Recovery of relative depth from a single observation using an uncalibrated(real-aperture) camera

Vinay P. Namboodiri Subhasis Chaudhuri Department of Electrical EngineeringIndian Institute of Technology, BombayPowai, Mumbai 400076, India.CVPR 2008

OutlineIntroductionDiffusion Based Modeling of

DefocusReverse Heat EquationDFD Using Graph CutsResultsAmbiguity in Depth Estimation

Using DefocusConclusion

IntroductionRecovering the depth layers in a scene

from a single defocused observation

Common resolution◦Multiple observations

This paper◦Single observation◦Uncalibrated camera

Diffusion Based Modeling of DefocusDepth from defocus

methodology(DFD)◦1987, Pentland

Point spread function (PSF)◦The resultant PSF has the general

shape of a 2-D Gaussian function

The resultant image

the blurred observation

the focused image of the scene

Reverse Heat Equation(1) can be formulated in terms of

the isotropic heat equation

The original image◦achieved by reversing time

the blurred observation

the diffusion coefficient

The breakdown of the heat

equation is indicated by the degeneration of the gradient

The relative depth in the scenethe approximate estimate of the depth at the location x

the reverse diffusion time at a location x

DFD Using Graph CutsThe depth estimate is further

refined by modeling the depth as a Markov random field(MRF)

ResultsA texture image from the Brodatz

texture database which is blurred with3 different blur regions

A general outdoor image

A sports scene

A complex lighting conditions

Ambiguity in Depth Estimation Using DefocusThe foreground is out of focus

and the background is in focus

The foreground is in focus and the background is out of focus

ConclusionThe reverse heat equation can be

used for restoring the image based on the amount of defocus blur

A graph cuts based method is proposed to estimate the depth in the scene thereby enforcing regularization