Mahajan Dhruv, Ramamoorthi Ravi, Curless Brian
Computer Science Department, Columbia University, 450 Computer Science Bldg, 500 W 120 Street, New York, NY 10027, USA.
IEEE Trans Pattern Anal Mach Intell. 2008 Feb;30(2):197-213. doi: 10.1109/TPAMI.2007.1162.
This paper develops a theory of frequency domain invariants in computer vision. We derive novel identities using spherical harmonics, which are the angular frequency domain analog to common spatial domain invariants such as reflectance ratios. These invariants are derived from the spherical harmonic convolution framework for reflection from a curved surface. Our identities apply in a number of canonical cases, including single and multiple images of objects under the same and different lighting conditions. One important case we consider is two different glossy objects in two different lighting environments. For this case, we derive a novel identity, independent of the specific lighting configurations or BRDFs, that allows us to directly estimate the fourth image if the other three are available. The identity can also be used as an invariant to detecttampering in the images. While this paper is primarily theoretical, it has the potential to lay the mathematical foundations for two important practical applications. First, we can develop more general algorithms for inverse rendering problems, which can directly relight and change material properties by transferring the BRDF or lighting from another object or illumination. Second, we can check the consistency of an image, to detect tampering or image splicing.
本文提出了一种计算机视觉中的频域不变量理论。我们使用球谐函数推导出了新颖的恒等式，球谐函数是角频率域中与诸如反射率等常见空间域不变量类似的量。这些不变量是从用于曲面反射的球谐卷积框架中推导出来的。我们的恒等式适用于许多典型情况，包括在相同和不同光照条件下物体的单幅和多幅图像。我们考虑的一个重要情况是在两种不同光照环境中的两个不同的光泽物体。对于这种情况，我们推导出了一个新颖的恒等式，它与特定的光照配置或双向反射分布函数（BRDF）无关，这使我们能够在已知其他三幅图像的情况下直接估计第四幅图像。该恒等式还可以用作检测图像篡改的不变量。虽然本文主要是理论性的，但它有可能为两个重要的实际应用奠定数学基础。首先，我们可以为逆渲染问题开发更通用的算法，通过从另一个物体或光照转移BRDF或光照来直接重新打光并改变材质属性。其次，我们可以检查图像的一致性，以检测篡改或图像拼接。
