A theory of differential photometric stereo for unknown isotropic BRDFs

This paper presents a comprehensive theory of photo-metric surface reconstruction from image derivatives. For unknown isotropic BRDFs, we show that two measurements of spatial and temporal image derivatives, under unknown light sources on a circle, suffice to determine the surface. This result is the culmination of a series of fundamental observations. First, we discover a photometric invariant that relates image derivatives to the surface geometry, regardless of the form of isotropic BRDF. Next, we show that just two pairs of differential images from unknown light directions suffice to recover surface information from the photometric invariant. This is shown to be equivalent to determining isocontours of constant magnitude of the surface gradient, as well as isocontours of constant depth. Further, we prove that specification of the surface normal at a single point com-pletely determines the surface depth from these isocontours. In addition, we propose practical algorithms that require additional initial or boundary information, but recover depth from lower order derivatives. Our theoretical results are illustrated with several examples on synthetic and real data. 1

Analysis of surface parametrizations for modern photometric stereo modeling

Tridimensional shape recovery based on Photometric Stereo (PS) recently received a strong improvement due to new mathematical models based on partial differential irradiance equation ratios. This modern approach to PS faces more realistic physical effects among which light attenuation and radial light propagation from a point light source. Since the approximation of the surface is performed with single step method, accurate reconstruction is prevented by sensitiveness to noise. In this paper we analyse a well-known parametrization of the tridimensional surface extending it on any auxiliary convex projection functions. Experiments on synthetic data show preliminary results where more accurate reconstruction can be achieved using more suitable parametrization specially in case of noisy input images

A fast 3D reconstruction system with a low-cost camera accessory

Photometric stereo is a three dimensional (3D) imaging technique that uses multiple 2D images, obtained from a fixed camera perspective, with different illumination directions. Compared to other 3D imaging methods such as geometry modeling and 3D-scanning, it comes with a number of advantages, such as having a simple and efficient reconstruction routine. In this work, we describe a low-cost accessory to a commercial digital single-lens reflex (DSLR) camera system allowing fast reconstruction of 3D objects using photometric stereo. The accessory consists of four white LED lights fixed to the lens of a commercial DSLR camera and a USB programmable controller board to sequentially control the illumination. 3D images are derived for different objects with varying geometric complexity and results are presented, showing a typical height error of <3 mm for a 50 mm sized object

A single-lobe photometric stereo approach for heterogeneous material

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.Roberto Mecca is a Marie Curie fellow of the “Istituto Nazionale di Alta Matematica” (Italy) for a project shared with University of Cambridge, Department of Engineering and the Department of Mathematics, University of Bologna

Photometric stereo and appearance capture

Ph.DDOCTOR OF PHILOSOPH