Precise Point Spread Function Estimation

Point spread function (PSF) plays a crucial role in many fields, such as shape from focus/defocus, depth estimation, and imaging process in fluorescence microscopy. However, the mathematical model of the defocus process is still unclear because several variables in the point spread function are hard to measure accurately, such as the f-number of cameras, the physical size of a pixel, the focus depth, etc. In this work, we develop a precise mathematical model of the camera's point spread function to describe the defocus process. We first derive the mathematical algorithm for the PSF and extract two parameters A and e. A is the composite of camera's f-number, pixel-size, output scale, and scaling factor of the circle of confusion; e is the deviation of the focus depth. We design a novel metric based on the defocus histogram to evaluate the difference between the simulated focused image and the actual focused image to obtain optimal A and e. We also construct a hardware system consisting of a focusing system and a structured light system to acquire the all-in-focus image, the focused image with corresponding focus depth, and the depth map in the same view. The three types of images, as a dataset, are used to obtain the precise PSF. Our experiments on standard planes and actual objects show that the proposed algorithm can accurately describe the defocus process. The accuracy of our algorithm is further proved by evaluating the difference among the actual focused images, the focused image generated by our algorithm, the focused image generated by others. The results show that the loss of our algorithm is 40% less than others on average. The dataset, code, and model are available on GitHub: https://github.com/cubhe/ precise-point-spread-function-estimation.