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.

翻译：光度立体视觉是指利用同一视点下多张输入图像中的光照与反射信息，计算物体三维形状的过程。最常用的反射模型是朗伯反射，但该模型无法处理输入图像中的镜面高光。本文针对采用Blinn-Phong反射模型模拟镜面效应时产生的非线性优化问题展开研究。为此，我们重点分析了正则化Levenberg-Marquardt方法，推导出基于给定数据评估该方法收敛可靠性的显式界，并展示了如何通过Scherzer条件获取迭代数值正确性的实验证据。本文核心的理论研究辅以真实图像数据的测试验证。