Our world is full of objects with complex reflectances situated in rich illumination environments. Though stunning, the diversity of appearance that arises from this complexity is also daunting. For this reason, past work on geometry recovery has tried to frame the problem into simplistic models of reflectance (such as Lambertian, mirrored, or dichromatic) or illumination (one or more distant point light sources). In this work, we directly tackle the problem of joint reflectance and geometry estimation under known but uncontrolled natural illumination by fully exploiting the surface orientation cues that become embedded in the appearance of the object. Intuitively, salient scene features (such as the sun or stained glass windows) act analogously to the point light sources of traditional geometry estimation frameworks by strongly constraining the possible orientations of the surface patches reflecting them. By jointly estimating the reflectance of the object, which modulates the illumination, the appearance of a surface patch can be used to derive a nonparametric distribution of its possible orientations. If only a single image exists, these strongly constrained surface patches may then be used to anchor the geometry estimation and give context to the less-descriptive regions. When multiple images exist, the distribution of possible surface orientations becomes tighter as additional context is given, though integrating the separate views poses additional challenges. In this paper we introduce two methods, one for the single image case, and another for the case of multiple images. The effectiveness of our methods is evaluated extensively on synthetic and real-world data sets that span the wide range of real-world environments and reflectances that lies between the extremes that have been the focus of past work.
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