Rational filter design for depth from defocus

The paper describes a new, simple procedure to determine the rational filters that are used in the depth from defocus (DfD) procedure previously researched by Watanabe and Nayar (1998) [4]. Their DfD uses two differently defocused images and the filters accurately model the relative defocus in the images and provide a fast calculation of distance. This paper presents a simple method to determine the filter coefficients by separating the M/P ratio into a linear and a cubic error correction model. The method avoids the previous iterative minimisation technique and computes efficiently. The model has been verified by comparison with the theoretical M/P ratio. The proposed filters have been compared with the previous for frequency response, closeness of fit to M/P, rotational symmetry, and measurement accuracy. Experiments were performed for several defocus conditions. It was observed that the new filters were largely insensitive to object texture and modelled the blur more precisely than the previous. Experiments with real planar images demonstrated a maximum RMS depth error of 1.18% for the proposed, compared to 1.54% for the previous filters. Complicated objects were also accurately measured.