Performance model of depth from defocus with an unconventional camera

Abstract

In this paper we present a generic performance model able to evaluate the accuracy of depth estimation using depth from defocus. This model only requires the sensor PSF at a given depth to evaluate the theoretical accuracy of depth estimation. Hence, it can be used for any (un)conventional system, using either one or several images. This model is validated experimentally on two unconventional DFD cameras, using either a coded aperture or a lens with chromatic aberration. Then we use the proposed model for the end-to-end design of a 3D camera using an unconventional lens with chromatic aberration, for the specific use-case of small UAV navigation.

Co-design of an active depth from defocus camera for surface inspection

“…Trouve et al 14 have proposed a performance model for the DFD technique based on the derivation of a Cramér Rao Lower Bound (CRB). Given the Point Spread Function (PSF) of a camera at a given depth, the noise level and the patch size, this model determines the theoretical accuracy of depth estimation.…”

“…This model is thus suitable for conventional and unconventional cameras and has been used for the co-design of a chromatic lens dedicated to SIDFD. 14 However, the derivation of the likelihood function from which the CRB is computed is based on a generic scene prior which is not always realistic depending on the observed scene. An adaptation of this model in the case of ADFD has been proposed in Buat et al 13 The CRB is calculated using learned covariance matrix from the known projected pattern.…”

Single image depth-from-defocus with a learned covariance: algorithm and performance model for co-design

“…As performances of a DFD method are highly related to the parameters of the sensor, a performance model is useful to design the optical system and his settings 9 . For multiple image DFD, papers have proposed performance models using a Cramér Rao bound (CRB) to optimize the blur ratio between a pair of images 16,17 in order to maximize the depth estimation accuracy while taking into account the influence of processing.…”

“…However, these models only consider the aperture shape and not the remaining of the optical system or the processing parameters and they only compare the results of depth estimation on different forms of coded aperture without providing a real accuracy nor information about the depth range of their systems. Trouve et al 9 propose a performance model based on the CRB only requiring the Point Spread Function (PSF) of a camera at at given depth to determine the theoretical accuracy of depth estimation, thus suitable for conventional and unconventional cameras. This model use a generic scene prior which is not always realistic depending on the observed scene.…”

“…Moreover, as performances of a DFD method are highly related to the parameters of the sensor, a performance model can be used to optimize jointly the optical system and his settings 9 . It is even more required when using unconventional optics, whose interaction with the processing cannot be anticipated using conventional optimization tools.…”