Depth from defocus using the hermite transform

This paper presents an algorithm for a dense computation of the difference in blur between two images. The two images are acquired by varying the intrinsic parameters of the camera. The image formation system is assumed to be passive. The algorithm is based on a local image decomposition technique using the Hermite polynomial basis. We show that any coefficient of the Hermite polynomial computed using the unfocused image is a function of the partial derivatives of the focused image and the blur difference. Hence, the blur difference can be computed by resolving a system of equations. An algorithm is presented for estimation of the blur in 1D and 2D images. The algorithm is tested using synthetic and real images. The results obtained are very encouraging.