Shape from shading (SfS) and stereo are two fundamentally different strategies for image-based 3-D reconstruction. While approaches for SfS infer the depth solely from pixel intensities, methods for stereo are based on a matching process that establishes correspondences across images. This difference in approaching the reconstruction problem yields complementary advantages that are worthwhile being combined. So far, however, most “joint” approaches are based on an initial stereo mesh that is subsequently refined using shading information. In this paper we follow a completely different approach. We propose a joint variational method that combines both cues within a single minimisation framework. To this end, we fuse a Lambertian SfS approach with a robust stereo model and supplement the resulting energy functional with a detail-preserving anisotropic second-order smoothness term. Moreover, we extend the resulting model in such a way that it jointly estimates depth, albedo and illumination. This in turn makes the approach applicable to objects with non-uniform albedo as well as to scenes with unknown illumination. Experiments for synthetic and real-world images demonstrate the benefits of our combined approach: They not only show that our method is capable of generating very detailed reconstructions, but also that joint approaches are feasible in practice.

中文翻译：

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结合阴影和立体的形状：估计深度、照明和反照率的联合变分方法

阴影形状 (SfS) 和立体是基于图像的 3-D 重建的两种根本不同的策略。虽然 SfS 的方法仅从像素强度推断深度，但立体方法基于在图像之间建立对应关系的匹配过程。这种处理重建问题的差异产生了值得结合的互补优势。然而，到目前为止，大多数“联合”方法都基于初始立体网格，随后使用着色信息进行细化。在本文中，我们采用了一种完全不同的方法。我们提出了一种联合变分方法，将两个线索结合在一个最小化框架中。为此，我们将朗伯 SfS 方法与稳健的立体模型融合在一起，并用保留细节的各向异性二阶平滑项补充所得的能量函数。此外，我们以一种联合估计深度、反照率和光照的方式扩展了结果模型。这反过来又使该方法适用于具有非均匀反照率的对象以及具有未知照明的场景。合成图像和真实世界图像的实验证明了我们组合方法的好处：它们不仅表明我们的方法能够生成非常详细的重建，而且联合方法在实践中是可行的。这反过来又使该方法适用于具有非均匀反照率的对象以及具有未知照明的场景。合成图像和真实世界图像的实验证明了我们组合方法的好处：它们不仅表明我们的方法能够生成非常详细的重建，而且联合方法在实践中是可行的。这反过来又使该方法适用于具有非均匀反照率的对象以及具有未知照明的场景。合成图像和真实世界图像的实验证明了我们组合方法的好处：它们不仅表明我们的方法能够生成非常详细的重建，而且联合方法在实践中是可行的。