A fast and non-iterative zonal estimation for the nonrectangulardata in the transparent surfacereconstruction from polarization analysis

In the method of surface reconstruction from polarization, the reconstructed area is generally non-rectangular and contains a large number of sampling points. There is a difficulty that the coefficient matrix in front of the height vector changes with the shape of the measured data when using the zonal estimation. The traditional iterative approaches consume more time for the reconstruction of this type of data. This paper presents a non-iterative zonal estimation to reduce the computing time and to accurately reconstruct the surface. The index vector is created according to the positions of both the valid and invalid elements in the difference and gradient matrices. It is used to obtain the coefficient matrix corresponding to the general data. The heights in the non-rectangular area are calculated non-iteratively by the least squares method. At the same time, the sparse matrix is applied for handling the large-scale data quickly. The simulation and the experiment are designed to verify the feasibility of the proposed method. The results show that the proposed method is highly efficient and accurate in the reconstruction of the non-rectangular data. (C) 2020 Optical Society of America