The normalform of a space curve and its application to surface design

x )=0 with ∥▿h∥=1. The normalform function h is (unlike the latter cases) not differentiable at curve points. Despite of this disadvantage the normalform is a suitable tool for designing surfaces which can be treated as common implicit surfaces. Many examples (bisector surfaces, constant distance sum/product surfaces, metamorphoses, blending surfaces, smooth approximation surfaces) demonstrate applications of the normalform to surface design. Published online: 25 July 2001     

Fractal analysis of tumor in brain MR images

Abstract. The purpose of this study is to discuss existing fractal-based algorithms and propose novel improvements of these algorithms to identify tumors in brain magnetic-response (MR) images. Considerable research has been pursued on fractal geometry in various aspects of image analysis and pattern recognition. Magnetic-resonance images typically have a degree of noise and randomness associated with the natural random nature of structure. Thus, fractal analysis is appropriate for MR image analysis. For tumor detection, we describe existing fractal-based techniques and propose three modified algorithms using fractal analysis models. For each new method, the brain MR images are divided into a number of pieces. The first method involves thresholding the pixel intensity values; hence, we call the technique piecewise-threshold-box-counting (PTBC) method. For the subsequent methods, the intensity is treated as the third dimension. We implement the improved piecewise-modified-box-counting (PMBC) and piecewise-triangular-prism-surface-area (PTPSA) methods, respectively. With the PTBC method, we find the differences in intensity histogram and fractal dimension between normal and tumor images. Using the PMBC and PTPSA methods, we may detect and locate the tumor in the brain MR images more accurately. Thus, the novel techniques proposed herein offer satisfactory tumor identification. Received: 13 October 2001 / Accepted: 28 May 2002 Correspondence to: K.M. Iftekharuddin     

Surface scratches: measuring, modeling and rendering

  One of the most important criticisms that can be made concerning synthesized images is the brand new and too clean aspect of objects. Surface color modifications can be used to introduce dirtiness or other aging-linked characteristics. Also, techniques such as bump or displacement mapping allow users to improve surface aspects by introducing geometrical perturbations. In parallel, the bidirectional reflectance distribution function (BRDF) is a crucial factor in achieving a high degree of realism. It turns out that surfaces are very often covered by defects such as scratches that are related to both textures and BRDFs due to their size. Scratches do not always affect the apparent geometry but nevertheless can remain strongly visible. None of the previously mentioned methods is suited for rendering these defects efficiently. We propose a new method, based on extensions to existing BRDFs and classical 2D texture mapping techniques, to render efficiently individually visible scratches. We use physical measurements on "real objects" to derive an accurate geometric model of scratches at small scale range (roughness scale), and we introduce a new geometric level between bump mapping and BRDFs. Beyond providing graphical results closely matching real cases, our method opens the way to a new class of considerations in computer graphics based on defects that require the coupling of both BRDFs and texturing techniques.     

Reconstructing 2D images with natural neighbour interpolation

In this paper, we explore image reconstruction by natural neighbour interpolation from irregularly spaced samples. We sample the image irregularly with techniques based on the Laplacian or the derivative in the direction of the gradient. Local coordinates based on the Voronoi diagram are used in natural neighbour interpolation to quantify the “neighbourliness” of data sites. Then we use natural neighbour interpolation in order to reconstruct the image. The main result is that the image quality is always very good in the case of the sampling techniques based on the Laplacian.     

Construction and application of fractal interpolation surfaces

Fractal geometry has unique advantages for a broad class of modeling problems, including natural objects and patterns. This paper presents an approach to the construction of fractal surfaces by triangulation. After introducing the notion of iterated function systems (IFSs), we prove theoretically that the attractors of this construction are continuous fractal interpolation surfaces (FISs). Two fast, parallel, and iterative algorithms are also provided. Several experiments in natural phenomena simulation verify that this method is suitable for generating complex 3D shapes with self-similar patterns.Project supported by the National Natural Science of China     

Coons型分形曲面的生成方法

将传统计算几何中的网函数插值方法与分形插值函数理论相结合，给出生成分形Coons型曲面的一种新方法.     

基于分形理论的深海钴结壳微地形仿真

文章对分形布朗函数的特性及自然地表分形特征进行了分析和总结,并结合深海钴结壳微地形所具有的自然特性,提出了具有方向性分形特征的中点随机位移法,实验结果表明该方法能较好地反映原始数据的总体轮廓,而且还能较好地再现原始微地形的粗糙起伏及各向异性,因而是一个切实可行的构造三维地形的插值方法。     

一种基于分形插值的复杂图像的亚像素算法

本文提出一种基于分形理论的亚像素算法,通过提取自然景物的分形参数,并利用图像的分形参数进行随机分形插值。试验结果表明,该算法可以达到很好的亚像素精度。     

Implementing compositionality for stochastic Petri nets

An implementation of compositionality for stochastic well-formed nets (SWN) and, consequently, for generalized stochastic Petri nets (GSPN) has been recently included in the GreatSPN tool. Given two SWNs and a labelling function for places and transitions, it is possible to produce a third one as a superposition of places and transitions of equal label. Colour domains and arc functions of SWNs have to be treated appropriately. The main motivation for this extension was the need to evaluate a library of fault-tolerant “mechanisms” that have been recently defined, and are now under implementation, in a European project called TIRAN. The goal of the TIRAN project is to devise a portable software solution to the problem of fault tolerance in embedded systems, while the goal of the evaluation is to provide evidence of the efficacy of the proposed solution. Modularity being a natural “must” for the project, we have tried to reflect it in our modelling effort. In this paper, we discuss the implementation of compositionality in the GreatSPN tool, and we show its use for the modelling of one of the TIRAN mechanisms, the so-called local voter. Published online: 24 August 2001     

Discovery of a perceptual distance function for measuring image similarity

For more than a decade, researchers have actively explored the area of image/video analysis and retrieval. Yet one fundamental problem remains largely unsolved: how to measure perceptual similarity between two objects. For this purpose, most researchers employ a Minkowski-type metric. Unfortunately, the Minkowski metric does not reliably find similarities in objects that are obviously alike. Through mining a large set of visual data, our team has discovered a perceptual distance function. We call the discovered function the dynamic partial function (DPF). When we empirically compare DPF to Minkowski-type distance functions in image retrieval and in video shot-transition detection using our image features, DPF performs significantly better. The effectiveness of DPF can be explained by similarity theories in cognitive psychology.     

基于遗传算法的图形的分形拟合

自仿分形插值函数作为数据拟合工具,能较好地拟合复杂度较高的曲线图形;但是在拟合过程中如何选择一组合适的纵向压缩因子进行匹配,仍然是一项繁琐的工作;针对这一难点,尝试利用遗传算法的全局最优化过程寻求一组合适的纵向压缩因子,以实现对复杂度较高的曲线图形的较佳分形拟合。     

基于分形编码拓扑特性的图像检索

为了更有效、更准确地进行图像检索，提出了一种利用分形编码这项重要的拓扑特性来处理图像索引的新方法，即将图像经分形编码，首先得到每张图像的迭代函数，然后将其伴随图像存人数据库中，成为该图像的索引文件最后对数据库进行搜索时，则通过对此索引文件的比对来找出与查询图像相似的图像。反观使用其他方法建立的图像索引数据库，则无法证明其建立的索引文件具有上述特质。实验显示，图像经过分形编码所表现出的几何性质以及独特的有效性和鲁棒性，证明该方法是一个更有效率、准确度高的检索方法。     

Use of potential functions in 3D rendering of fractal images from complex functions

Computer graphics is important in developing fractal images visualizing the Mandelbrot and Julia sets from a complex function. Computer rendering is a central tool for obtaining nice fractal images. We render 3D objects with the height of each complex point of a fractal image considering the diverging speed of its orbit. A potential function helps approximate this speed. We propose a new method for estimating the normal vector at the surface points given by a potential function. We consider two families of functions that exhibit interesting fractal images in a bounded region: a power function,f _{, c}(z)=z +c, where is a real number, and the Newton form of an equation, where ¦¦=1 and >0.     

Coupling Use Cases and Class Models as a Means for Validation and Verification of Requirements Specifications

In many applications, especially from the business domain, the requirements specification mainly deals with use cases and class models. Unfortunately, these models are based on different modelling techniques and aim at different levels of abstraction, such that serious consistency and completeness problems are induced. To overcome these deficiencies, we refine activity graphs to meet the needs for a suitable modelling element for use case behaviour. The refinement in particular supports the proper coupling of use cases via activity graphs and the class model. The granularity and semantics of our approach allow for a seamless, traceable transition of use cases to the class model and for the verification of the class model against the use case model. The validation of the use case model and parts of the class model is supported as well. Experience from several applications has shown that the investment in specification, validation and verification not only pays off during system and acceptance testing but also significantly improves the quality of the final product.