Analysis and approximation of some Shape-from-Shading models for non-Lambertian surfaces

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.Comment: Accepted version to Journal of Mathematical Imaging and Vision, 57 page

Object-based 2D-to-3D video conversion for effective stereoscopic content generation in 3D-TV applications

Three-dimensional television (3D-TV) has gained increasing popularity in the broadcasting domain, as it enables enhanced viewing experiences in comparison to conventional two-dimensional (2D) TV. However, its application has been constrained due to the lack of essential contents, i.e., stereoscopic videos. To alleviate such content shortage, an economical and practical solution is to reuse the huge media resources that are available in monoscopic 2D and convert them to stereoscopic 3D. Although stereoscopic video can be generated from monoscopic sequences using depth measurements extracted from cues like focus blur, motion and size, the quality of the resulting video may be poor as such measurements are usually arbitrarily defined and appear inconsistent with the real scenes. To help solve this problem, a novel method for object-based stereoscopic video generation is proposed which features i) optical-flow based occlusion reasoning in determining depth ordinal, ii) object segmentation using improved region-growing from masks of determined depth layers, and iii) a hybrid depth estimation scheme using content-based matching (inside a small library of true stereo image pairs) and depth-ordinal based regularization. Comprehensive experiments have validated the effectiveness of our proposed 2D-to-3D conversion method in generating stereoscopic videos of consistent depth measurements for 3D-TV applications

Photometric Depth Super-Resolution

This study explores the use of photometric techniques (shape-from-shading and uncalibrated photometric stereo) for upsampling the low-resolution depth map from an RGB-D sensor to the higher resolution of the companion RGB image. A single-shot variational approach is first put forward, which is effective as long as the target's reflectance is piecewise-constant. It is then shown that this dependency upon a specific reflectance model can be relaxed by focusing on a specific class of objects (e.g., faces), and delegate reflectance estimation to a deep neural network. A multi-shot strategy based on randomly varying lighting conditions is eventually discussed. It requires no training or prior on the reflectance, yet this comes at the price of a dedicated acquisition setup. Both quantitative and qualitative evaluations illustrate the effectiveness of the proposed methods on synthetic and real-world scenarios.Comment: IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI), 2019. First three authors contribute equall

Recovering refined surface normals for relighting clothing in dynamic scenes

In this paper we present a method to relight captured 3D video sequences of non-rigid, dynamic scenes, such as clothing of real actors, reconstructed from multiple view video. A view-dependent approach is introduced to refine an initial coarse surface reconstruction using shape-from-shading to estimate detailed surface normals. The prior surface approximation is used to constrain the simultaneous estimation of surface normals and scene illumination, under the assumption of Lambertian surface reflectance. This approach enables detailed surface normals of a moving non-rigid object to be estimated from a single image frame. Refined normal estimates from multiple views are integrated into a single surface normal map. This approach allows highly non-rigid surfaces, such as creases in clothing, to be relit whilst preserving the detailed dynamics observed in video