In range finding, the depth from defocus (DFD) is a simple and effective method. The DFD yields the absolute depth, and does not have the image-to-image matching and occlusion problems. Therefore, we use the DFD method to analyze the defocused images to obtain depth information using Gaussian blurred function. In order to find the range of objects, a sigma value of the Gaussian function due to edges out of focus is necessary. Because the sigma value of the Gaussian function depicts on the intensity of images grabbed by imaging devices, we employ an approximate method, the radial basis function networks (RBFN), to approach the sigma value directly in the spatial domain. The RBFN regularizes the center position and the sigma value of the Gaussian function to fit the profile of the defocused image by three layers of neural networks based on the radial basis function. It has accurate ranging results with less than 8% of the root mean square error in sigma value approaching and 5% of the relative error in ranging, imaging system ranges from 220 mm to 355 mm and focuses at 400 mm.
Shyh-Ming Jong, Jeng-Sheng Huang, "Using Radial Basis Function Networks to Approach the Depth from Defocus" in Journal of Imaging Science and Technology, 2001, pp 400 - 406, https://doi.org/10.2352/J.ImagingSci.Technol.2001.45.4.art00013