5 research outputs found
A unified approach to the well-posedness of some non-Lambertian models in Shape-from-Shading theory
In this paper we show that the introduction of an attenuation factor in the
%image irradiance brightness equations relative to various perspective Shape
from Shading models allows to make the corresponding differential problems
well-posed. We propose a unified approach based on the theory of viscosity
solution and we show that the brightness equations with the attenuation term
admit a unique viscosity solution. We also discuss in detail the possible
boundary conditions that we can use for the Hamilton-Jacobi equations
associated to these models
Analysis and approximation of some Shape-from-Shading models for non-Lambertian surfaces
The reconstruction of a 3D object or a scene is a classical inverse problem
in Computer Vision. In the case of a single image this is called the
Shape-from-Shading (SfS) problem and it is known to be ill-posed even in a
simplified version like the vertical light source case. A huge number of works
deals with the orthographic SfS problem based on the Lambertian reflectance
model, the most common and simplest model which leads to an eikonal type
equation when the light source is on the vertical axis. In this paper we want
to study non-Lambertian models since they are more realistic and suitable
whenever one has to deal with different kind of surfaces, rough or specular. We
will present a unified mathematical formulation of some popular orthographic
non-Lambertian models, considering vertical and oblique light directions as
well as different viewer positions. These models lead to more complex
stationary nonlinear partial differential equations of Hamilton-Jacobi type
which can be regarded as the generalization of the classical eikonal equation
corresponding to the Lambertian case. However, all the equations corresponding
to the models considered here (Oren-Nayar and Phong) have a similar structure
so we can look for weak solutions to this class in the viscosity solution
framework. Via this unified approach, we are able to develop a semi-Lagrangian
approximation scheme for the Oren-Nayar and the Phong model and to prove a
general convergence result. Numerical simulations on synthetic and real images
will illustrate the effectiveness of this approach and the main features of the
scheme, also comparing the results with previous results in the literature.Comment: Accepted version to Journal of Mathematical Imaging and Vision, 57
page
Generalised Perspective Shape from Shading with Oren-Nayar Reflectance
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 result- ing 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 cor- responding 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