Shape Recovery using Stochastic Heat Flow

Vinay P. Namboodiri and Subhasis Chaudhuri Department of Electrical Engineering Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India. {vinaypn,sc}, at ee dot iitb dot ac dot in

1

Depth from Defocus Object O

Blur Radius 2R

The defocus cone Projected Image I

The defocus cone can be modeled by a circularly symmetric Gaussian This defocus process can be modeled by the diffusion process (Favaro et al., CVPR 2003)

2

Need for Stochastic Heat Flow

Illustration of deformation of kernel due to self occlusion

Depth from Defocus due to diffusion has two shortcomings • Does not handle departure from Gaussian assumption for instance due to self occlusion • Does not address the non-convex nature of diffusion

3

Stochastic Heat Flow

• Stochastic Perturbation to Heat flow to handle departure from Gaussian assumption – Stability proved by N.K.Yip for dendritic crystal growth

• Stochastic level sets to perform the nonconvex optimization – Stochastic level sets proposed by O.Juan et al. for object segmentation

4

Results Input Images

Experiment on synthetic image shows that given method handles non Convex optimization better

Result, (Favaro et al.)

Result, (Proposed method)

5

Results – Hair data set

Input images from S. Hasinoff and K. Kutulakos (ECCV 2006) 6

Results – Hair data set Favaro et al.(C2003)

S.Hasinoff and K.Kutulakos (E2006)

7

Proposed method

Results – Hair data set (proposed method)

8

Results Input images (From Favaro [CVPR 2003])

Depth Map: Proposed Method

9

Perspective View -1

Perspective View 2