Covariant Derivatives and Vision - Todor Georgiev

More documents

Recommendations

Info

Derivatives in a Fiber BundleIf we represent the section in terms of the functionsthat define it in a given basis (not writing thebasis vectors), the last equation can be written as:The functions are called “color channels” inPhotoshop, and D is called “Covariant Derivative”.It corresponds to the derivative in the Cartesianproduct model.18
The covariant derivative is a rigorous mathematical toolfor perceptual pixel comparison in the fiber bundle modelof image space. It replaces the conventional derivative ofthe Cartesian product model as:19
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 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 and 42: Gradient Domain HDR CompressionChan
Page 43 and 44: Conclusion:The covariant (adapted)
Page 45: Bilateral(1)Same procedure on the l

Covariant Derivatives and Vision - Todor Georgiev

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?