Depth from defocus (DFD) based on VFISTA optimization algorithm in micro/nanometer vision

Abstract

In the three-dimensional (3D) morphological reconstruction of micro/nano-scale vision, the global depth from defocus algorithm (DFD) transforms the depth information of the scene into a dynamic optimization problem to solve. In order to improve the problem of dynamic optimization in the recovery process of global DFD, a variable-step-size fast iterative shrinkage-thresholding algorithm (VFISTA) is proposed. The traditional iterative shrinkage-thresholding algorithm (ISTA) is often used to solve this dynamic optimization problem in the global DFD method. The ISTA algorithm is an extension of the gradient descent method, which is close to the minimal value point of the optimization process, and the convergence speed is slow. What is more, the ISTA algorithm uses fixed step length in the iterative process, The search direction tend to be “orthogonal”, prone to “saw tooth” phenomenon, so close to the minimum point when the convergence rate is slower. First, the VFISTA algorithm joins the acceleration operator on the basis of the ISTA algorithm. Further, it combines linear search method to find the optimal iteration length, and changes the limit of the ISTA algorithm step fixed. Finally, it is applied to the depth measurement of defocus scene in micro/nanometer scale vision. The experimental results show that the proposed fast depth from defocus algorithm based on VFISTA has faster convergent speed. Moreover, the precision of the measurement is obviously improved in micro/nanometer scale vision.