Direct Shape Recovery from Photometric Stereo with Shadows

Abstract

Abstract-Reconstruction of 3D objects based on images is useful in many applications. One of the methods based on multi-image data is the Photometric Stereo technique relying on several photographs of the observed object from the same point of view, each one taken under a different illumination condition. The common approach is to estimate the gradient field of the surface by minimizing a functional, integrating the distance from the camera and thereby obtaining the geometry of the observed object. We propose an alternative method that consists of a novel differential approach for multi-image Photometric Stereo and permits a direct solution of a novel PDE based model without going through the gradient field while naturally dealing with shadowed regions. The mathematical well-posedness of the problem in terms of numerical stability yields a fast algorithm that efficiently converges, even for pictures of sizes in the order of several megapixels affected by noise.

Semi-Calibrated Near Field Photometric Stereo

“…Image ratios Images acquired for PS reconstruction have constant overlapping information due to the monocular procedure; this overlapping information allows for simplification of the problem by considering ratios of images. After being introduced by Davis and Soderblom [13], this approach has been often used [23,24,51,26,18,48,42,30,28]. Mecca et al [29] proposed a novel approach embedding the nonlinear parameterization of a point light source into a differential problem of hyperbolic PDEs.…”

Dense 3D facial reconstruction from a single depth image in unconstrained environment

“…Photometric Stereo (PMS) is another 3D reconstruction method based on shape from shading. By capturing a scene multiple times with different directional illuminations, PMS can recover a continuous depth map (Mecca et al 2013). However, the camera should stay very still when capturing these images to make sure that the contents in these images are not moving.…”

Height from photometric ratio with model-based light source selection

“…Recently, there has been renewed interest in exploiting ratios for photometric stereo, led by Mecca and coworkers [42,43,44,45,46]. Their line of work uses photometric ratios to construct PDEs for which they can prove well-posedness and solve using upwind or semiLagrangian schemes.…”

“…Initially they considered the classical photometric stereo set up of orthographic viewer and distant point light sources [43], proving the uniqueness of the two image case in the presence of boundary conditions. This was extended to a practically useful situation [42] by considering cast shadows in three image photometric stereo. In shadow regions, a shadowed observation is given zero weight (it is assumed that at least two observations are unshadowed), allowing the surface to be recovered in spite of the missing data.…”

“…To do this, the problem must be posed in terms of surface height. This idea is not new and has recently gained popularity with a number of methods [42,43,44,45,46,47] exploiting the simplified relationship between surface height and image intensity that arises when photometric ratios are taken.…”