Minimal Operator Set for Passive Depth from Defocus

Abstract

A fundamental problem in depth from defocus is the measurement of relative defocus between images. 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. 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 I%, irrespective of texture frequency. Depth accuracy is found to be 0.5- 1.2 % of the distance of the object, from the imaging optics. quency, a single broadband filter that produces an aggregate estimate of defocus for an unknown texture cannot lead to accurate depth estimates. One solution is to use an large bank of narrow-band filters and compute depth in a least-squares sense using all dominant frequencies of the texture [Xiong and Shafer-1995, Gokstorp-l994]. However, this requires one to forego computational efficiency. Subbarao and Surya [Subbarao and Surya-19941 proposed t8he §- Transform and applied it to deplh from defocus. They modeled the image as a third-order polynomial in spatial domain, and arrived at a, simple and elegant expression [Subbarao and Surya- 19941: 1