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Image Inpainting

M. Bertalmio, A.L. Sapiro, V. Caselles, C. Ballester M. Bertalmio, A.L. Bertozzi & G. Sapiro presented by Roman Stanchak. Image Inpainting. Navier Stokes, Fluid Dynamics and Image and Video Inpainting. Navier Stokes, Fluid Dynamics and Image and Video Inpainting. Goal.

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Image Inpainting

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  1. M. Bertalmio, A.L. Sapiro, V. Caselles, C. Ballester M. Bertalmio, A.L. Bertozzi & G. Sapiro presented by Roman Stanchak Image Inpainting Navier Stokes, Fluid Dynamics and Image and Video Inpainting Navier Stokes, Fluid Dynamics and Image and Video Inpainting

  2. Goal • Given image with significant portions missing or damaged • Reconstitute missing regions with data consistent with the rest of the image

  3. Cracks in Photos

  4. Scratches in Film

  5. Add or remove elements

  6. Professional Inpainters Approach • Goal: • Subjectively restore unity to artwork • General Approach: • Structure of surrounding area continued into gap • Color of surrounding area is continued into gap • Texture is added

  7. Gestalt Law of Continuation • Principle holding that there is an innate tendence to perceive a line as continuing its established direction

  8. General Algorithm • Iteratively • Continue structure of surrounding area into gap • Continue color of surrounding area into gap

  9. Algorithm • Define image update as follows: • It(i,j) = dL(i,j) . N(i,j) • It(i,j) is change in intensity to used to update the image • L(i,j) is the information to propagate • N(i,j) is the propagation direction • dL(i,j) . N(i,j) is the change in information along the propagation direction

  10. Propagation Direction • Want to preserve angle of 'arrival' • Propagate along isophotes • lines of equivalent intensity levels Isophotes

  11. Propagation Direction • More formally: • Image gradient • largest change • Perpindicular • smallest change • this is the isophote = N(i,j) Isophote is this boundary

  12. Algorithm • What information to propagate? • 'smoothness' • Laplacian == Ixx(i,j) +Iyy(i,j) = L(i,j)

  13. Algorithm • Repeat this image update step to restore image • When to stop? • Stop when update value is negligible • i.e. It(i,j) < epsilon for all i,j • Stop after n iterations

  14. Some results

  15. Some results

  16. Some results

  17. More results

  18. More results

  19. More results

  20. Navier-Stokes equations • Nonlinear partial differential equations • Describe the flow of fluids such as liquids and gases • Air currents • Ocean currents • Water flow in a pipe

  21. Navier-Stokes equations

  22. Relation to Inpainting • Inpainting • Propagation of intensity along isophote according to smoothness • Fluid mechanics • Convection of fluid along velocity field according to vorticity

  23. Relation to Inpainting • Mapping • Image intensity == Stream function • Isophote direction == fluid velocity • Smoothness == vorticity • Propels inpainting into an established field with a wealth of theoretical and numerical literature!

  24. Super Resolution Result Navier-Stokes inpainting Up scaled image Bicubic sampled

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