Covariant Derivatives and Vision - Todor Georgiev

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Gradient Domain HDR CompressionEuler-Lagrange equation for the above energy:Exactly reproduces the result of the Fattal-Lischinski-Werman paper. They assume log; we derive log.Any good visual system needs to be logarithmic!42
Conclusion:The covariant (adapted) derivative providesa way to perform perceptual image processingaccording to how we see images as opposed to -how images are recorded by the camera.Useful for Poisson editing, inpainting or any PDE,HDR compression, surface reconstruction fromgradients, night/day cloning, graph cuts, bilateral<strong>and</strong> trilateral filters in terms of jet bundles, <strong>and</strong>practically any perceptual image editing.43
Page 1 and 2: Covariant Derivatives and VisionTod
Page 3 and 4: Selection to clone3
Page 5 and 6: Selection to clone5
Page 7 and 8: PoissoncloningCovariantcloning(see
Page 10 and 11: Thanks to Jan Koenderink10
Page 12 and 13: Models of Image Space:12
Page 14 and 15: (2) Fiber Bundle• Two spaces and
Page 16 and 17: Derivatives in a Fiber BundleDefini
Page 18 and 19: Derivatives in a Fiber BundleIf we
Page 21 and 22: - Reconstructing images with thecov
Page 23 and 24: PoissoncloningCovariantcloning23
Page 25 and 26: Detailed Example:25
Page 27 and 28: Laplace27
Page 29 and 30: Laplace29
Page 31 and 32: Poisson31
Page 33 and 34: InpaintingThanks to Guillermo Sapir
Page 35 and 36: Covariant Inpainting35
Page 37 and 38: Night37
Page 39 and 40: Poisson cloning from day39
Page 41: Gradient Domain HDR CompressionChan
Page 45: Bilateral(1)Same procedure on the l

Covariant Derivatives and Vision - Todor Georgiev

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