diffusion curves
DESCRIPTION
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”. - PowerPoint PPT PresentationTRANSCRIPT
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Dr. Scott Schaefer
Diffusion Curves
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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 curveOriginal paper uses linear
color changeModification: Control
points can have any color
3/49Image 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
4/49Image 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
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Implementation (Simplified)
Colored pixels are constraints Find a harmonic function satisfying
constraintsHarmonic function has Laplacian zero
everywhere
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Implementation (Simplified)
Colored pixels are constraints Find a harmonic function satisfying
constraintsHarmonic function has Laplacian zero
everywhere
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1
1
1
1
0 0
0 0
Implementation (Simplified)
Colored pixels are constraints Find a harmonic function satisfying
constraintsHarmonic function has Laplacian zero
everywhereEach value is average of
its neighbors
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-4
1
1
1
1
0 0
0 0
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
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Problem
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Problem
11/49Final Result
Problem
12/49100 Iterations
Problem
13/49200 Iterations
Problem
14/49400 Iterations
Problem
15/49800 Iterations
Problem
16/491600 Iterations
Problem
17/496400 Iterations
Problem
18/49Infinity Iterations
Problem
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256
Simple Multi-Grid
Create power of 2 down-sampled imagesAverage value of all non-black pixels
For each level, starting at second to lastUp-sample previous level
Copy pixel value to black high-res pixels (non-black pixels are constraints)
For some number of iterationsFor each non-constrained pixel, replace with color
of its neighbors from previous iteration
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Example
21/49Original 512x512
Example
22/49Down-sampled 256x256
Example
23/49Down-sampled 128x128
Example
24/49Down-sampled 64x64
Example
25/49Down-sampled 32x32
Example
26/49Down-sampled 16x16
Example
27/49Down-sampled 8x8
Example
28/49Down-sampled 4x4
Example
29/49Down-sampled 2x2
Example
30/49Down-sampled 1x1
Example
31/49Up-sampled
Example
32/49Smoothed
Example
33/49Up-sampled
Example
34/49Smoothed
Example
35/49Up-sampled
Example
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Example
37/49Up-sampled
Example
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Example
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Example
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Example
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Example
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Example
43/49Up-sampled
Example
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Example
45/49Up-sampled
Example
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Example
47/49Up-sampled
Example
48/49Smoothed
Example
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