A $$L^1$$-TV Algorithm for Robust Perspective Photometric Stereo with Spatially-Varying Lightings

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15234The contribution was presented at SSVM 2015 :http://ssvm2015.math.u-bordeaux.fr/ Abstract. We tackle the problem of perspective 3D-reconstruction of Lambertian surfaces through photometric stereo, in the presence of outliers to Lambert's law, depth discontinuities, and unknown spatiallyvarying lightings. To this purpose, we introduce a robust L 1 -TV variational formulation of the recovery problem where the shape itself is the main unknown, which naturally enforces integrability and permits to avoid integrating the normal field.

Some illumination models for industrial applications of photometric stereo

“…Secondary reflections from the surface onto the surface are neglected in this work, though they can be recovered implicitely by refining the illumination vector s during the reconstruction process. 2 Though Lambert's law is a simple model, which may seem quite unrealistic for real-world applications of PS, it is actually a rather realistic one for modelling the luminance of an extended primary source, since manufacturers of lighting systems (LEDs, LCD screens etc.) usually guarantee isotropy, as much as possible.…”

Unifying diffuse and specular reflections for the photometric stereo problem

“…In fact, our formulation considers the global minimum over the image domain, having as unknown the depth, as for instance in [31]. Proceeding so, integrability of normals is not an issue, since piecewisesmooth surfaces are recovered directly, without relying on a posteriori use of dedicated solvers, which are either fast but not robust to discontinuities [32], or robust to discontinuities but slow [7,30].…”

“…Merging PS data We remark that most of the previous works proposing robust approaches to the PS problem as [13,22,31,35,38] derived the mathematical formulation by considering each irradiance equation independently from the others. Since our model is derived by coupling irradiance equations considering their ratios, the unifying equation exploits the single view acquisition simplifying the complexity of the problem due to heterogeneous materials.…”

“…Image Ratios New PS models based on non-linear PDEs have attracted increasing interest in the last few years [4,18,20,31]. Most of these approaches considered image ratios in order to yield photometric invariant equations [9,15], and modeled the irradiance equations via PDEs.…”

“…In order to enhance robustness to noise (inherent to the acquisition process) and outliers (such as shadows, or nondifferentiable elements of the surface), we consider L 1 optimization, following the recent sparsity-enhancing approaches described in [13,31]. Adapting such framework to the context of quasilinear system of PDEs (13), we consider the following optimization problem…”