等值面的高质量显示算法实现三维物体表面的重建

介绍了一个能有效消除等值面显示中易出现的锯齿状走样现 象,可以生成非常细腻的三维物体表面图象的等值面高质量显示算法。论述了采用体素级的 等值面直接显示算法实现三维物体表面重构的基本方法。     

一种医学图像三维表面重建的快速算法

阐述了医学图像三维重建的方法和过程,提出了一种基于跨距空间的快速种子体素搜索算法,利用等值面繁衍算法快速提取三角形等值面,并对由中点近似产生的共面三角形等值面进行合并。实验结果显示,本文提出的算法加快了重建的速度,有利于实现对基于医学图像的大规模数据三维重建的实时绘制和交互。     

一种由二维轮廓线重建物体表面的方法

本文提出一种通过体数据转换实现由轮廓线重建物体表面的方法 .该方法根据“表面投影区”比较两相邻切平面上对应像素点的状态函数值 ,以确定影响等值面生成的像素点 ,从而只进行影响等值面生成的像素点的距离函数的计算 ,并可在根据需要对相邻切平面上的对应点进行插值计算后 ,生成分辨率较高的体数据 .本文采用改进的 MT算法生成等值面 ,完成物体的表面重建 .该方法缩短了体数据的构造时间 ,在保证了重建正确性的前提下提高了整个表面的重建速度     

基于Double Marching Cubes的表面重建算法

为克服基于Marching Cubes的表面重建算法在绘制三维表面时因二义性面的存在而使生成的表面网格易出现错误连接而形成层间空洞的不足,提出了基于Double Marching Cubes的表面重建算法.该算法采用双立方体体素作为生成表面网格的基本单元,以双立方体的12个特征点的标记情况为依据,建立一个双立方体体素索引表,通过查找索引表的方法绘制三维表面.该算法在建立双立方体索引表时就排除掉了二义性面的所有错误连接方式,因而生成的表面网格不会出现层间空洞,避免了为消除二义性面所进行的复杂计算,加快了表面重建的速度.     

基于标签化医学图像的多阈值三维重建算法

针对传统面绘制重建方法 MC无法一次性提取多个阈值器官的问题,提出一种将MRI图像中靶区及其周边组织进行标签化分割的多阈值三维重建算法。该算法通过将二维图像中的多阈值器官标签化为简单的整数,降低提取等值面时的数据存储量,进而提高等值面的绘制速度。同时,定义了多阈值三维重建时体素顶点索引方式和等值面相交形态,减少了传统MC算法提取多个阈值器官时存在三角面片与顶点复用的情况,且仅需一次性扫描即可重建多个器官等值面。实验结果表明,本文算法较传统MC算法,重建器官数量越多,器官彼此结构越紧密,三角面片与顶点复用情况减少越明显,在保证重建效果的同时,绘制速度可提高30%。     

基于气象雷达回波3D重建的Marching Cubes改进算法

根据气象雷达回波数据的三维极坐标分布特点,提出一种改进的Marching Cubes三维重建算法.该算法将Marching Cubes常规算法中的单位正立方体构建转换为直接对回波极坐标数据的拟柱体构建,生成相应的等值三角面,并对三角面的顶点数据进行地曲订正,供OpenGL显示.为进一步提高重建算法的效率,该算法避免了对高仰角远距离无回波区的重建.实验表明,该算法有效实现了雷达回波的三维重建.     

基于最近邻Marching Cubes的医学图像三维重建

在医学图像三维可视化中,移动立方体算法（Marching Cubes,MC）是面绘制的经典算法。针对MC算法计算插值点导致执行速度慢、效率不高的缺点,提出一种基于最近邻逼近的MC算法,该方法在n次等分点量化序列中寻找等值面最近邻点代替线性或非线性插值,既避免了插值的大量计算又保证了误差精度,还可改善三角面片结构。利用可视化工具开发包VTK对人体脸部和脚部CT数据集进行三维重建,实验表明改进算法明显缩短了绘制时间,提高了重建效率。     

移动立方体算法与移动四面体算法的对比与评估

等值面提取在标量场体数据可视化和隐函数曲面显示中具有重要应用,经典算法包括移动立方体算法和移动四面体算法,其核心是在立方体或四面体体素单元中用线性的三角面片逼近原始曲面.文中以可计算的代数曲面为例,对上述2种等值面提取算法的逼近精度、时间和空间效率等方面进行了详细的对比,为各种应用中等值面提取算法的选取提供了参考依据.     

空间相关MC算法的VTK实现

移动立方体是面绘制的经典算法,但要求对所有空间所有体素进行处理,执行效率不高.通过对空间相关性进行研究,即六面体体素如果与等值面相交,则等值面一定会在该六面体的6个面的方面延续,对标准的MC算法进行改进,只处理那些与等值面相交的六面体体素.可视化工具包封装了许多常用的可视化算法,为研究人员提供了极大的便利.通过空间相关性,对VTK中已有库函数vtkMarchingCubes进行改进,提高了原有算法的执行速度,同时又扩充了VTK已有的类.     

基于面绘制技术的医学影像立体显示

医学影像立体显示技术利用二维医学图像序列重建出三维模型,为医生提供了直观、全面、准确的病灶和正常组织信息,给临床诊断和治疗带来了巨大进步,是当今医学领域研究的热点。三维重建有体绘制和面绘制两种方法,本文主要介绍了面绘制方法的原理和实现,选择基于体素的表面重建方法,利用国际上广泛应用的可视化工具包VTK提供的MC算法实现面绘制,并对轴、冠、矢三个方向的任意切面进行显示。     

System for reconstruction of three-dimensional micro objects from multiple photographic images

We introduce a system to reconstruct a three-dimensiojnal (3D) polygonal model of 3D micro objects with outer dimensions ranging from several hundred microns to several millimeters from multiple two-dimensional (2D) images of an object taken from different views. The data acquisition system consists of a digital microscope that captures still images at a resolution of 1600 × 1200 pixels and a computer-controlled turntable. We employ the shape-from-silhouette (SFS) method to construct a voxel-based 3D model from silhouette images. The concave shapes are further carved by using the space carving technique. In order to make the resulting model compatible with a commercial CAD/CAM system, the voxel model is converted into a triangular mesh using the marching cubes algorithm. Because the mesh generated from the voxel model by using the marching cubes algorithm inherits the staircase effect, the mesh is adjusted to recover the object precisely by using silhouette images. Finally, we evaluate the accuracy of the proposed method. The reconstructed models of complex micro objects indicate the effectiveness of the 3D shape reconstruction system for micro objects.     

体素可视外壳并行优化建模方法

基于体的可视外壳重建不需要复杂的几何计算,易于实现,但其精度和效率仍不理想。提出一种基于统一计算架构(CUDA)和行进立方体(MC)的体素可视外壳并行优化建模方法,将体素相交判断和等值面抽取过程并行分解,利用CUDA的内核多线程机制加速建模;在MC网格化阶段,提取准确交点并消除冗余边计算;利用像素着色器实现混合权重的纹理映射,提高模型精度。在多摄像机采集装置DreamWorld上的实验结果表明,本文方法能够对多个动态物体进行实时准确的3维建模。     

Topological equivalence between a 3D object and the reconstruction of its digital image

Digitization is not as easy as it looks. If one digitizes a 3D object even with a dense sampling grid, the reconstructed digital object may have topological distortions and, in general, there exists no upper bound for the Hausdorff distance. This explains why so far no algorithm has been known which guarantees topology preservation. However, as we will show, it is possible to repair the obtained digital image in a locally bounded way so that it is homeomorphic and close to the 3D object. The resulting digital object is always well-composed, which has nice implications for a lot of image analysis problems. Moreover, we will show that the surface of the original object is homeomorphic to the result of the marching cubes algorithm. This is really surprising since it means that the well-known topological problems of the marching cubes reconstruction simply do not occur for digital images of r-regular objects. Based on the trilinear interpolation, we also construct a smooth isosurface from the digital image that has the same topology as the original surface. Finally, we give a surprisingly simple topology preserving reconstruction method by using overlapping balls instead of cubical voxels. This is the first approach of digitizing 3D objects which guarantees topology preservation and gives an upper bound for the geometric distortion. Since the output can be chosen as a pure voxel presentation, a union of balls, a reconstruction by trilinear interpolation, a smooth isosurface, or the piecewise linear marching cubes surface, the results are directly applicable to a huge class of image analysis algorithms. Moreover, we show how one can efficiently estimate the volume and the surface area of 3D objects by looking at their digitizations. Measuring volume and surface area of digital objects are important problems in 3D image analysis. Good estimators should be multigrid convergent, i.e., the error goes to zero with increasing sampling density. We will show that every presented reconstruction method can be used for volume estimation and we will give a solution for the much more difficult problem of multigrid-convergent surface area estimation. Our solution is based on simple counting of voxels and we are the first to be able to give absolute bounds for the surface area.     

A surface reconstruction algorithm for topology optimization

For mechanical structural design, topology optimization is often utilized. During this process, a topologically optimized model must be converted into a parametric CAD solid model. The key point of conversion is that a discretized shape of a topologically optimized model must be smoothed, but features such as creases and corners must be retained. Thus, a surface reconstruction algorithm to produce the parametric CAD solid model from a topologically optimized model is proposed in this paper. Our presented algorithm consists of three parts: (1) an enclosed isosurface geometry from which the topologically optimized model is generated, (2) features detected and (3) the parametric CAD solid model reconstructed as biquartic surface splines. In order to generate an enclosed isosurface model effectively, we propose an algorithm based upon the marching cubes method to detect elements intersected by an isosurface. After generating an enclosed isosurface model, we produce biquartic surface splines. By applying our algorithm to an enclosed isosurface model, it is possible to produce smoothed biquartic surface splines with features retained. Some examples are shown and the effectiveness of our algorithm is discussed in this paper.     

Surface reconstruction with higher-order smoothness

This work proposes a method to reconstruct surfaces with higher-order smoothness from noisy 3D measurements. The reconstructed surface is implicitly represented by the zero-level set of a continuous valued embedding function. The key idea is to find a function whose higher-order derivatives are regularized and whose gradient is best aligned with a vector field defined by the input point set. In contrast to methods based on the first-order variation of the function that are biased toward the constant functions and treat the extraction of the isosurface without aliasing artifacts as an afterthought, we impose a higher-order smoothness directly on the embedding function. After solving a convex optimization problem with a multiscale iterative scheme, a triangulated surface can be extracted using the marching cubes algorithm. We demonstrated the proposed method on several data sets obtained from raw laser-scanners and multiview stereo approaches. Experimental results confirm that our approach allows us to reconstruct smooth surfaces from points in the presence of noise, outliers, large missing parts, and very coarse orientation information.     

Volumetric Reconstruction of Objects and Scenes Using Range Images

This paper reviews volumetric methods for fusing sets of range images to create 3D models of objects or scenes. It also presents a new reconstruction method, which is a hybrid that combines several desirable aspects of techniques discussed in the literature. The proposed reconstruction method projects each point, or voxel, within a volumetric grid back onto a collection of range images. Each voxel value represents the degree of certainty that the point is inside the sensed object. The certainty value is a function of the distance from the grid point to the range image, as well as the sensor's noise characteristics. The super-Bayesian combination formula is used to fuse the data created from the individual range images into an overall volumetric grid. We obtain the object model by extracting an isosurface from the volumetric data using a version of the marching cubes algorithm. Results are shown from simulations and real range finders.     

A type-merging algorithm for extracting an isosurface from volumetric data

A new approach for reducing the number of triangles representing an isosurface in volumetric data is presented. The basic idea is to classify the configurations of the marching cubes approach into types. Surface patches traversing neighboring cubes of the same type can be merged into patches, which can be approximated with fewer and larger triangles. Experimental results show that the number of triangles is about 50% of that obtained with the marching cubes algorithm, with comparable image quality. The execution time is somewhat longer than that of the marching cubes algorithm.     

On marching cubes

A characterization and classification of the isosurfaces of trilinear functions is presented. Based upon these results, a new algorithm for computing a triangular mesh approximation to isosurfaces for data given on a 3D rectilinear grid is presented. The original marching cubes algorithm is based upon linear interpolation along edges of the voxels. The asymptotic decider method is based upon bilinear interpolation on faces of the voxels. The algorithm of this paper carries this theme forward to using trilinear interpolation on the interior of voxels. The algorithm described here will produce a triangular mesh surface approximation to an isosurface which preserves the same connectivity/separation of vertices as given by the isosurface of trilinear interpolation.     

采用空间分割的平滑曲面重构算法

面绘制是科学计算可视化中一个重要的研究方向，移动立方体是实现面绘制的一个重要算法，八叉树是一种有效的表示三维物体的方法，该文在八叉树生成的基础上，提出一种基于空间分割的表面重构算法，将绘制空间分别按X轴、Y轴和Z轴进行分割，生成的树的节点个数小于等于8个，与八叉树方法相比，减少了所生成叶结点数量，再通过移动立方体算法生成三角面片。三角面片通过平滑处理，提高了图形显示质量。