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- Shape from Shading (2) (remove)
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Shape from Shading (SFS) is a classic problem in computer vision. In recent years many perspective SFS models have been studied that yield useful SFS approaches when a photographed object is close to the camera. However, while the ambiguities inherent to the classical, orthographic SFS models are well-understood, there has been no discussion of possible ambiguities in perspective SFS models. In this paper we deal with the latter issue. Therefore we adopt a typical perspective SFS setting. We show how to transform the corresponding image irradiance equation into the format of the classical orthographic setting by employing spherical coordinates. In the latter setting we construct a convex-concave ambiguity for
perspective SFS. It is to our knowledge the first time in the
literature that this type of ambiguity is constructed and verified
for a perspective SFS model.
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.