Recap from Monday. Frequency domain analytical tool computational shortcut compression tool

Transcription

1 Recap from Monday Frequency domain analytical tool computational shortcut compression tool

2 Fourier Transform in 2d in Matlab, check out: imagesc(log(abs(fftshift(fft2(im)))));

3 Image Blending (Szeliski 9.3.4) Google Street View Many slides from Alexei Efros CS129: Computational Photography James Hays, Brown, Spring 2011

4 Compositing Procedure 1. Extract Sprites (e.g using Intelligent Scissors in Photoshop) 2. Blend them into the composite (in the right order) Composite by David Dewey

5 Need blending

6 Alpha Blending / Feathering I blend = I left + (1- )I right =

7 Setting alpha: simple averaging Alpha =.5 in overlap region

8 Setting alpha: center seam Distance Transform bwdist Alpha = logical(dtrans1>dtrans2)

9 Setting alpha: blurred seam Distance transform Alpha = blurred

10 Setting alpha: center weighting Distance transform Alpha = dtrans1 / (dtrans1+dtrans2) Ghost!

11 Affect of Window Size 1 left 1 0 right 0

12 Affect of Window Size

13 Good Window Size 1 0 Optimal Window: smooth but not ghosted

14 Band-pass filtering Gaussian Pyramid (low-pass images) Laplacian Pyramid (subband images) Created from Gaussian pyramid by subtraction

15 Laplacian Pyramid Need this! Original image How can we reconstruct (collapse) this pyramid into the original image?

16 Pyramid Blending Left pyramid blend Right pyramid

17 Pyramid Blending

18 laplacian level 4 laplacian level 2 laplacian level 0 left pyramid right pyramid blended pyramid

19 Laplacian Pyramid: Blending General Approach: 1. Build Laplacian pyramids LA and LB from images A and B 2. Build a Gaussian pyramid GR from selected region R 3. Form a combined pyramid LS from LA and LB using nodes of GR as weights: LS(i,j) = GR(I,j,)*LA(I,j) + (1-GR(I,j))*LB(I,j) 4. Collapse the LS pyramid to get the final blended image

20 Blending Regions

21 Horror Photo david dmartin (Boston College)

22 Chris Cameron

23 Simplification: Two-band Blending Brown & Lowe, 2003 Only use two bands: high freq. and low freq. Blends low freq. smoothly Blend high freq. with no smoothing: use binary alpha

24 Don t blend, CUT! (project 4) So far we only tried to blend between two images. What about finding an optimal seam?

25 Project 3 and 4 -Minimal error boundary overlapping blocks vertical boundary 2 _ = overlap error min. error boundary

26 Graphcuts What if we want similar cut-where-thingsagree idea, but for closed regions? Dynamic programming can t handle loops

27 Graph cuts (simple example à la Boykov&Jolly, ICCV 01) hard constraint n-links t a cut s hard constraint Minimum cost cut can be computed in polynomial time (max-flow/min-cut algorithms)

28 Kwatra et al, 2003 Actually, for this example, dynamic programming will work just as well

29 Gradient Domain Image Blending In Pyramid Blending, we decomposed our image into 2 nd derivatives (Laplacian) and a low-res image Let s look at a more direct formulation: No need for low-res image Idea: captures everything (up to a constant) Differentiate Composite Reintegrate

30 Gradient Domain blending (1D) Two signals bright dark Regular blending Blending derivatives

31 Gradient Domain Blending (2D) Trickier in 2D: Take partial derivatives dx and dy (the gradient field) Fidle around with them (smooth, blend, feather, etc) Reintegrate But now integral(dx) might not equal integral(dy) Find the most agreeable solution Equivalent to solving Poisson equation Can use FFT, deconvolution, multigrid solvers, etc.

32 Perez et al., 2003

33 Perez et al, 2003 Limitations: editing Can t do contrast reversal (gray on black -> gray on white) Colored backgrounds bleed through Images need to be very well aligned

34 Putting it all together Compositing images Have a clever blending function Feathering Center-weighted blend different frequencies differently Gradient based blending Choose the right pixels from each image Dynamic programming optimal seams Graph-cuts Now, let s put it all together: Interactive Digital Photomontage, 2004 (video)

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