Recovering Surfaces from the Gauss Map

DOI：

 作者 单位 胡茂林 安徽大学 智能计算与信号处理实验室,安徽 合肥 230039 安徽大学 数学与计算科学学院,安徽 合肥 230039 谢世朋 安徽大学 智能计算与信号处理实验室,安徽 合肥 230039 安徽大学 数学与计算科学学院,安徽 合肥 230039

从另一个角度研究三维曲面的恢复,即根据曲面法向量,考虑多块曲面的重构.算法输入的数据是估计的曲面法向量,比如输入的数据是根据从阴影恢复形状或从纹理恢复形状等计算机视觉低层次处理中得到.通过球面坐标变换把曲面法向量分解成两个函数;然后再对这两个函数进行滤波处理,通过对这两个分割的叠加将空间曲面分割成几个子曲面;最后利用Green函数分别恢复各个子曲面.虽然只利用了一般的图像处理技术,却能得到比传统的基于曲面法向量的方法更好的结果,特别是边界部分的恢复.这是因为传统的方法只是考虑恢复一个曲面模型,因此在不同曲面的边界上会产生模糊.最后利用模拟数据和由阴影恢复形状算法获取真实数据来评价提出的算法,并都与传统的方法进行了比较.

This paper studies 3D surface integration from novel angle. The authors consider the construction to the multiple surface patches, not one surface, from the Gauss map. The algorithm takes as its input a 2D field of surface normal estimates, delivered, for instance, by a shape-from-shading or shape-from-texture procedure. The authors disintegrate the Gauss map into two functions by the spherical coordinates, and then borrow the ideas from routine image processing theory to filter the two functions and to segment the space surface into several subsurface, at last the authors use the integrability to recover the subsurface individually. The method only exploits the general techniques in image processing, but can supply better results than the previous researches, which are only based on one function model, especially in the preservence the edges between different surfaces. The method is evaluated on synthetic and real data delivered by a shape-from-shading algorithm. The approach provides an actually way to use the normal maps of the surface.
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