Ordering and Parameterizing Scattered 3D Data for B-Spline Surface Approximation
Ordering and Parameterizing Scattered 3D Data for B-Spline Surface Approximation
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对 B 样条曲面近似的分散 3D 数据进行排序和参数化
DOI：
10.1109/34.862203
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
C. Pintavirooj
中科院分区：
文献类型：
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作者：
F. Cohen;W. S. Ibrahim;C. Pintavirooj
表面表示对于医学成像、计算机视觉和计算机图形学中的许多应用是固有的。提出了一种基于B样条曲面造型的方法。B样条构造平滑表面，其最佳地拟合从结构光系统（测距仪）或从一组表面切片的外部轮廓上的点坐标获得的一组散射无序3D范围数据点，例如在组织学冠状脑切片中。B样条是最有效的曲面表示方法之一。它具有许多属性，如有界性，连续性，局部形状可控性，仿射变换的不变性，使它非常适合和有吸引力的表面表示。尽管B样条具有很好的性质，但它在三维散乱数据的表示中并没有得到广泛的应用。这可能是由于在寻找B样条的拓扑参数的排序和选择中的问题，该B样条的拓扑参数导致基于分散的数据集的物理上有意义的表面参数化。基于曲面扩展高斯映射的测地线，计算B样条曲面构造所需的参数，以及找到数据点的排序。通过求解最佳曲面拟合的最小均方误差问题来解析计算控制点集。对于噪声免疫建模，我们选择使用近似而不是插值B样条。我们还研究了使B样条拟合技术对局部变形和噪声具有鲁棒性的方法。
Surface representation is intrinsic to many applications in medical imaging, computer vision, and computer graphics. We present a method that is based on surface modeling by B-spline. The B-spline constructs a smooth surface that best fits a set of scattered unordered 3D range data points obtained from either a structured light system (a range finder), or from point coordinates on the external contours of a set of surface sections, as for example in histological coronal brain sections. B-spline stands as of one the most efficient surface representations. It possesses many properties such as boundedness, continuity, local shape controllability, and invariance to affine transformations that makes it very suitable and attractive for surface representation. Despite its attractive properties, however, B-spline has not been widely applied for representing a 3D scattered nonordered data set. This may be due to the problem in finding an ordering and a choice for the topological parameters of the B-spline that lead to a physically meaningful surface parameterization based on the scattered data set. The parameters needed for the B-spline surface construction, as well as finding the ordering of the data points, are calculated based on the geodesics of the surface extended Gaussian map. The set of control points is analytically calculated by solving a minimum mean square error problem for best surface fitting. For a noise immune modeling, we elect to use an approximating rather than an interpolating B-spline. We also examine ways of making the B-spline fitting technique robust to local deformation and noise.