Introducing more physics into variational depth–from–defocus

Abstract

Given an image stack that captures a static scene with different focus settings, variational depth–from–defocus methods aim at jointly estimating the underlying depth map and the sharp image. We show how one can improve existing approaches by incorporating important physical properties. Most formulations are based on an image formation model (forward operator) that explains the varying amount of blur depending on the depth. We present a novel forward operator: It approximates the thin–lens camera model from physics better than previous ones used for this task, since it preserves the maximum–minimum principle w.r.t. the unknown image intensities. This operator is embedded in a variational model that is minimised with a multiplicative variant of the Euler–Lagrange formalism. This offers two advantages: Firstly, it guarantees that the solution remains in the physically plausible positive range. Secondly, it allows a stable gradient descent evolution without the need to adapt the relaxation parameter. Experiments with synthetic and real–world images demonstrate that our model is highly robust under different initialisations. Last but not least, the experiments show that the physical constraints are essential for obtaining more accurate solutions, especially in the presence of strong depth changes.