Improving Least-Squares Surface Reconstruction through Fourth-Order Adams Method and Iterative Compensation

The Southwell model stands as a prominent algorithm within the realm of the least squares surface reconstruction, finding wide application. This algorithm boasts notable merits, including rapid computation and an approximation of the reconstructed surface that closely mirrors reality. Nevertheless, it is not without its drawbacks, as it exhibits substantial reconstruction errors and proves to be susceptible to the presence of noisy data. To enhance the precision of the reconstructed object’s three-dimensional surface, this paper puts forth an enhanced least squares surface reconstruction algorithm based on the fourth-order Adams method and iterative compensation. Initially, the fourth-order Adams method is employed to establish the connection between the measured gradient and the unknown surface height in the Southwell model. Subsequently, Tikhonov regularization is introduced to mitigate the impact of noise on the model. Ultimately, the accuracy is augmented through the utilization of an iterative compensation technique. Simulation experiments substantiate that, in comparison to alternative Southwell model algorithms, the proposed algorithm exhibits reduced time consumption and superior surface fitting accuracy.