Generalised Perspective Shape from Shading with Oren-Nayar Reflectance

Ju, Yong Chul; Tozza, Silvia; Breuß, Michael; Bruhn, Andrés; Kleefeld, Andreas

doi:10.5244/c.27.42

Cited by 12 publications

(16 citation statements)

References 23 publications

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“…Observe that, if A(z, ρ) and b(z, ρ) were constant, problem (19) would be a linear least squares problem with respect to z. Let us remark that (19) can be easily extended to include more realistic reflectance [15,16] and lighting [28,31] models, as well as more robust estimators [14,33]: this only requires to change the definition of f , which stands for the global reprojection error E R .…”

Section: Discretisationmentioning

confidence: 99%

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Optimisation of Classic Photometric Stereo by Non-convex Variational Minimisation

et al. 2018

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Estimating shape and appearance of a three dimensional object from a given set of images is a classic research topic that is still actively pursued. Among the various techniques available, photometric stereo is distinguished by the assumption that the underlying input images are taken from the same point of view but under different lighting conditions. The most common techniques provide the shape information in terms of surface normals. In this work, we instead propose to minimise a much more natural objective function, namely the reprojection error in terms of depth. Minimising the resulting non-trivial variational model for photometric stereo allows to recover the depth of the photographed scene directly. As a solving strategy, we follow an approach based on a recently published optimisation scheme for non-convex and non-smooth cost functions.The main contributions of our paper are of theoretical nature. A technical novelty in our framework is the usage of matrix differential calculus. We supplement our approach by a detailed convergence analysis of the resulting optimisation algorithm and discuss possibilities to ease the computational complexity. At hand of an experimental evaluation we discuss important properties of the method. Overall, our strategy achieves more accurate results than competing approaches. The experiments also highlights some practical aspects of the underlying optimisation algorithm that may be of interest in a more general context. G. Radow · L. Hoeltgen · M. Breuß Chair for Applied Mathematics

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Section: Discretisationmentioning

confidence: 99%

“…Because of the structure of A, defined in (15), and our choice of the Jacobian matrix as per Definition 1, the Jacobian matrix of A has the form…”

Section: Lipschitz Constant For the Gradient Of Fmentioning

confidence: 99%

Optimisation of Classic Photometric Stereo by Non-convex Variational Minimisation

et al. 2018

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“…In [22,17], the orthographic Lambertian model is replaced by a perspective Lambertian one (pinhole camera and light source at the optical center). In [16], a more general setup, which combines a spherical surface parametrization with the non-Lambertian Oren-Nayar reflectance model, is considered obtaining a robust approach that allows to deal with an arbitrary position of the light source. Moreover, models for non-Lambertian surfaces (like e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, models for non-Lambertian surfaces (like e.g. [21,6,20]) have been proposed in [1,2,26,16]. All these models, when formulated in terms of a differential equation, do not resolve the concave/convex ambiguity (see [25] for an analysis on them).…”

Section: Introductionmentioning

confidence: 99%

A Unified Approach to the Well-Posedness of Some Non-Lambertian Models in Shape-from-Shading Theory

Camilli¹,

Tozza²

2017

SIAM J. Imaging Sci.

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In this paper we show that the introduction of an attenuation factor in the 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 solutions 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.

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“…Recent works have considered more complicated scenarios, e.g. the case when light source is not at the optical center under perspective camera projection [35]. It is possible to consider in addition other supplementary issues, as the estimation of the albedo [86,5,65,64] or of the direction of the light source that are usually considered known quantities for the model but in practice are hardly available for real images.…”

Section: Introductionmentioning

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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Generalised Perspective Shape from Shading with Oren-Nayar Reflectance

Cited by 12 publications

References 23 publications

Optimisation of Classic Photometric Stereo by Non-convex Variational Minimisation

Optimisation of Classic Photometric Stereo by Non-convex Variational Minimisation

A Unified Approach to the Well-Posedness of Some Non-Lambertian Models in Shape-from-Shading Theory

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

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