Shape from Shading
Shape from Shading
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阴影形状
DOI：
10.1002/9780470050118.ecse628
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Y. Yeshurun
中科院分区：
文献类型：
--
作者：
A. Tankus;N. Sochen;Y. Yeshurun
从明暗恢复形状(Shape-From-Shading，SFS)是计算机视觉的一个基本问题。它的目标是基于曲面的单幅图像重建曲面深度(即与相机平面的距离)。这个问题是由霍恩在20世纪70年代初提出的。在这一领域中，一个非常常见的假设是图像投影是正交的。我们将给出从明暗恢复正交形状的问题及其解决的算法：Kimmel和Sethian的快速行进方法。然后，我们将在透视投影假设下重新检查SFS的基础，即图像辐照度方程。所得到的方程不直接依赖于深度函数，而是依赖于其自然对数，因此它不随深度函数的尺度变化而变化。然后描述了一种基于透视公式的重建方法，它是对前述正交快速行进方法的改进。在此基础上，比较了正射快速行进、透视快速行进以及合成图像上的Prados和Faugeras的透视算法。两种透视方法各有优势，重建效果均好于正交法。然后，我们比较了内窥镜图像上快速行进方法的正射和透视版本。透视算法的性能优于正交法。这些发现表明，与正畸SFS相比，透视SFS的一组更现实的假设显著改善了重建。这些发现还提供了证据，表明透视SFS可以用于内窥镜检查等领域的现实应用。
关键词：
计算机视觉；
从阴影到形状；
从X开始的形状；
透视投影；
正射投影；
快速行进；
曲面重建；
深度恢复
Shape-from-shading (SfS) is a fundamental problem in computer vision. Its goal is reconstruction of surface depth (i.e., distance from camera plane) based on a single image of the surface. The problem was introduced in the early 1970s by Horn. A very common assumption in this field is that image projection is orthographic. We will present the orthographic shape-from-shading problem and an algorithm for its solution: the fast marching method of Kimmel and Sethian. We shall than reexamine the basis of SfS, which is the image irradiance equation, under a perspective projection assumption. The resultant equation does not depend on the depth function directly, but on its natural logarithm, and as such it is invariant to scale changes of the depth function. A reconstruction method based on the perspective formula is then described; it is a modification of the aforementioned orthographic fast marching method. Then, a comparison of the orthographic fast marching, perspective fast marching, and the perspective algorithm of Prados and Faugeras on synthetic images is are presented. The two perspective methods equate with each other and show better reconstruction results than the orthographic. We then compare the orthographic and perspective versions of the fast marching method on endoscopic images. The perspective algorithm outperformed the orthographic one. These findings suggest that the more realistic set of assumptions of perspective SfS improves reconstruction significantly with respect to orthographic SfS. The findings also provide evidence that perspective SfS can be used for real-life applications in fields such as endoscopy.
Keywords:
computer vision;
shape from shading;
shape from X;
perspective projection;
orthographic projection;
fast marching;
surface reconstruction;
depth recovery