Unbiased Photometric Stereo for Colored Surfaces: A Variational Approach

Quéau, Yvain; Mecca, Roberto; Durou, Jean‐Denis

doi:10.1109/cvpr.2016.472

Cited by 39 publications

(40 citation statements)

References 54 publications

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“…Indeed, we assume that the albedo is known. In contrast, since existing methods [9,31] are based on image ratios, knowledge of the albedo is not required. As a consequence, their 3 It is stated in [12] that "the running time is nearly linear in practice".…”

Section: An Efficient Methods For Solving the Ps2 Problemmentioning

confidence: 99%

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Photometric stereo with only two images: A theoretical study and numerical resolution

Quau

Mecca

Durou

et al. 2017

Image and Vision Computing

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Section: An Efficient Methods For Solving the Ps2 Problemmentioning

confidence: 99%

“…When m ≥ 3 images are available, it was shown in [31] that variational models such as Eq. (14) may be considered in several more difficult situations such as color PS, PS with pointwise sources or perspective PS, even without a boundary condition.…”

Section: Differential Formulations Of the Ps2 Problemmentioning

confidence: 99%

Photometric stereo with only two images: A theoretical study and numerical resolution

Quau

Mecca

Durou

et al. 2017

Image and Vision Computing

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“…Recently, new PS models based on nonlinear PDEs have attracted increasing interest [9,10,36,39,40,50,54]. However, such methods remain computationally very intensive: it is simpler to eliminate the nonlinearity, through image ratios, as done in [36,39,40,51,54]. This system of nonlinear PDEs can be solved using calculus of variations [50] or proximal methods [20].…”

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confidence: 99%

“…This system of nonlinear PDEs can be solved using calculus of variations [50] or proximal methods [20]. However, in all these works, the shape reconstruction process required additional initial or boundary information, which are not required in the linear least-squares variational approach proposed recently in [51,54]. Chandraker, Bai, and Ramamoorthi [10] considered more general irradiance equations with unknown light sources and computed the photometric invariants describing the surface through its isocontours [1].…”

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confidence: 99%

“…Chandraker, Bai, and Ramamoorthi [10] considered more general irradiance equations with unknown light sources and computed the photometric invariants describing the surface through its isocontours [1]. In addition, depth information is only propagated through a single direction, in contrast to robust variational solvers that simultaneously estimate the depth at all pixels [20,50,51,54]. Mecca and coauthors [36,39,40] used specific irradiance equations for diffuse surfaces only, proving uniqueness of the solution by characteristic strip expansion and assuming known light information (i.e., direction or position).…”

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A Single-Lobe Photometric Stereo Approach for Heterogeneous Material

Mecca¹,

Quéau²,

Logothetis³

et al. 2016

SIAM J. Imaging Sci.

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Shape from shading with multiple light sources is an active research area, and a diverse range of approaches have been proposed in recent decades. However, devising a robust reconstruction technique still remains a challenging goal, as the image acquisition process is highly nonlinear. Recent Photometric Stereo variants rely on simplifying assumptions in order to make the problem solvable: light propagation is still commonly assumed to be uniform, and the Bidirectional Reflectance Distribution Function is assumed to be diffuse, with limited interest for specular materials. In this work, we introduce a well-posed formulation based on partial differential equations (PDEs) for a unified reflectance function that can model both diffuse and specular reflections. We base our derivation on ratio of images, which makes the model independent from photometric invariants and yields a well-posed differential problem based on a system of quasi-linear PDEs with discontinuous coefficients. In addition, we directly solve a differential problem for the unknown depth, thus avoiding the intermediate step of approximating the normal field. A variational approach is presented ensuring robustness to noise and outliers (such as black shadows), and this is confirmed with a wide range of experiments on both synthetic and real data, where we compare favorably to the state of the art.Reflectance. Most of the research done till now for the PS technique has assumed purely diffuse reflectance as the Bidirectional Reflectance Distribution Function (BRDF). Unlike (a) and (b), shape recovery from specular shading still remains a challenging goal since most of the common materials provide specular highlights that prevent reasonable reconstructions by the PS technique.Regarding shading models for specular highlights, several dedicated irradiance equations have been presented so far. First, Torrance and Sparrow [56] presented a physical model based on radiometry principles. Later, Phong [48] showed an empirical model which basically extended the cosine law, making it depend also on the viewer direction. The Blinn-Phong shading model [4] extended further the previous one by eliminating some limitation in the analytical formulation. Then Cook and Torrance [14] provided a well-known specular model based on a strongly nonlinear physical theory. Other important models for specular BRDFs can be found in [33], and interesting comparisons among some of them have been performed in [44].Instead of simplifying the PS problem by removing specularity, other works dealt with the images as they are, having both specular and diffuse components. Nayar, Ikeuchi, and Kanade [43] assumed hybrid surfaces by summing diffuse and specular components using the Beckmann and Spizzichino [3] reflection model, allowing them to locally reconstruct the shape of the object. Ikeuchi [28] faced the PS problem with specular reflectance by introducing a smoothness prior on the surface, which was shown to be realistic for several industrial applications, though this approach is limite...

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