On Differential Photometric Reconstruction for Unknown, Isotropic BRDFs
On Differential Photometric Reconstruction for Unknown, Isotropic BRDFs
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DOI：
10.1109/tpami.2012.217
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发表时间：
2013-12-01
影响因子：
23.6
通讯作者：
Ramamoorthi, Ravi
中科院分区：
文献类型：
--
作者：
Chandraker, Manmohan;Bai, Jiamin;Ramamoorthi, Ravi
本文提出了一个全面的理论光度表面重建的图像导数在存在一个一般的，未知的各向同性BRDF。我们推导出精确的拓扑类的表面可以确定，并指定一个完整的几何重建精确的先验。这些结果是一系列基本观察的结果。首先，我们利用线性的链式法则微分发现光度不变量，涉及图像导数的表面几何形状，无论形式的各向同性BRDF。对于从阴影的形状的问题，我们表明，重建可以执行到恒定大小的梯度的等值线。对于光度立体的问题，我们表明，只有两个测量的空间和时间的图像导数，从未知的光方向上的一个圆圈，足以恢复表面信息的光度不变量。令人惊讶的是，不变量的形式与光流有惊人的相似之处;然而，它不受孔径问题的影响。这个光度流被示出，以确定表面的表面梯度的恒定幅度的等值线，以及恒定深度的等值线。此外，我们证明，规范的表面法线在一个单一的点完全决定了表面深度从这些等值线。此外，我们提出了实用的算法，需要额外的初始或边界信息，但恢复深度从低阶导数。我们的理论结果说明了几个例子的合成和真实的数据。
This paper presents a comprehensive theory of photometric surface reconstruction from image derivatives in the presence of a general, unknown isotropic BRDF. We derive precise topological classes up to which the surface may be determined and specify exact priors for a full geometric reconstruction. These results are the culmination of a series of fundamental observations. First, we exploit the linearity of chain rule differentiation to discover photometric invariants that relate image derivatives to the surface geometry, regardless of the form of isotropic BRDF. For the problem of shape-from-shading, we show that a reconstruction may be performed up to isocontours of constant magnitude of the gradient. For the problem of photometric stereo, we show that just two measurements of spatial and temporal image derivatives, from unknown light directions on a circle, suffice to recover surface information from the photometric invariant. Surprisingly, the form of the invariant bears a striking resemblance to optical flow; however, it does not suffer from the aperture problem. This photometric flow is shown to determine the surface up to isocontours of constant magnitude of the surface gradient, as well as isocontours of constant depth. Further, we prove that specification of the surface normal at a single point completely determines the surface depth from these isocontours. In addition, we propose practical algorithms that require additional initial or boundary information, but recover depth from lower order derivatives. Our theoretical results are illustrated with several examples on synthetic and real data.