1. Recovery of relative depth from a single observation using an uncalibrated (real-aperture) camera Vinay P. Namboodiri Subhasis Chaudhuri Department of Electrical Engineering Indian Institute of Technology, Bombay Powai, Mumbai 400076, India. CVPR 2008

2. Outline Introduction Diffusion Based Modeling of Defocus Reverse Heat Equation DFD Using Graph Cuts Results Ambiguity in Depth Estimation Using Defocus Conclusion

3. Introduction Recovering the depth layers in a scene from a single defocused observation Common resolution ◦ Multiple observations This paper ◦ Single observation ◦ Uncalibrated camera

4. Diffusion Based Modeling of Defocus Depth 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

5. 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

6. The breakdown of the heat equation is indicated by the degeneration of the gradient The relative depth in the scene the approximate estimate of the depth at the location x the reverse diffusion time at a location x

8. DFD Using Graph Cuts The depth estimate is further refined by modeling the depth as a Markov random field(MRF)

9. Results Results A texture image from the Brodatz texture database which is blurred with3 different blur regions A general outdoor image

10. A sports scene A complex lighting conditions

11. Ambiguity in Depth Estimation Using Defocus The foreground is out of focus and the background is in focus The foreground is in focus and the background is out of focus

12. Conclusion The 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