Shape from Shading for Rough Surfaces: Analysis of the Oren-Nayar Model

Ju, Yong Chul; Breuß, Michael; Bruhn, Andrés; Galliani, Silvano

doi:10.5244/c.26.104

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…Recently, such perspective SfS models with the light source located at the optical centre of the camera have been extended to non-Lambertian reflectance models [2,24] such as the aforementioned Oren-Nayar model [2]. This model has also been investigated in [10] for use with the highly efficient fast marching (FM) method [21].…”

Section: Introductionmentioning

confidence: 99%

Generalised Perspective Shape from Shading with Oren-Nayar Reflectance

Ju¹,

Tozza²,

Breuß³

et al. 2013

Procedings of the British Machine Vision Conference 2013

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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.

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Section: Introductionmentioning

confidence: 99%

Generalised Perspective Shape from Shading with Oren-Nayar Reflectance

Ju¹,

Tozza²,

Breuß³

et al. 2013

Procedings of the British Machine Vision Conference 2013

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“…Facet model for surface patch dA consisting of many V-shaped Lambertian cavities.Figure adapted from[34].…”

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confidence: 99%

Analysis and Approximation of Some Shape-from-Shading Models for Non-Lambertian Surfaces

Tozza

Falcone

2016

J Math Imaging Vis

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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.

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A Comparison of Non-Lambertian Models for the Shape-from-Shading Problem

Tozza

Falcone

2016

Mathematics and Visualization

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In this paper we present in a unified approach Shape-from-Shading models under orthographic projection for non-Lambertian surfaces and compare them with the classical Lambertian model. Those non-Lambertian models have been proposed in the literature by various authors in order to take into account more realistic surfaces such as rough and specular surfaces. The advantage of our unified mathematical model is the possibility to easily modify a single differential model to various situations just changing some control parameters. Moreover, the numerical approximation we propose is valid for that general model and can be easily adapted to the real situation. Finally, we compare the models on some benchmarks including real and synthetic images

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Shape from Shading for Rough Surfaces: Analysis of the Oren-Nayar Model

Cited by 4 publications

References 25 publications

Generalised Perspective Shape from Shading with Oren-Nayar Reflectance

Generalised Perspective Shape from Shading with Oren-Nayar Reflectance

Analysis and Approximation of Some Shape-from-Shading Models for Non-Lambertian Surfaces

A Comparison of Non-Lambertian Models for the Shape-from-Shading Problem

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