Blinn-Phong光度立体的正则化Levenberg-Marquardt方法
On the Regularising Levenberg-Marquardt Method for Blinn-Phong Photometric Stereo
摘要：
光度立体是指使用来自同一视点的若干输入图像的关于照明和反射的信息来计算对象的3D形状的过程。最常用的反射率模型是朗伯反射率，但这不包括输入图像中的镜面高光。在本文中，我们考虑所产生的非线性优化问题时，采用Blinn-Phong反射建模镜面效果。为此，我们专注于正规化Levenberg-Marquardt计划。我们展示了如何推导出一个明确的界限，提供信息的方法的收敛可靠性取决于给定的数据，我们展示了如何获得实验证据的数值正确性的迭代利用Scherzer条件。作为本文核心的理论研究得到了一些真实图像测试的补充。
英文摘要：
Photometric stereo refers to the process to compute the 3D shape of an object using information on illumination and reflectance from several input images from the same point of view. The most often used reflectance model is the Lambertian reflectance, however this does not include specular highlights in input images. In this paper we consider the arising non-linear optimisation problem when employing Blinn-Phong reflectance for modeling specular effects. To this end we focus on the regularising Levenberg-Marquardt scheme. We show how to derive an explicit bound that gives information on the convergence reliability of the method depending on given data, and we show how to gain experimental evidence of numerical correctness of the iteration by making use of the Scherzer condition. The theoretical investigations that are at the heart of this paper are supplemented by some tests with real-world imagery.
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