二维准分形形状的定性表示和建模

本文提出了二维准分形形状的一种定性表示式－－－正则生成系统，研究了一类准分形形状的建模方法，改进了Ｐｒｕｓｉｎｋｉｅｗｉｃｚ和Ｇｕｊａｒ等人的工作。     

基于分形几何的真实场景物体表示及应用

介绍了分形维数的概念,对利用自拟似分形和自仿射分形实现分形物体的绘制算法进行了描述。实现了场景中不规则自然景物几何形状的真实感表达。     

一类基于实数局部的分形

通过将整数同余的概念推广到实数范围,定义了实数“局部”的概念。即通过某种７方式将实数表示在无限序列,称无限序列中包含的有限序列为实数的“局部”,具有相同局部的实数称为“同局”。考察实值函数函数值的局部,有如下结论：函数值同局的点组成的集合构成二值分形,构成规则图形是特例;     

空间对象的几何表示

1 引言空间推理是指利用空间理论和人工智能技术对空间对象建模、描述和表示,并据此对空间对象间的空间关系进行的定性或定量的分析和处理过程。目前,空间推理被广泛应用于地理信息系统、机器人导航、高级视觉、自然语言理解、工程设计和物理位置的常识推理等,是人工智能领域的一个研究热点。     

几何分形图形的动态方向准则

本文提出了一种新的生成自相似几何分形集的技术准则：动态方向准则，并给出了动态方向准则的应用原则，在该原则下，提出了符号移位法，以实现递归过程中方向的动态 控制。动态方向准则继承了传统方法中生成几何自相似集的机理，同时增加了由一种生成元和初始元所能生成的分形图形的种类。     

分形几何在计算机图形学中的应用

介绍了分形几何理论的基础以及分形图形的主要生成方法,阐述了分形几何学在计算机图形学中的应用。     

基于分形几何的甲骨文字形识别方法

甲骨文是流行于我国古代商朝的成熟文字系统,本质上是一种平面图形,笔画和结构不是非常稳定。很多字形具有图画性质,难以区分明显的结构,难写难记。已有的编码输入方法受众面小,效率很低,使用受限。该文分析了甲骨文字形的分形性质,在此基础上,通过字形的重心建立二维平面直角坐标系,将甲骨文字形的平面图形划分为四个象限。利用分形几何的原理,通过计算字形以及各个象限的分形维数,将甲骨文字形形式化为一组分形描述码。再通过与甲骨文字形的分形特征库进行配准,从而识别甲骨文字形。实验结果显示,利用分形几何可以较好地识别甲骨文字形。     

《分形几何初步》专题学习网站设计

我们精心设计了《分形几何初步》网络探究课程，依托《分形几何初步》专题学习网站．开展了信息技术与分形几何整合的课程改革实验研究．取得一系列成果．借此文与专家、同行进行交流。     

基于分形的DNA序列可视化表示研究

DNA序列可视化表示对于研究其结构与功能具有至关重要的意义,它有助于重复子序列的识别、内含子与外显子的区分以及DNA序列进化研究等等。本文首先介绍了生成DNA序列分形图像的Hao方法和经典的混沌游戏方法,然后深入分析和比较了这两种方法的异同点,并讨论了禁止子序列中回文子序列情况;紧接着,阐述了迭代函数系统产生分形吸引子的数学机理,并根据Moore自动机与迭代函数系统定义了混沌自动机,然后详细研究了以DNA序列驱动混沌自动机产生分形图像的方法;最后提出DNA序列三联密码子的分形图像表示方法,并对其进行了初步研究。     

基于数学形态学分形几何图的产生

我们已经讨论过采用概率逻辑神经网产生一类自（互）相似（分形）图的方法，本文将采用数学形态学的方法，产生类似的分形几种图，并讨论不同产生方法所具有的特点。     

遥感地形图象的灰度与分形分析

为了能够更加充分、准确地在遥感地形图象中利用分形信息,需要将其与其他特征配合使用。文章通过从视觉成像的角度,深入地剖析物体不同区域的形状和位置对成像灰度的影响,进而将有关结论与图象分形指数数据相结合,应用于基于图象内容的遥感图象的区域(标识)分割,取得了令人满意的效果,从中检查出分形数据中对应于图象深灰度区无意义的数值部分,从而保证了分形数据的可靠性,同时也说明了结合灰度或其它信息于分形图象应用的图象分析方式是十分必要的。     

Inferring Finite Automata with Stochastic Output Functions and an Application to Map Learning

It is often useful for a robot to construct a spatial representation of its environment from experiments and observations, in other words, to learn a map of its environment by exploration. In addition, robots, like people, make occasional errors in perceiving the spatial features of their environments. We formulate map learning as the problem of inferring from noisy observations the structure of a reduced deterministic finite automaton. We assume that the automaton to be learned has a distinguishing sequence. Observation noise is modeled by treating the observed output at each state as a random variable, where each visit to the state is an independent trial and the correct output is observed with probability exceeding 1/2. We assume no errors in the state transition function.Using this framework, we provide an exploration algorithm to learn the correct structure of such an automaton with probability 1 – , given as inputs , an upper bound m on the number of states, a distinguishing sequence s, and a lower bound > 1/2 on the probability of observing the correct output at any state. The running time and the number of basic actions executed by the learning algorithm are bounded by a polynomial in ^–l, m, |s|, and (1/2-)^–1.We discuss the assumption that a distinguishing sequence is given, and present a method of using a weaker assumption. We also present and discuss simulation results for the algorithm learning several automata derived from office environments.     

Interactive modeling of complex geometric details based on empirical mode decomposition for multi-scale 3D shapes

In this paper we develop an interactive modeling system for complex geometric details transformation based on empirical mode decomposition (EMD) on multi-scale 3D shapes. Given two models, we aim to transfer geometric details from one model to another one in an interactive manner. Taking full advantages of the multi-scale representation computed via EMD, different-scale geometric details can be transferred individually or in a concerted way, which makes our algorithm much more flexible than cut-and-paste and cloning based methods in transferring geometry details. In this process, the target surface with new transferred details could be generated by a mesh reconstruction method widely used in Laplacian surface editing. With the original positions of target surface serving as the soft constraints, the overall shape of the target model will be fully preserved. Our method can also support real-time continuous details transfer. Compared with state-of-the-art algorithms, our method provides an easier-to-use modeling tool and produces varied modeling results. We demonstrate the effectiveness of our modeling tool with various applications, such as detail transfer and enrichment, model reuse and recreation, and detail recovery for shape completion.     

Trimming implicit surfaces

Algorithms for trimming implicit surfaces yielding surface sheets and stripes are presented. These two-dimensional manifolds with boundaries result from set-theoretic operations on an implicit surface and a solid or another implicit surface. The algorithms generate adaptive polygonal approximation of the trimmed surfaces by extending our original implicit surface polygonization algorithm. The presented applications include modeling several spiral shaped surface sheets and stripes (based on M. Eschers artworks) and extraction of ridges on implicit surfaces. Another promising application of the presented algorithms is modeling heterogeneous objects as implicit complexes.     

An approach to integrating shape and biomedical attributes in vascular models

Computational models have been used widely in tissue engineering research and have proven to be powerful tools for bio-mechanical analysis (i.e., blood flow, growth models, drug delivery, etc). This paper focuses on developing higher-fidelity models for vascular structures and blood vessels that integrate computational shape representations with biomedical properties and features. Previous work in computer-aided vascular modeling comes from two communities. For those in biomedical imaging, the goal of past research has been to develop image understanding techniques for the interpretation of x-ray, magnetic resonance imaging (MRI), or other radiological data. These representations are predominantly discrete shape models that are not tied to physiological properties. The other corpus of existing work comes from those interested in developing physiological models for vascular growth and behavior based on bio-medical attributes. These models usually either have a highly simplified shape representation, or lack one entirely. Further, neither of these representations are suitable for the kind of interactive modeling required by tissue engineering applications.This paper aims to bridge these two approaches and develop a set of mathematical tools and algorithms for feature-based representation and computer-aided modeling of vascular trees for use in computer-aided tissue engineering applications. The paper offers a multi-scale representation based on swept volumes and a feature-based representation that can attribute the geometric representation with information about blood flow, pressure, and other biomedical properties. The paper shows how the resulting representation can be used as part of an overall approach for designing and visualizing vascular scaffolds. As a real-world example, we show how this computational model can be used to develop a tissue scaffold for liver tissue engineering. Such scaffolds may prove useful in a number of biomedical applications, including the growth of replacement tissue grafts and in vitro study of the pharmacological affects of new drugs on tissue cultures.     

Hierarchical aggregation for efficient shape extraction

This paper presents an efficient framework which supports both automatic and interactive shape extraction from surfaces. Unlike most of the existing hierarchical shape extraction methods, which are based on computationally expensive top-down algorithms, our framework employs a fast bottom-up hierarchical method with multiscale aggregation. We introduce a geometric similarity measure, which operates at multiple scales and guarantees that a hierarchy of high-level features are automatically found through local adaptive aggregation. We also show that the aggregation process allows easy incorporation of user-specified constraints, enabling users to interactively extract features of interest. Both our automatic and the interactive shape extraction methods do not require explicit connectivity information, and thus are applicable to unorganized point sets. Additionally, with the hierarchical feature representation, we design a simple and effective method to perform partial shape matching, allowing efficient search of self-similar features across the entire surface. Experiments show that our methods robustly extract visually meaningful features and are significantly faster than related methods.