Hara Kenji, Nishino Ko
Department of Visual Communication Design, Faculty of Design, Kyushu University, 4–9–1 Shiobaru, Minami-ku, Fukuoka-shi, 815-8540 Japan.
J Opt Soc Am A Opt Image Sci Vis. 2011 Feb 1;28(2):136-46. doi: 10.1364/JOSAA.28.000136.
Estimating the illumination and the reflectance properties of an object surface from a few images is an important but challenging problem. The problem becomes even more challenging if we wish to deal with real-world objects that naturally have spatially inhomogeneous reflectance. In this paper, we derive a novel method for estimating the spatially varying specular reflectance properties of a surface of known geometry as well as the illumination distribution of a scene from a specular-only image, for instance, recovered from two images captured with a polarizer to separate reflection components. Unlike previous work, we do not assume the illumination to be a single point light source. We model specular reflection with a spherical statistical distribution and encode its spatial variation with a radial basis function (RBF) network of their parameter values, which allows us to formulate the simultaneous estimation of spatially varying specular reflectance and illumination as a constrained optimization based on the I-divergence measure. To solve it, we derive a variational algorithm based on the expectation maximization principle. At the same time, we estimate optimal encoding of the specular reflectance properties by learning the number, centers, and widths of the RBF hidden units. We demonstrate the effectiveness of the method on images of synthetic and real-world objects.
从少量图像估计物体表面的光照和反射特性是一个重要但具有挑战性的问题。如果我们希望处理自然具有空间不均匀反射率的现实世界物体，这个问题将变得更具挑战性。在本文中，我们推导了一种新颖的方法，用于从仅包含镜面反射的图像（例如，从用偏振器拍摄的两张图像中恢复以分离反射分量）估计已知几何形状表面的空间变化镜面反射特性以及场景的光照分布。与之前的工作不同，我们不假设光照是单个点光源。我们用球形统计分布对镜面反射进行建模，并用其参数值的径向基函数（RBF）网络对其空间变化进行编码，这使我们能够将空间变化镜面反射和光照的同时估计表述为基于I散度度量的约束优化问题。为了解决这个问题，我们基于期望最大化原理推导了一种变分算法。同时，我们通过学习RBF隐藏单元的数量、中心和宽度来估计镜面反射特性的最优编码。我们在合成物体和现实世界物体的图像上展示了该方法的有效性。
