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Ordering and parameterizing scattered 3D data for B-spline surface approximation

机译:为B样条曲面近似排序和参数化分散的3D数据

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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.
机译:表面表示是医学成像,计算机视觉和计算机图形学中许多应用程序固有的。我们提出一种基于B样条的曲面建模的方法。 B样条曲线构建的平滑表面最适合从结构化照明系统(测距仪)或一组表面截面的外部轮廓上的点坐标获得的一组分散的无序3D范围数据点,例如组织学冠状脑切片的例子。 B样条曲线是最有效的表面表示之一。它具有许多特性,例如有界性,连续性,局部形状可控性以及仿射变换的不变性,这使其非常适合表面表示并具有吸引力。尽管具有吸引人的特性,但B样条尚未广泛应用于表示3D分散的无序数据集。这可能是由于在查找B样条的拓扑参数的顺序和选择时存在问题,这些问题导致基于散乱数据集在物理上有意义的表面参数化。根据曲面扩展的高斯图的测地线计算出B样条曲面构造所需的参数以及找到数据点的顺序。通过解决最小均方误差问题以获得最佳表面拟合,可以分析性地计算出一组控制点。对于抗噪建模,我们选择使用近似B样条而不是插值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。

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