Adaptive estimation of normals and surface area for discrete 3-D objects:: Application to snow binary data from X-ray tomography
Adaptive estimation of normals and surface area for discrete 3-D objects:: Application to snow binary data from X-ray tomography
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DOI：
10.1109/tip.2005.846021
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发表时间：
2005-05-01
影响因子：
10.6
通讯作者：
Delesse, JF
中科院分区：
文献类型：
--
作者：
Flin, F;Brzoska, JB;Delesse, JF
离散三维物体边界法向量场的估计是绘制和图像测量问题的关键。大多数现有的算法不能准确地确定存在边缘的形状的法向量场。在这里，我们提出了一种新的简单的计算方法，以便在所有类型的形状上获得准确的结果，无论其局部凸度如何。该方法基于物体距离图的梯度向量场分析。该矢量场使用角度和对称标准自适应地过滤每个表面体素，以便尽可能多地考虑相关贡献。这优化了数字化效果的平滑，同时保留了被处理数值对象的相关细节。由于获得了精确的法向场，因此可以提出一种投影方法来立即从原始离散物体中导出表面积。在连续极限情况下，给出了该算法有效性的经验证明。给出了模拟数据和x射线层析成像雪图像的一些结果，并与行军立方体和凸包结果进行了比较，并进行了讨论。
Estimating the normal vector field on the boundary of discrete three-dimensional objects is essential for rendering and image measurement problems. Most of the existing algorithms do not provide an accurate determination of the normal vector field for shapes that present edges. Here, we propose a new and simple computational method in order to obtain accurate results on all types of shapes, whatever their local convexity degree. The presented method is based on the gradient vector field analysis of the object distance map. This vector field is adaptively filtered around each surface voxel using angle and symmetry criteria so that as many relevant contributions as possible are accounted for. This optimizes the smoothing of digitization effects while preserving relevant details of the processed numerical object. Thanks to the precise normal field obtained, a projection method can be proposed to immediately derive the surface area from a raw discrete object. An empirical justification of the validity of such an algorithm in the continuous limit is also provided. Some results on simulated data and snow images from X-ray tomography are presented, compared to the Marching Cubes and Convex Hull results, and discussed.