciphertext at a comparable operating efficiency. The keystream generated by the Renyi chaotic map passes the randomness tests set by the United States National Institute of Standards and Technology, and so the proposed scheme is sensitive to the key.

Fractal Block Coding:A New Method

Fractal image compression is a completely new method to compress images by searching and exploiting the self similarity of the whole image . Fractal Block Coding (FBC) is a practicable fractal coding scheme with annoying slow encoding speed . In this paper, we classify the image blocks by Classified Vector Quantization (CVQ) technique and present an Adaptive Block Truncation Coding (ABTC) scheme to process the midrange blocks in the image. By this method , we reduce the encoding time to one forty fifth comparing to ordinary FBC method with little change in compression ratio and a little decreased coded image quality.

A Fast Fractal Image Compression Coding Method

Fast algorithms for reducing encoding complexity of fractal image coding have recently been an important research topic. Search of the best matched domain block is the most computation intensive part of the fractal encoding process. In this paper, a fast fractal approximation coding scheme implemented on a personal computer based on matching in range block's neighbours is presented.Experimental results show that the proposed algorithm is very simple in implementation, fast in encoding time and high in compression ratio while PSNR is almost the same as compared with Barnsley's fractal block coding .

A HIGH SPEED ADAPTIVE FRACTAL IMAGE CODING ALGORITHM USING FLEXIBLE CLASSIFICATION TECHNIQUE

Traditionally, fractal image compression suffers from lengthy encoding time in measure ofhours. In this paper, combined with characteristlcs of human visual system, a flexible classification technique is proposed. This yields a corresponding adaptive algorithm which can cut down the encoding timeinto second's magnitude. Experiment results suggest that the algorithm can balance the overall encodingperformance efficiently, that is, with a higher speed and a better PSNR gain.

A Compression Algorithm of Hyperspectral Remote Sensing Image Based on 3-D Wavelet-Fractal Coder

In this paper, the 3-D Wavelet-Fractal coder was used to compress the hyperspectral remote sensing image, which is a combination of 3-D improved set partitioning in hierarchical trees （SPIHT） coding and 3-D fractal coding. Hyperspectral image date cube was first translated by 3-D wavelet and the 3-D fractal compression ceding was applied to lowest frequency subband. The remaining coefficients of higher frequency sub-bands were encoding by 3-D improved SPIHT. We used the block set instead of the hierarchical trees to enhance SPIHT＇s flexibility. The classical eight kinds of affme transformations in 2-D fractal image compression were generalized to nineteen for the 3-D fractal image compression. The new compression method had been tested on MATLAB. The experiment results indicate that we can gain high compression ratios and the information loss is acceptable.

Fractal characteristics of filamentous bacteria in activated sludge and its significance

On the basis of fractal theory, the fractal characteristics of filamentous bacteria in activated sludge are studied by image dissector system. The results show that the spatial distribution structure of filamentous bacteria in activated sludge has high self similarity in statistics and the filamentous bacteria have clear phenomenon of fractal growth. The critical fractal dimension values of filamentous bacteria bulking such as Eikelboom 021N, Eikelboom 1701, Sphaerotilus natans and Eikelboom 0041 are determined initially. The fractal dimensions can be taken as a parameter to describe filamentous bacteria of activated sludge quantitatively and bring to light the disorder in appearance and the rule in inherence of filamentous bacteria system.

AN EFFECTIVE IMAGE RETRIEVAL METHOD BASED ON KERNEL DENSITY ESTIMATION OF COLLAGE ERROR AND MOMENT INVARIANTS

In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The proposed method is called CHK (KDE of Collage error and Hu moment) and it is tested on the Vistex texture database with 640 natural images. Experimental results show that the Average Retrieval Rate (ARR) can reach into 78.18%, which demonstrates that the proposed method performs better than the one with parameters respectively as well as the commonly used histogram method both on retrieval rate and retrieval time.

Combining IFS and VQ in Fractal Image Coding

A novel paradigm for fractal coding selectively corrects the fractal code for selected domain blocks with an image-adaptive VQ codebook. The codebook is generated from the initial uncorrected fractal code and is, therefore, available at the decoder. An efficient trade-off is generated between incremental performance and bit rate.

On-line Detection of Gas Pipeline Based on the Real-Time Algorithm and Network Technology with Robot

The detection system integrates control technology, network technology, video encoding and decoding, video transmiss-ion, multi-single chip microcomputer communication, dat-abase technology, computer software and robot technology. The robot can adaptively adjust its status according to diameter (from 400 mm to 650 mm) of pipeline. The maximum detection distance is up to 1 000 m. The method of video coding in the system is based on fractal transformation. The experiments show that the coding scheme is fast and good PSNR. The precision of on-line detection is up to 3% thickness of pipeline wall. The robot can also have a high precision of location up to 0.03 m. The control method is based on network and characterized by on-line and real-time. The experiment in real gas pipeline shows that the performance of the detection system is good.