Ultra-Fast Multi-Scale Shape Estimation of Light Transport Matrix for Complex Light Reflection Objects

Abstract

3D measurement of target objects characterized by specular reflection or subsurface scatterings cannot be measured by traditional 3D measurement methods because these targets have multiple light paths that make it difficult to determine the unique surface. We define these objects as complex light reflection objects. In this case, 3D measurement methods based on Light Transport (LT) Matrix estimation may be a solution to measure these complex light reflection objects, because LT Matrix captures every light path, and we can identify all 3D points on the target shape by using LT Matrix. However, these methods either provide low resolution results, or they are too slow for use in robot vision in practice. In this paper, we suppress the computational cost of LT Matrix estimation by dividing LT Matrix estimation into multi-scale. The proposed method reduces the number of candidate combinations between camera pixels and projector pixels greatly by using the information given by low resolution observations. The proposed algorithm allows high resolution measurement of the LT Matrix very efficiently. Furthermore, careful implementation of our method by using a sparse matrix representation achieves memory efficiency. We evaluated our method by measuring 3D points for a 256 × 256 resolution projector and camera system, which is an LT matrix 4096 times larger than that developed in our previous study [1] and 100 times faster than our naïve implementation of [2].