A Generic and Provably Convergent Shape-from-Shading Method for Orthographic and Pinhole Cameras

Prados, Emmanuel; Faugeras, Olivier

doi:10.1007/s11263-005-3844-1

Cited by 36 publications

(80 citation statements)

References 51 publications

(91 reference statements)

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“…For example, Prados and Faugeras [93] use a perspective projection and assume that the viewer and light source are co-located. Under these conditions they use viscosity solutions to derive a provably convergent shape-from-shading algorithm which is able to obtain coarse face shape estimates.…”

Section: Face Shape and Reflectance Estimationmentioning

confidence: 99%

Inverse Rendering of Faces with a 3D Morphable Model

Aldrian

Smith

2013

IEEE Trans. Pattern Anal. Mach. Intell.

176

160

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In this thesis, we present a complete framework to inverse render faces with a 3D Morphable Model. By decomposing the image formation process into a geometric and photometric part, we are able to state the problem as a multilinear system which can be solved accurately and efficiently. As we treat each contribution as independent, the objective function is convex in the parameters and a globally optimal solution can be found. We start by recovering 3D shape using a novel algorithm which incorporates generalisation errors of the model obtained from empirical measurements. The algorithm is extended so it can efficiently deal with mixture distributions. We then describe three methods to recover facial texture, and for the second and third, diffuse lighting, specular reflectance and camera properties from a single image. These methods make increasingly weak assumptions and can all be solved in a linear fashion. We further modify our framework so it accounts for global illumination effects. This is achieved by incorporating statistical models for ambient occlusion and bent normals into the image formation model. We show that solving for ambient occlusion and bent normal parameters as part of the fitting process improves the accuracy of the estimated texture map and illumination environment. We present results on challenging data, rendered under complex natural illumination with both specular reflectance and occlusion of the illumination environment. We evaluate our findings on publicly available datasets, where we are able to obtain state-ofthe-art results. Finally, we present a practical method to synthesise a larger population from a small training-set and show how the new instances can be used to build a flexible PCA model.

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Section: Face Shape and Reflectance Estimationmentioning

confidence: 99%

Inverse Rendering of Faces with a 3D Morphable Model

Aldrian

Smith

2013

IEEE Trans. Pattern Anal. Mach. Intell.

176

160

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show abstract

“…They are convex and (in practice, generally) coercive in the gradient variable and they have the same regularity of I(x) in the state variable (see [15] for a detailed discussion of this point). Moreover they admit a subsolution which plays a key role in the uniqueness of the solution.…”

Section: Assumptions and Preliminariesmentioning

confidence: 99%

“…where H is one of the SfS Hamiltonians considered in literature (see [6], [13], [15], [20]). Under the previous assumptions on I, the Hamiltonian H : R N × R N −→ R turns out to be measurable in x for any p, continuous, strictly convex and coercive (i.e.…”

Section: Assumptions and Preliminariesmentioning

confidence: 99%

“…Remark 1 For a continuous image brightness, the existence of C 1 subsolutions for the various SfS Hamiltonians is studied in details in [15]. If I is only L ∞ , the subsolutions constructed in [15] are Lipschitz continuous.…”

Section: Assumptions and Preliminariesmentioning

confidence: 99%

“…I(x) = 1. This difficulty is general and applies to all the models considered in literature (see [15]). …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Shape-from-Shading with discontinuous image brightness

Camilli

Prados²

2006

Applied Numerical Mathematics

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The Shape-from-Shading models in image analysis lead to first order HamiltonJacobi equations which may have several weak solutions (in the viscosity sense). Moreover, for real images, these equations are highly discontinuous in the space variable. The lack of uniqueness and the irregularity of the coefficients involve some troubles when we try to compute a solution. In order to avoid these difficulties, here we use recent results in the theory of viscosity solutions to characterize the maximal solution of these equations. Moreover we describe an approximation procedure via smooth equations with a unique viscosity solution.

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Fast Marching Method for Generic Shape from Shading

Prados

Soatto

2005

Lecture Notes in Computer Science

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Abstract. We develop a fast numerical method to approximate the solutions of a wide class of equations associated to the Shape From Shading problem. Our method, which is based on the control theory and the interfaces propagation, is an extension of the "Fast Marching Method" (FMM) [30,25]. In particular our method extends the FMM to some equations for which the solution is not systematically decreasing along the optimal trajectories. We apply with success our one-pass method to the Shape From Shading equations which are involved by the most relevant and recent modelings [22,21] and which cannot be handled by the most recent extensions of the FMM [26,8].

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A Generic and Provably Convergent Shape-from-Shading Method for Orthographic and Pinhole Cameras

Cited by 36 publications

References 51 publications

Inverse Rendering of Faces with a 3D Morphable Model

Inverse Rendering of Faces with a 3D Morphable Model

Shape-from-Shading with discontinuous image brightness

Fast Marching Method for Generic Shape from Shading

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