Optimization of Fractal Iterated Function System(IFS) with Probability and Fractal Image Generation

There are several methods for rendering fractal images based on IFS (Iterated Function System) in computer graphic; but one concern of the computer graphic community has been the efficiency rendering algorithms. The invariant measures arising from IFSP (Iterate Function System with Probability) using the probabilistic algorithm are also known as chaos games. The role of these probabilities to generate the image of the attractor has been investigated using a multi-fractal analysis. The conventional choice of probability associated with each set /S/ to generate the attractor in least time possible is introduced, then a new method based on the self similarity and multi-fractal analysis is presented. The efficiency of the new method has been proved over the conventional method.

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.

Realization of Fractal Affine Transformation

This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its corresponding mathematical equations which are essential in fractal image construction.

ON SPACES OF FRACTAL FUNCTIONS

In this paper we Ointroduce linear-spaces consisting of continuous functions whose graphs are the attactars of a special class of iterated function systems. We show that such spaces are finite dimensional and give the bases of these spaces in an implicit way. Given such a space, we discuss how to obtain a set of knots for whah the Lagrange interpolation problem by the space is uniquely solvable.

DETECTION OF KNOWN SIGNALS IN 1/f FRACTAL NOISE

Based on the whitening property of wavelet transformation for 1/f noise, this paper addresses the problem of detecting deterministic signals in the presence of 1/f fractal noise. The transfer function of whitening filter is provided as well as the condition for whitening. The receiver structure based on Karhunen-Loeve expansion and the decision rule are also given. Finally performance of the detector is analyzed.

Multi-fractal Behaviors of Relative Humidity over China

The multi-fractal behaviors of relative humidity over China are studied using the multi-fractal detrended fluctuation analysis (DFA) method. Three multi-fractal parameters (the spectrum width Δα, the asymmetry Δα as , and the long-range correlation exponent α 0 ) of the singularity spectrum are introduced to quantify the multi-fractal behaviors. The results show that multi-fractality exists in daily humidity records over most stations in China and is mainly due to the broad distribution of the probability density of the sequence values. Strong multifractal behaviors over some stations in the Yunnan, Guangdong, and Inner Mongolia provinces are obvious. These behaviors are mainly caused by different longrange correlations between large and small fluctuations. The asymmetry of the singularity of relative humidity records is weak, except for a small number of stations in the far east and west of China, where the singularity spectrum is left-skewed. Finally, the long-range correlations in North China are stronger than those in South China, which indicates better predictability in North China. By studying the parameters of the multi-fractal spectrum, various data of long-range power law correlations of the relative humidity records are obtained, which may provide theoretical support for climate prediction.

Simulation of tree and its swaying with wind generated by L-system

This paper constructs a tree model by using the 3D stochastic and L system with brackets. Adjusting the range of the parameters, the present method ensures a favorable randomness and reflects the reality and the real time. Based on a simple mechanical model, the simulation of the phenomenon of wind swaying trees satisfies visual effects well.

Fractal-based algorithmic design of Chinese ice-ray lattices

Chinese ice-ray lattices are perhaps one of the earliest and controlled designs of asymmetric and complex patterns applied as a traditional motif in windows.Such intricate and complex designs developed centuries back have created an evident curiosity to explore its underlying geometric rules.Some scholars used the Shape Grammar as a tool to explain and recreate similar patterns.The previous studies conceive the ice-ray lattice design as the iterative subdivisions of a polygon.However,they missed explaining this geometric quality through the discussion of fractal geometry,which can explain the shapes consuming selfsimilar or self-affine repetitions of itself at different scales.As a novel approach,this paper analytically focuses on the fractal characters of ice-ray lattice designs and uses fractal geometry as a unique tool for generating different types of ice-ray lattices.The significance of this study is the demonstration of the efficacy of fractal geometry and the simple geometric rule of IFS for analyzing and algorithmically modeling complex lattices and cracked-like patterns.

一种L系统与IFS相互融合的植物模拟方法

提出了一种L系统与IFS相互融合的植物形态模拟新方法。利用L系统进行植物生长规律和拓扑结构的控制和模拟,由IFS方法模拟植物具有纹理的各组成部分,由此将两种方法的优点结合在一起。此外,为便于该融合方法的具体实现,还对传统L系统的实现算法进行了改进。模拟实验结果表明:提出的方法可以方便、自由地模拟各种植物的形态,且具有更加自然与逼真的效果。

USING NEURAL NETWORK BASED NONLINEAR IFS TO MODEL TIME SEQUENCES

A novel neural network based iterated function system (IFS) model is presented in this paper while the precondition to ensure the model is also explored. Applying it to some practical data, the given signal can be approximated exactly by the attractor generated by this model, which provides another way to resolve fractal inverse problem.

Dynamic Fractal Transform with Applications to Image Data Compression

A recent trend in computer graphics and image processing is to use Iterated Function System (IFS) to generate and describe both man-made graphics and natural images. Jacquin was the first to propose a fully automatic gray scale image compression algorithm which is referred to as a typical static fractal transform based algorithm in this paper. By using this algorithm, an image can be condensely described as a fractal transform operator which is the combination of a set of fractal mappings. When the fractal transform operator is iteratedly applied to any initial image, a unique attractor (reconstructed image) can be achieved. In this paper) a dynamic fractal transform is presented which is a modification of the static transform. Instead of being fixed, the dynamic transform operator varies in each decoder iteration, thus differs from static transform operators. The new transform has advantages in improving coding efficiency and shows better convergence for the decoder.

分区IFS图像压缩编码

本文提出了一种基于“区”的ＩＦＳ图像压缩编码算法，简述了其原理及实现过程。实验结果表明，其性能优于ＪＰＥＧ算法及Ｊａｃｑｕｉｎ的基于“块”

一种基于IFS的图像边缘检测方法

首次提出了一种基于IFS的图像边缘检测方法，该方法以IFS理论为基础、以MSE为失真测度，对图像进行边缘检测，改进的局部快速算法可以有效减少检测搜索时间。实验结果表明，本文所采用的边缘检测方法是一种有效的图像边缘检测方法。

一种基于IFS的二维真彩分形变形方法

提出了一种由迭代函数系统(IFS)所描述的二维真彩分形变形的新方法。首先建立二维真彩IFS分形模型,然后通过仿射变换的对应、规范化、匹配及插值实现了变形过程。实验结果表明:分形吸引子形状颜色过渡自然,这为分形的生成与动画提供了新的有效途径。

基于IFS的非规则分形组织设计方法

针对L系统在绘制织物分形组织图方面存在的局限,基于IFS的生成规则,研究不受任何基本组织形式限制的非规则分形组织设计方法。该方法以非规则、大循环的基本组织为应用对象,运用VC++编程,利用Kronecker叉积进行组织矩阵的迭代运算,快捷地生成此类基本组织的分形组织图。在此基础上,利用分形组织自相似结构所具有的多级层次关系,通过选择不同的填充组织,设计形成结构复杂、风格多变的分形织物。通过织造实验证明,此分形组织设计方法形成的织物纹理效果具有复杂性强,不易模仿等特点。

局部放电超声信号的自仿射IFS模型

通过仿射变换建立了变压器局部放电超声信号的分段自仿射 IFS模型。该模型用于在线监测中可实现局部放电信号数据的压缩 ,并通过计算 IFS分形维数为局部放电模式识别提供新的特征参数。

基于L系统的织物分形组织设计方法

为探索一条与传统方法不同的织物组织设计新途径,基于L系统理论,以4枚破斜纹、5枚缎纹等组织为例,尝试提出一种新的织物组织设计方法。该方法运用L系统的链式语言生成规则与计算机图形技术,生成具有自相似性特征与相互嵌套、多层次结构的分形组织,并通过选择合适的填充组织,构造出实用且与传统形式不同的织物分形组织。在此基础上,借助电子提花机进行了织物成型实验,由此对分形织物组织所产生的织物效果进行了初步的探讨。