Diffusion curves
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Diffusion Curves PowerPoint PPT Presentation


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Diffusion Curves. Dr. Scott Schaefer. Diffusion Curves. Vector graphics-based representation for 2D images Images are piecewise smooth with discontinuities represented as curves. Image taken from “Diffusion Curves: A Vector Representation for Smooth-Shaded Images”.

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Diffusion Curves

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Diffusion Curves

Dr. Scott Schaefer


Diffusion Curves

  • Vector graphics-based representation for 2D images

  • Images are piecewise smooth with discontinuities represented as curves

Image taken from “Diffusion Curves: A Vector Representation for Smooth-Shaded Images”


Representation

  • Bezier curves represent discontinuities

  • Give each curve a color function on left/right side of curve

    • Original paper uses linear color change

    • Modification: Control points can have any color

Image taken from “Diffusion Curves: A Vector Representation for Smooth-Shaded Images”


Image Construction

Use curves as boundary constraints

Find a harmonic function that interpolates those boundary constraints

Image taken from “Diffusion Curves: A Vector Representation for Smooth-Shaded Images”


Implementation (Simplified)

Define a left/right color for points

Use a background color to represent no data (black)

Draw curve as a polygon made of quads (thick) with smooth shading


Implementation (Simplified)

  • Colored pixels are constraints

  • Find a harmonic function satisfying constraints

    • Harmonic function has Laplacian zero everywhere


Implementation (Simplified)

1

0

0

-4

1

1

0

0

  • Colored pixels are constraints

  • Find a harmonic function satisfying constraints

    • Harmonic function has Laplacian zero everywhere

1


Implementation (Simplified)

1

0

0

-4

1

1

0

0

  • Colored pixels are constraints

  • Find a harmonic function satisfying constraints

    • Harmonic function has Laplacian zero everywhere

    • Each value is average of its neighbors

1


Implementation (Simplified)

  • Draw curves as quads

  • Read pixel buffer back from OpenGL

  • Repeat a lot

    • For all pixels whose initial value was black, replace with average color of its neighbors from previous iteration


Problem


Problem

Final Result


Problem

100 Iterations


Problem

200 Iterations


Problem

400 Iterations


Problem

800 Iterations


Problem

1600 Iterations


Problem

6400 Iterations


Problem

Infinity Iterations


Problem

256


Simple Multi-Grid

  • Create power of 2 down-sampled images

    • Average value of all non-black pixels

  • For each level, starting at second to last

    • Up-sample previous level

      • Copy pixel value to black high-res pixels (non-black pixels are constraints)

    • For some number of iterations

      • For each non-constrained pixel, replace with color of its neighbors from previous iteration


Example

Original 512x512


Example

Down-sampled 256x256


Example

Down-sampled 128x128


Example

Down-sampled 64x64


Example

Down-sampled 32x32


Example

Down-sampled 16x16


Example

Down-sampled 8x8


Example

Down-sampled 4x4


Example

Down-sampled 2x2


Example

Down-sampled 1x1


Example

Up-sampled


Example

Smoothed


Example

Up-sampled


Example

Smoothed


Example

Up-sampled


Example

Smoothed


Example

Up-sampled


Example

Smoothed


Example

Up-sampled


Example

Smoothed


Example

Up-sampled


Example

Smoothed


Example

Up-sampled


Example

Smoothed


Example

Up-sampled


Example

Smoothed


Example

Up-sampled


Example

Smoothed


Example


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