This study aims to address the challenging problem of recovering the 3D depth of a scene from a single image. Most current approaches for depth recovery from a single defocused image model the point spread function as a 2D Gaussian function. However

these methods are influenced by noise

and a high quality of recovery is difficult to achieve. Unlike the previous depth calculations from defocus methods

we propose an approach to estimate the amount of spatially varying defocus blurs at the locations of image edges on the basis of a Cauchy distribution point-spread function model. The input defocused image is reblurred twice with two respective Cauchy distribution kernels. The amount of defocus blur at edge locations can be obtained from the ratio between the gradients of the two re-blurred images and the two scale parameters of Cauchy distribution. A full depth map is recovered by propagating the blur amount at edge locations to the entire image via matting interpolation. The original “Lenna” image and a rotated noise “Lenna” image are used

and a Gaussian noise is used to simulate the image noise and edge position error. Then

the average error of the Cauchy gradient ratio is compared with that of a Gaussian gradient ratio. Various real-scene image data are also used to compare our depth recovery results with those of existing methods. Experimental results show that the average error of the Cauchy gradient ratio is less than that of a Gaussian gradient ratio. Experimental results on several real images demonstrate the effectiveness of our method in estimating the defocus map from a single defocused image. Our method is robust to image noise

inaccurate edge location

and interference of neighboring edges. The proposed method can generate more accurate scene depth maps as compared with most existing methods based on a Gaussian model. Our results also demonstrate that a non-Gaussian model for DSF is feasible.