Soonmin Bae & Frédo Durand Computer Science and Artificial Intelligence Laboratory

1. Defocus Magnification SoonminBae & FrédoDurand Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology Proceedings of EUROGRAPHICS 2007 DEMO Presented by DebaleenaChattopadhyay

2. The Problem Definition To present an image- processing technique that creates a defocus map that can be used to magnify existing defocus given a single photo. Defocus Map Input Image

3. The Algorithm Input Photo Defocus Map Blur Estimation Blur Propagation Detect Edges Estimate Blur Refine Blur Estimation Cross Bilateral Filtering Use Sharpness Bias

4. Edge Detection Multi-scale edge detector working formulae : The constants and thresholds: • Sensor noise n(x, y) is modeled as a stationary, additive, zero-mean white noise process; with standard deviation sn (sn = 2.5), • Reliability is defined in terms of an overall significance level αI for the entire image and a pointwise significance level αp. : (αI = 0.0001 %)

5. Edge Detection Multi-scale edge detector working formulae : The edge detection scale • For each pixel, multiscale responses are computed to the steerable Gaussian first derivative filters and steerable second derivative of Gaussian filters. The gradient direction θ is computed using the steerable Gaussian first derivative basis filters. • The filter responses are then tested for reliability using certain thresholds. • The right scale for edge detection as defined in the paper is : σ1 = {64 32 16 8 4 2 1 0.5} and σ2 = {32 16 8 4 2 1 0.5} pixels

6. d 2nd derivative Blur Estimation • Fit response models of various sizes less blurry edge more blurry response model

7. Blur Estimation Where the response model is given as (σb is the size of the blur kernel) :

8. Refining Blur Estimation The biased cross bilateral filtering of a sparse set of blur measures, BM at an edge pixel p is formulated as the following: Where, b(BM)= exp(-BM/2) gσ (x)= exp( -x2/2 σ 2) σr= 10% of the image range σs= 10% of the image size

9. Blur Propagation Blur Propagation • Given a sparse set of the blur measure (BM) • Propagate the blur measure to the entire image • Assumption : blurriness (B)is smooth except at image edges We minimize

10. RESULT 1

11. RESULT 3

12. RESULT 4

13. Input Result Defocus Map

14. Input Result Defocus Map Slide Credit: Bae & Durand

15. Remarks • Edge detection using multiscale method was implemented. • The blur estimation using Elder and Zucker as well as Bae and Durand was implemented. • The Bae and Durand method was implemented in a variant form along with their refinement algorithm. • For Blur propagation the smoothing of blurred edges in defocus did not work resulting into a distorted defocus map. • The algorithm would give better results with a set of better resolution images, as the edge energy change information degrades with size reduction.

16. Thank you