基于局部蔓延的多层次实体模型检索

针对不同层次需求,根据层次之间蔓延区域的属性,利用局部蔓延生成一种多层次蔓延骨架图的实体模型表示方法;并基于该骨架图研究了子图群的匹配方法,提出多层次相似评价方法,高效、准确地完成了层次图的匹配.实验结果表明:该检索方式不仅具有很好的查全率与查准率,而且能够针对不同设计阶段的用户高效地给出满足用户需求的检索结果.     

基于多分辨率的快速迭代最近点配准算法

针对迭代最近点(Iterative Closest Point,ICP)算法计算时间长的问题,提出一种基于多分辨率配准点的ICP算法。使用自适应体素网格滤波器对原始点云进行多分辨率采样,利用低分辨率点云快速迭代获得两点云间初始变换矩阵;利用高分辨率点云在初始变换基础上做更精确配准。实验结果表明,该算法在配准精度基本不变的情况下,可以显著降低配准时间,且随着点云点数增加,速度提升效果越明显。     

改进的多分辨率形状匹配算法研究

形状匹配算法虽然在基于内容的视频检索中应用广泛，但由于视频数据量非常大，匹配非常耗时，因此形状匹配算法通常会成为实时视频检索的瓶颈，为了快速准确地进行形状匹配和检索，提出了一种改进的多分辨率Hausdorff距离变换算法，该算法是通过对后向匹配算法进行优化来使匹配速度大大加速，可用干进行实时车型比较和识别。实验结果表明，该改进算法在车型识别上具有速度快和准确性高的优点，尤其在模板图像比较大的情况下，此改进算法优势明显。     

目标特征指导的多分辨率体绘制算法

多分辨率体绘制是解决海量数据体绘制的一种有效方法。但对于数据散乱分布、同质区域较小的体绘制数据（比如物探领域的地震信号数据）,传统的基于香农熵或均方差的多分辨率方式均难以有效实现降低数据量的效果。本文提出了一种基于目标特征的多分辨率体绘制方法。以数据体中的目标特征为指导,适当降低非目标区域的分辨率,在尽可能不丢失其目标区域信息的情况下,实现有效的多分辨率体绘制。本文方法能够在目标保证数据量的前提下,尽可能的通过丢弃非目标区域的信息量,进而保护数据体的关键信息,以得到较好的绘制效果。实验结果表明,本文方法能与传统方法相比能够更好的保证关键区域绘制效果,同时进一步的降低用于绘制的数据量。     

多分辨率BSP树的生成及应用

CAD和科学可视化应用要求能够让用户对复杂场景进行交互式显示或者处理,因此,多细节层次技术被广泛应用于图形系统中以提高处理效率.通过构造一种新的BSP(binaryspacepartitioningtree)树形式来加速多细节层次模型的绘制,这种技术已成功地应用于所开发的多分辨率模型编辑系统.同时,详细描述了新的BSP树结构的构造和绘制过程.     

基于小波的网络多分辨率体绘制

为了能在网络环境下，快速地进行三维绘制，提出了一种网络环境下的基于小波的体数据多分辨率体绘制方法，该方法采取基于客户端的三维重建方案，首先利用三维小波的多分辨率分析方法，将体数据分解为不同分辨率下的离散逼近信号与高频细节信号；然后按先离散逼近信号，后高频细节信号的次序将数据传输到客户端；最后在客户端实现由粗及精的、渐进式的三维绘制。在这个过程中，一种3D的Mallat滤波器组被用来加速体数据的3D小波分解与重构，一种离散的简略化小波域体绘制方程被用来满足体绘制的实时性。实验结果表明，由于该方法仅需要12．5％或更低的数据量，即可以绘制出品质良好的图像或图像的概貌，所以非常适宜于需要频繁选择、交互的三维图像网络系统。     

基于多分辨率裁剪纹理的体裁剪技术

为解决单分辨率裁剪纹理的数据规模过大的问题,该文提出了一种具有INDEX-DATA二级结构的多分辨率裁剪纹理.文章主要介绍了多分辨率裁剪纹理的定义和结构,并讨论多分辨率纹理的构建方法和基于多分辨率纹理的体裁剪方法,最后对实验结果进行了分析讨论.该文方法已在自主知识产权可视化软件SVIP中得到应用,取得了令人满意的结果.     

一种动态交互的多分辨率地形生成

实现了一种动态实时交互的多分辨率地形生成，详细讨论了该生成算法的技术细节和特点。实验表明，该算法简单、有效，大大加快了图形显示和节约了内存空间，为后序研究提供了借鉴。     

基于多分辨率的图象压缩系统结构分析

本文着重对图象多分辨率技术进行分析，并提出了相应的系统结构成框架，同时还探讨了以图象多分辨率处理为核心，采用了 新的压缩编码的可能性。     

一种三维实体模型的离散表示方法

在计算机中,传统的三维几何模型只能描述表面数据,要描述模型内部属性时,这种模型显得无能为力。体图形学(VolumeGraphics,简称VG)是计算机图形学中新发展起来的一个重要分支。三维模型的体素表示是体图形学中的基本方法,体素化是体图形学中一个不可缺少的前处理过程,其任务是把物体的表面几何形式表示离散成最接近该物体的体素表示形式,产生体数据集。该文将基于Z-buffer扩展的深度缓存原理扩展到x,y,z三个方向上,实现了复杂三维网格模型的体素化表示。实验表明该算法具有很高的执行效率,并且算法的复杂度不依赖于模型的复杂度。     

Area-Based Medial Axis of Planar Curves

A new definition of affine invariant medial axis of planar closed curves is introduced. A point belongs to the affine medial axis if and only if it is equidistant from at least two points of the curve, with the distance being a minimum and given by the areas between the curve and its corresponding chords. The medial axis is robust, eliminating the need for curve denoising. In a dynamical interpretation of this affine medial axis, the medial axis points are the affine shock positions of the affine erosion of the curve. We propose a simple method to compute the medial axis and give examples. We also demonstrate how to use this method to detect affine skew symmetry in real images.     

基于整数中轴骨架的3维模型检索算法

针对3维模型检索算法性能较低的问题,提出了一种基于整数中轴骨架的3维模型检索算法。在对3维模型进行姿态调整和各向同向性预处理后,提取模型的整数中轴骨架,并记录每个骨架点相应的几何信息,对提取的骨架按不同的空间区域划分,形成模型骨架二叉树。为了能够描述骨架二叉树的不同节点对模型整体相似性匹配的影响程度,为每个节点定义一个特征权值,其大小由该节点对应的骨架区域大小所决定。最后,采用由粗到细逐步淘汰的策略计算不同模型的相似度。对一个标准3维模型测试数据库的检索实验结果表明,由于将模型的拓扑结构和统计特征相结合,该算法可以得到较好的检索性能。     

二维Voronoi图和中轴的特征区分

对多边形Voronoi图和中轴两个概念进行了重新定义以适应更广泛的工程应用.分析对比了含直线段、圆弧和自由曲线的区域轮廓边界Voronoi图和中轴的各自的特征,给出了二者在凸多边形、简单多边形等不同情况下的相互关系及证明.     

Automatic Reconstruction of Unstructured 3D Data: Combining a Medial Axis and Implicit Surfaces

This paper presents a new method that combines a medial axis and implicit surfaces in order to reconstruct a 3D solid from an unstructured set of points scattered on the object's surface. The representation produced is based on iso-surfaces generated by skeletons, and is a particularly compact way of defining a smooth free-form solid. The method is based on the minimisation of an energy representing a “distance” between the set of data points and the iso-surface, resembling previous reserach¹⁹. Initialisation, however, is more robust and efficient since there is computation of the medial axis of the set of points. Instead of subdividing existing skeletons in order to refine the object's surface, a new reconstruction algorithm progressively selects skeleton-points from the pre- computed medial axis using an heuristic principle based on a “local energy” criterion. This drastically speeds up the reconstruction process. Moreover, using the medial axis allows reconstruction of objects with complex topology and geometry, like objects that have holes and branches or that are composed of several connected components. This process is fully automatic. The method has been successfully applied to both synthetic and real data.     

LSMAT Least Squares Medial Axis Transform

The medial axis transform has applications in numerous fields including visualization, computer graphics, and computer vision. Unfortunately, traditional medial axis transformations are usually brittle in the presence of outliers, perturbations and/or noise along the boundary of objects. To overcome this limitation, we introduce a new formulation of the medial axis transform which is naturally robust in the presence of these artefacts. Unlike previous work which has approached the medial axis from a computational geometry angle, we consider it from a numerical optimization perspective. In this work, we follow the definition of the medial axis transform as ‘the set of maximally inscribed spheres’. We show how this definition can be formulated as a least squares relaxation where the transform is obtained by minimizing a continuous optimization problem. The proposed approach is inherently parallelizable by performing independent optimization of each sphere using Gauss–Newton, and its least‐squares form allows it to be significantly more robust compared to traditional computational geometry approaches. Extensive experiments on 2D and 3D objects demonstrate that our method provides superior results to the state of the art on both synthetic and real‐data.     

Untangling the Blum Medial Axis Transform

For over 30 years, Blum's Medial Axis Transform (MAT) has proven to be an intriguing tool for analyzing and computing with form, but it is one that is notoriously difficult to apply in a robust and stable way. It is well documented how a tiny change to an object's boundary can cause a large change in its MAT. There has also been great difficulty in using the MAT to decompose an object into a hierarchy of parts reflecting the natural parts-hierarchy that we perceive. This paper argues that the underlying cause of these problems is that medial representations embody both the substance of each part of an object and the connections between adjacent parts. A small change in an object's boundary corresponds to a small change in its substance but may involve a large change in its connection information. The problems with Blum's MAT are generated because it does not explicitly represent this dichotomy of information. To use the Blum MAT to it's full potential, this paper presents a method for separating the substance and connection information of an object. This provides a natural parts-hierarchy while eliminating instabilities due to small boundary changes. The method also allows for graded, fuzzy classifications of object parts to match the ambiguity in human perception of many objects.     

Medial Axes and Mean Curvature Motion II: Singularities

What happens to the medial axis of a curve that evolves through MCM (Mean Curvature Motion)? We explore some theoretical results regarding properties of both medial axes and curvature motions. Specifically, using singularity theory, we present all possible topological transitions of a symmetry set (of which the medial axis is a subset) whose originating curve undergoes MCM. All calculations are presented in a clear and organized fashion and are easily generalized for other front motions. A companion article deals with non-singular points of the medial axis through direct calculations.     

Medial Axis Construction in Three Dimensions and its Application to Mesh Generation

An algorithm for the construction of the medial axis of a three-dimensional body given by a triangulation of its bounding surface is described. The indirect construction is based on the Delaunay-triangulation of a set of sample points on the bounding surface. The point set is refined automatically so as to capture the correct topology of the medial axis. The computed medial axis (or better medial surface) is then used for hex-dominant mesh generation. Quad-dominant meshes are generated on the medial subfaces first and extruded to the boundary of the body at both sides. The resulting single cell layer is subdivided in direction normal to the boundary, yielding columns of hexahedral and three-sided prismatic cells. The resulting volume mesh is orthogonal at the boundary and ‘semi-structured’ between boundary and medial surface. Mixed cell types (tets, pyramids, degenerate hexahedra) may result along the medial surface. An advancing front algorithm (paving) is used for meshing the subfaces of the medial surface. Development of the mesh generator has not been fully completed with respect to degenerate parts of the medial axis. First medium-complexity bodies have been meshed, however, showing moderate meshing times.