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In spite of significant advances in Shape from Shading (SfS) over the last years, it
is still a challenging task to design SfS approaches that are flexible enough to handle a
wide range of input scenes. In this paper, we address this lack of flexibility by proposing
a novel model that extends the range of possible applications. To this end, we consider
the class of modern perspective SfS models formulated via partial differential equations
(PDEs). By combining a recent spherical surface parametrisation with the advanced
non-Lambertian Oren-Nayar reflectance model, we obtain a robust approach that allows
to deal with an arbitrary position of the light source while being able to handle rough
surfaces and thus more realistic objects at the same time. To our knowledge, the resulting
model is currently the most advanced and most flexible approach in the literature on
PDE-based perspective SfS. Apart from deriving our model, we also show how the corresponding
set of sophisticated Hamilton-Jacobi equations can be efficiently solved by
a specifically tailored fast marching scheme. Experiments with medical real-world data
demonstrate that our model works in practice and that is offers the desired flexibility.
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.
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. In this paper we propose a joint variational method that combines the advantages of both strategies. By integrating recent stereo and SfS models into a single minimisation framework, we obtain an approach that exploits shading information to improve upon the reconstruction quality of robust stereo methods. 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 novel model in such a way that it jointly estimates depth, albedo and illumination. This in turn makes it applicable to objects with non-uniform albedo as well as to scenes with unknown illumination. Experiments for synthetic and real-world images show the advantages of our combined approach: While the stereo part overcomes the albedo-depth ambiguity inherent to all SfS methods, the SfS part improves the degree of details of the reconstruction compared to pure stereo methods.