A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima
A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima
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DOI：
10.1007/s11263-013-0665-5
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发表时间：
2013-10
影响因子：
19.5
通讯作者：
Thoma Papadhimitri;P. Favaro
中科院分区：
文献类型：
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作者：
Thoma Papadhimitri;P. Favaro
一个物体在不同光照下的图像可以提供关于物体表面的强烈线索。如何恢复这样一个表面的法线图的数学形式化导致了所谓的未校准的光度立体问题。在最简单的例子中，这个问题可以简化为只识别三个参数的任务：所谓的广义浅浮雕（GBR）歧义。挑战在于找到关于对象的其他一般假设，以唯一地标识这些参数。当前的方法是不一致的，也就是说，在同一数据上多次运行时，它们提供了不同的解决方案。为了解决这一限制，我们建议利用局部漫反射（LDR）最大值，即场景中法向量平行于照明方向的点（见图1）。我们证明了这些极大值的几个值得注意的性质：封闭解、计算效率和GBR一致性。LDR最大值产生GBR参数空间中对应半圆的简单闭型解（见图2）；由于在不同图像中只需两个弥散极大值即可识别唯一解，因此可以非常有效地实现GBR参数的识别；最后，算法是一致的，因为它总是在给定相同数据的情况下返回相同的解。我们的算法也非常健壮：即使在检测到的最大值中存在极高水平的异常值（高达80%的观测值），它也可以获得对GBR参数的准确估计。该方法在实际数据上得到了验证，取得了较好的效果。
Images of an object under different illumination are known to provide strong cues about the object surface. A mathematical formalization of how to recover the normal map of such a surface leads to the so-called uncalibrated photometric stereo problem. In the simplest instance, this problem can be reduced to the task of identifying only three parameters: the so-called generalized bas-relief (GBR) ambiguity. The challenge is to find additional general assumptions about the object, that identify these parameters uniquely. Current approaches are not consistent, i.e., they provide different solutions when run multiple times on the same data. To address this limitation, we propose exploitinglocal diffuse reflectance(LDR) maxima, i.e., points in the scene where the normal vector is parallel to the illumination direction (see Fig. 1). We demonstrate several noteworthy properties of these maxima: a closed-form solution, computational efficiency and GBR consistency. An LDR maximum yields a simple closed-form solution corresponding to a semi-circle in the GBR parameters space (see Fig. 2); because as few as two diffuse maxima in different images identify a unique solution, the identification of the GBR parameters can be achieved very efficiently; finally, the algorithm is consistent as it always returns the same solution given the same data. Our algorithm is also remarkably robust: It can obtain an accurate estimate of the GBR parameters even with extremely high levels of outliers in the detected maxima (up to 80 % of the observations). The method is validated on real data and achieves state-of-the-art results.