An Optimal Illumination Method For Surface Reconstruction

Abstract

We solve the shape from narrow light beam projections problem, a new approach to surface reconstruction. In this approach a surface is recovered from sparse depth data obtained from the projection of a narrow light beam on this surface. This projection will yield a small light spot whose location can be easily measured in the camera image. From the (x, y)-position of this spot and from the location of the light source we can obtain the surface depth at the point (x, y). Furthermore, a method for the placement of the light sources is proposed, and it is shown that the proposed positioning is optimal or, in other words, it will result in the smallest error among all other possible placements of the lights. The spline algorithm that will recover the surface from the obtained data is constructed and it is shown to yield the smallest possible error among all algorithms that can be used to solve the problem. The spline algorithm is linear, and can be constructed easily and with a low cost.