The Discrete Focal Stack Transform

This paper describes the Discrete Focal Stack Transform (DFST) that computes the focal stack (a collection of photographs focused at different depths) from a lightfield. It proposes a new discretization of the Photography operator based on the interpolation of the lightfield by means of 4D trigonometric polynomials and an approximation to the integration process. Our approach combines the Fourier decomposition of the Photography operator with a generalization of the discrete Radon transform and provides a fast and exact computation of the focal stack. We also generalize our formulation to compute the modified laplacian stack that can be used to solve the depth estimation problem. Finally we provide some computational results that show the validity of the approach.