Perspective Photometric Stereo with Shadows

Abstract

Abstract. High resolution reconstruction of 3D surfaces from images remains an active area of research since most of the methods in use are based on practical assumptions that limit their applicability. Furthermore, an additional complication in all active illumination 3D reconstruction methods is the presence of shadows, whose presence cause loss of information in the image data. We present an approach for the reconstruction of surfaces via Photometric Stereo, based on the perspective formulation of the Shape from Shading problem, solved via partial differential equations. Unlike many photometric stereo solvers that use computationally costly variational methods or a two-step approach, we use a novel, well-posed, differential formulation of the problem that enables us to solve a first order partial differential equation directly via an alternating directions raster scanning scheme. The resulting formulation enables surface computation for very large images and allows reconstruction in the presence of shadows.

Solving Uncalibrated Photometric Stereo Using Total Variation

“…It is for that reason that TV-u performs better. It is possible to apply Gaussian filtering before calculating the numerical derivatives in (36) and (38), which reduces the impact of these approximations and improves the results of the TV-M method. This modified method is referred to as TV-M (G.f).…”

“…Although direct depth estimation may be carried out [36], an additional step is usually needed to "integrate" the normal field into a depth map (see Fig. 2-d).…”

“…Assuming orthographic projection (the problem was also studied in the perspective case [36]), the surface to be reconstructed is represented by a Monge patch (x, y, u(x, y)) ⊤ over a domain Ω ⊂ R 2 , where the depth function u(x, y) is assumed to be twice differentiable, at least piecewise. The vector field of unit outward normals is given by N (x, y) = 1…”

Real-Time 3D Shape of Micro-Details

“…They approximated the depth function as a linear combination of individual element basis functions. Other perspective methods are applied by Galo and Tozzi [13], Tankus and Kiryati [62] and Mecca et al [37], while the Lambertian reflectance is applied in all these researches. Concerning more general non Lambertian reflectance models based on perspective PS, Khanian et al proposed the application of perspective Blinn-Phong model [5,46] for the signal reconstruction and corresponding lightening conditions in [26] and for the 3D reconstruction with different perspective techniques in [27].…”