A coaxial optical scanner for synchronous acquisition of 3D geometry and surface reflectance

Abstract

Shifted sinusoidal illumination patterns are useful for appearance capture because they simultaneously separate local and non-local reflections and allow the recovery of surface geometry. Here we show that the same illumination patterns can be used to estimate the local surface reflectance (BRDF) as well, provided that an appropriate correction factor is applied. We derive a closed-form expression for this correction factor, validate it experimentally, and discuss its implications. PreliminariesConsider the system in Fig. 1. A thin-lens camera observes a planar surface patch that is illuminated by a custom light assembly, and this light assembly consists of a planar Lambertian area source placed at the focal plane of another thin lens. The area source in this light assembly produces radiance patterns that are shifted horizontal sinusoids with fixed frequency f , amplitude A, and DC offset G. The shifts are represented by a discrete set of phase values: {φ k } k=1...M , so we can write the radiance at a point p = (p, q) on the focal plane of the source asIllumination from the source is focused at a point x on a planar surface patch, and this patch is observed by a thin-lens camera, which is also focused at x. A pixel (or any square region) on the image plane that is centered at the projection of x and has dimensions w × w measures flux due to the radiance from a neighborhood of the point x on the surface, and assuming that the camera is a linear device, the intensity recorded at the pixel is proportional to this flux. Under the sinusoidal illumination of Eq. 1, the pixel response can be written in the form,where u = Π c (x) is the projection of x (the center of the pixel), and γ = 2πf (t k+1 − t k ), the product of the spatial frequency and the displacement of the sinusoid between consecutive shifts. This relation plays a central role in phase mapping techniques (e.g.[4]), since the apparent phase φ(u) provides information about the depth of the surface along the ray that is back-projected from pixel u.Presently, we are interested in the apparent amplitude α(u) since, as we will show, it provides information about the local surface reflectance (the BRDF at x) and can be used for reflectometry. We show that, in addition to the BRDF, this expression depends on the intrinsic parameters of the lightsource and camera, as well as their positions and orientations relative to the surface.

3D mass digitization: a milestone for archeological documentation

“…Setups to capture geometry, texture and optical material properties can range from very simple to very complex setups differing significantly regarding their performance. (Holroyd, Larence, & Zickler, 2010) move a co-axial setup of a camera and a light-source around an artefact during acquisition with an identical setup looking down on the artefact from above. (Schwartz & Klein, 2012) use a multiview/multilight setup of 151 consumer cameras and LED lights called the DOME to capture the shape as well as the appearance model of an artefact's surface.…”

Design and Implementation of Practical Bidirectional Texture Function Measurement Devices Focusing on the Developments at the University of Bonn

“…Several setups propose to have the light source or the detector at a fixed position and achieve the necessary angular configurations by changing the orientation of the material sample [2,19,20,41–44]. The setups proposed in [45,46] instead move both, sensor and light source, around the sample.…”

“…The authors of [21,59,60] employ additional auxiliary 3D scanners and register the geometry to the reflectance measurement. Several other devices [23,45,55,69–71,74] instead rely on an integrated structured light approach. This holds the advantage that the geometry is already registered with the reflectance measurements.…”

“…Finally, Holroyd et al [45] and Filip et al [46] presented setups that put both, light source and camera, on robot arms. This eliminates the necessity to tilt the sampleholder and hence allows to acquire the same range of delicate materials and 3D objects as leveled mirror setups and camera array setups do.…”

“…The setup of Holroyd et al [45] has one design detail that is different to all other presented gonioreflectometers: it uses a light source and camera with a beam-splitter on each robot arm to allow a coaxial arrangement of light and view direction. This gives view to the important retro-reflection configuration as well as directly creating reciprocal image pairs.…”