Physically inspired depth-from-defocus*

•Novel forward operator preserving essential physical properties is pro-posed.•No equifocal assumption is required.•Joint handling of depth-from-defocus and denoising can improve the re-construction quality.•Robustification leads to a better reconstruction at strong depth changes.•Positivity constrained minimisation strategy increases the efficiency.

We propose a novel variational approach to the depth-from-defocus problem. The quality of such methods strongly depends on the modelling of the image formation (forward operator) that connects depth with out-of-focus blur. Therefore, we discuss different image formation models and design a forward operator that preserves essential physical properties such as a maximum-minimum principle for the intensity values. This allows us to approximate the thin-lens camera model in a better way than previous approaches. Our forward operator refrains from any equifocal assumptions and fits well into a variational framework. Additionally, we extend our model to the multi-channel case and show the benefits of a robustification. To cope with noisy input data, we embed our method in a joint depth-from-defocus and denoising approach. For the minimisation of our energy functional, we show the advantages of a multiplicative Euler-Lagrange formalism in two aspects: First, it constrains our solution to the plausible positive range. Second, we are able to develop a semi-implicit gradient descent scheme with a higher stability range. While synthetic experiments confirm the achieved improvements, experiments on real data illustrate the applicability of the overall method.