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1.
We present an algorithm for constructing isosurfaces in any dimension. The input to the algorithm is a set of scalar values in a d-dimensional regular grid of (topological) hypercubes. The output is a set of (d-1)-dimensional simplices forming a piecewise linear approximation to the isosurface. The algorithm constructs the isosurface piecewise within each hypercube in the grid using the convex hull of an appropriate set of points. We prove that our algorithm correctly produces a triangulation of a (d-1 )-manifold with boundary. In dimensions three and four, lookup tables with 2/sup 8/ and 2/sup 16/ entries, respectively, can be used to speed the algorithm's running time. In three dimensions, this gives the popular marching cubes algorithm. We discuss applications of four-dimensional isosurface construction to time varying isosurfaces, interval volumes, and morphing.  相似文献   

2.
Largest and Smallest Convex Hulls for Imprecise Points   总被引:2,自引:0,他引:2  
Assume that a set of imprecise points is given, where each point is specified by a region in which the point may lie. We study the problem of computing the smallest and largest possible convex hulls, measured by length and by area. Generally we assume the imprecision region to be a square, but we discuss the case where it is a segment or circle as well. We give polynomial time algorithms for several variants of this problem, ranging in running time from O(nlog n) to O(n 13), and prove NP-hardness for some other variants.  相似文献   

3.
本文提出一种基于凸包的齿痕点的快速定位方法.在详细讨论了如何将图形学中的经典凸包算法应用于数字化中医舌诊的齿痕定位中后,通过相关舌图做实验,证明了该方法在快速齿痕点特征提取中的可行性、有效性和准确性.  相似文献   

4.
图像目标外接多边形及凸壳的一种构造方法   总被引:1,自引:0,他引:1  
对二值图像进行Hough变换后,在(ρ,θ)空间中选取了一组边界对应点,通过计算与这些边界对应点对应的图像空间中直线的交点,构造了图像目标的外接多边形;通过比较相距π/2 rad的投影区间长度是否相等,或区间长度的乘积是否为最小,得到了形状外接正方形和外接最小面积矩形;利用构造形状外接多边形的方法并通过增加边的数目,构造了形状的近似凸壳.实验和理论分析表明,文中算法具有好的抗噪性能和广泛的适用范围.  相似文献   

5.
用兴趣点凸包和SVM加权反馈实现图像检索   总被引:4,自引:0,他引:4  
针对采用环状颜色直方图的图像检索方法存在的不足,提出一种基于兴趣点凸包的图像特征提取方法,通过对用小波变换检测出的必趣点递归求出它们的凸包,并将每个凸包上的兴趣点按一定的算法安插在相应的桶内,对每个桶求出颜色直方图,利用桶与桶之间的相似度定义两幅图像的相似度.这种特征提取方法可有效抑制兴趣点集合中出现游离兴趣点的情况,结合基于兴趣点的空间离散度和Gabor小波纹理等特征实现图像检索,可有效提高图像检索精度.最后,提出一种新的相关反馈方法,通过利用支持向量机分类结果设置权值来改进移动查询点相关反馈方法.实际图像数据库上的实验表明,引入这种反馈方法后可将图像检索的查准率提高20%左右,查全率提高10%左右.  相似文献   

6.
The problem of data visualization in the analysis of two classes in a multidimensional feature space is considered. The two orthogonal axes by which the classes are maximally separated from each other are found in the mapping of classes as a result of linear transformation of coordinates. The proximity of the classes is estimated based on the minimum-distance criterion between their convex hulls. This criterion makes it possible to show cases of full class separability and random outliers. A support vector machine is used to obtain orthogonal vectors of the reduced space. This method ensures the obtaining of the weight vector that determines the minimum distance between the convex hulls of classes for linearly separable classes. Algorithms with reduction, contraction, and offset of convex hulls are used for intersecting classes. Experimental studies are devoted to the application of the considered visualization methods to biomedical data analysis.  相似文献   

7.
Persistent Semi-Dynamic Ordered Partition Index   总被引:1,自引:0,他引:1  
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8.
We study some minimum-area hull problems that generalize the notion of convex hull to star-shaped and monotone hulls. Specifically, we consider the minimum-area star-shaped hull problem: Given an n -vertex simple polygon P , find a minimum-area, star-shaped polygon P * containing P . This problem arises in lattice packings of translates of multiple, nonidentical shapes in material layout problems (e.g., in clothing manufacture), and has been recently posed by Daniels and Milenkovic. We consider two versions of the problem: the restricted version, in which the vertices of P * are constrained to be vertices of P , and the unrestricted version, in which the vertices of P * can be anywhere in the plane. We prove that the restricted problem falls in the class of ``3sum-hard' (sometimes called ``n 2 -hard') problems, which are suspected to admit no solutions in o(n 2 ) time. Further, we give an O(n 2 ) time algorithm, improving the previous bound of O(n 5 ) . We also show that the unrestricted problem can be solved in O(n 2 p(n)) time, where p(n) is the time needed to find the roots of two equations in two unknowns, each a polynomial of degree O(n) . We also consider the case in which P * is required to be monotone, with respect to an unspecified direction; we refer to this as the minimum-area monotone hull problem. We give a matching lower and upper bound of Θ(n log n) time for computing P * in the restricted version, and an upper bound of O(n q(n)) time in the unrestricted version, where q(n) is the time needed to find the roots of two polynomial equations in two unknowns with degrees 2 and O(n) . Received November 1996; revised March 1997.  相似文献   

9.
Projective Visual Hulls   总被引:1,自引:0,他引:1  
This article presents a novel method for computing the visual hull of a solid bounded by a smooth surface and observed by a finite set of cameras. The visual hull is the intersection of the visual cones formed by back-projecting the silhouettes found in the corresponding images. We characterize its surface as a generalized polyhedron whose faces are visual cone patches; edges are intersection curves between two viewing cones; and vertices are frontier points where the intersection of two cones is singular, or intersection points where triples of cones meet. We use the mathematical framework of oriented projective differential geometry to develop an image-based algorithm for computing the visual hull. This algorithm works in a weakly calibrated setting–-that is, it only requires projective camera matrices or, equivalently, fundamental matrices for each pair of cameras. The promise of the proposed algorithm is demonstrated with experiments on several challenging data sets and a comparison to another state-of-the-art method.  相似文献   

10.
Hardware-Accelerated Rendering of Photo Hulls   总被引:1,自引:0,他引:1  
  相似文献   

11.
Carved Visual Hulls for Image-Based Modeling   总被引:3,自引:0,他引:3  
This article presents a novel method for acquiring high-quality solid models of complex 3D shapes from multiple calibrated photographs. After the purely geometric constraints associated with the silhouettes found in each image have been used to construct a coarse surface approximation in the form of a visual hull, photoconsistency constraints are enforced in three consecutive steps: (1) the rims where the surface grazes the visual hull are first identified through dynamic programming; (2) with the rims now fixed, the visual hull is carved using graph cuts to globally optimize the photoconsistency of the surface and recover its main features; (3) an iterative (local) refinement step is finally used to recover fine surface details. The proposed approach has been implemented, and experiments with seven real data sets are presented, along with qualitative and quantitative comparisons with several state-of-the-art image-based-modeling algorithms.  相似文献   

12.
自由拍摄视点下的可见外壳生成算法   总被引:2,自引:0,他引:2  
给出了一种使用手持相机拍摄的多幅图像构造可见外壳的方法,该方法无需对相机运动方式作任何限定,而是利用多幅图像上的对应特征点求出每一幅图像的拍摄方位,因而可以非常灵活地获取某些较大规模的室外场景的几何模型.实验结果表明,利用该方法生成的可见外壳模型准确真实,能够满足虚拟现实等应用中的要求.  相似文献   

13.
三维模型的重建和表示是计算机图形和计算机视觉中一个重要的领域,其广泛应用于自动识别,工业自动化设计以及虚拟场景的重建。文中实现一个从照片序列重建三维物体多面体模型的系统,使用由轮廓恢复形体(SFS),通过经由轮廓光锥相交得到包围物体的虚拟壳。在系统中采用的共极线几何和增量运算把所有的三维的相交计算投射到二维平面的退化多边形求交来降低相交计算的复杂度。与传统多面体虚拟壳重构相比,算法有以下几点改进:在图像平面以退化多边形组织投影锥体和物体轮廓的交集,把任意锥面与物体轮廓的交集归一到一个退化多边形;基于退化多边形的二维平面上多边形快速相交算法。通过这些改进可以减少虚拟壳的生成时间并有助于实时绘制的实现。  相似文献   

14.
Convex Optimization   总被引:1,自引:0,他引:1  
  相似文献   

15.
We compute all translations resulting in the union of two finite, convex sets being again convex. Convexity will be established by conditions on the outside of the convex hull. Computations are of low degree polynomial bounds on the worst case number of steps. This results in a set estimator for a mobile robot's translation value.  相似文献   

16.
A definition of convexity of digital solids is introduced. Then it is proved that a digital solid is convex if and only if it has the chordal triangle property. Other geometric properties which characterize convex digital regions are shown to be only necessary, but not sufficient, conditions for a digital solid to be convex. An efficient algorithm that determines whether or not a digital solid is convex is presented.  相似文献   

17.
Convex multiresolution analysis   总被引:2,自引:0,他引:2  
A standard wavelet multiresolution analysis can be defined via a sequence of projectors onto a monotone sequence of closed vector subspaces possessing certain properties. We propose a nonlinear extension of this framework in which the vector subspaces are replaced by convex subsets. These sets are chosen so as to provide a recursive, monotone approximation scheme that allows for various signal and image features to be investigated. Several classes of convex multiresolution analyses are discussed and numerical applications to signal and image-processing problems are demonstrated  相似文献   

18.
Convex Control Systems and Convex Optimal Control Problems With Constraints   总被引:1,自引:0,他引:1  
This note discusses the concepts of convex control systems and convex optimal control problems. We study control systems governed by ordinary differential equations in the presence of state and target constraints. Our note is devoted to the following main question: under which additional assumptions is a sophisticated constrained optimal control problem equivalent to a simple convex minimization problem in a related Hilbert space. We determine some classes of convex control systems and show that, for suitable cost functionals and constraints, optimal control problems for these classes of systems correspond to convex optimization problems. The latter can be reliably solved using standard numerical algorithms and effective regularization schemes. In particular, we propose a conceptual computational approach based on gradient-type methods and proximal point techniques.  相似文献   

19.
This paper gives a definition for the convexity of B-spline surfaces and points out the conditions, on which the convexity depends.A back shift smoothing method is introduced. This method is built on the basis of the convexity conditions. Application of this smoothing method gives a strictly convex curve.  相似文献   

20.
In this paper centered convex previsions are introduced as a special class of imprecise previsions, showing that they retain or generalise most of the relevant properties of coherent imprecise previsions but are not necessarily positively homogeneous. The broader class of convex imprecise previsions is also studied and its fundamental properties are demonstrated, introducing in particular a notion of convex natural extension which parallels that of natural extension but has a larger domain of applicability. These concepts appear to have potentially many applications. In this paper they are applied to risk measurement, leading to a general definition of convex risk measure which corresponds, when its domain is a linear space, to the one recently introduced in risk measurement literature.  相似文献   

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