Quantitative analysis of error bounds in the recovery of depth from defocused images

Depth from defocus involves estimating the relative blur between a pair of defocused images of a scene captured with different lens settings. When a p riori information about the scene is available, it is possible to estimate the depth even from a single image. However, experimental studies indicate that the depth estimate improves with multiple observations. We provide a m athematical underpinning to this evidence by deriving and comparing the the oretical bounds for the error in the estimate of blur corresponding to the case of a single image and for a pair of defocused images. A nem theorem is proposed that proves that the Cramer-Rao bound on the variance of the erro r in the estimate of blur decreases with an increase in the number of obser vations. The difference in the bounds turns out to be a function of the rel ative blurting between the observations. Hence one can indeed get better es timates of depth from multiple defocused images compared with those using o nly a single image, provided that these images are differently blurred. Res ults on synthetic as well as real data are given to further validate the cl aim. (C) 2000 Optical Society of America [S0740-3232(00)02310-3]. OCIS code s: 150.5670, 150.6910, 100.3190, 100.2960.