The integration of surface normals is a classic and fundamental task in computer vision. In this paper we deal with a highly efficient fast marching (FM) method to perform the integration. In doing this we build upon a previous work of Ho and his coauthors. Their FM scheme is based on an analytic model that incorporates the eikonal equation. Our method is also built upon this equation, but it makes use of a complete discrete formulation for constructing the FM integrator (DEFM). We not only provide a theoretical justification of the proposed method, but also illustrate at hand of a simple example that our approach is much better suited to the task. Several more sophisticated tests confirm the robustness and higher accuracy of the DEFM model. Moreover, we present an extension of DEFM that allows to integrate surface normals over non-trivial domains, e.g. featuring holes. Numerical results confirm desirable qualities of this method.

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.

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Shape from shading (SfS) and stereo are two fundamentally different strategies for imagebased 3-D reconstruction. While approaches for SfS infer the depth solely from pixel intensities, methods for stereo are based on finding 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 detailpreserving 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 the approach applicable to objects with non-uniform albedo as well as to scenes with unknown illumination.

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Due to their improved capability to handle realistic illumination scenarios, nonLambertian reflectance models are becoming increasingly more popular in the Shape from Shading (SfS) community. One of these advanced models is the Oren-Nayar model which is particularly suited to handle rough surfaces. However, not only the proper selection of the model is important, also the validation of stable and efficient algorithms plays a fundamental role when it comes to the practical applicability. While there are many works dealing with such algorithms in the case of Lambertian SfS, no such analysis has been performed so far for the Oren-Nayar model. In our paper we address this problem and present an in-depth study for such an advanced SfS model. To this end, we investigate under which conditions, i.e. model parameters, the Fast Marching (FM) method can be applied -a method that is known to be one of the most efficient algorithms for solving the underlying partial differential equations of Hamilton-Jacobi type. In this context, we do not only perform a general investigation of the model using Osher's criterion for verifying the suitability of the FM method. We also conduct a parameter dependent analysis that shows, that FM can safely be used for the model for a wide range of settings relevant for practical applications. Thus, for the first time, it becomes possible to theoretically justify the use of the FM method as solver for the Oren-Nayar model which has been applied so far on a purely empirical basis only. Numerical experiments demonstrate the validity of our theoretical analysis. They show a stable behaviour of the FM method for the predicted range of model parameters.