Rational filters for passive depth from defocus

A fundamental problem in depth from defocus is the measurement of relative defocus between images. The performance of previously proposed focus operators are inevitably sensitive to the frequency spectra of local scene textures. As a result, focus operators such as the Laplacian of Gaussian result in poor depth estimates. An alternative is to use large filter banks that densely sample the frequency space. Though this approach can result in better depth accuracy, it sacrifices the computational efficiency that depth from defocus offers over stereo and structure from motion. We propose a class of broadband operators that, when used together, provide invariance to scene texture and produce accurate and dense depth maps. Since the operators are broadband, a small number of them are sufficient for depth estimation of scenes with complex textural properties. In addition, a depth confidence measure is derived that can be computed from the outputs of the operators. This confidence measure permits further refinement of computed depth maps. Experiments are conducted on both synthetic and real scenes to evaluate the performance of the proposed operators. The depth detection gain error is less than 1%, irrespective of texture frequency. Depth accuracy is found to be 0.5 similar to 1.2% of the distance of the object from the imaging optics.