1 dr. scott schaefer diffusion curves. 2/38 diffusion curves vector graphics-based representation...
DESCRIPTION
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 3/49 Image taken from “Diffusion Curves: A Vector Representation for Smooth-Shaded Images”TRANSCRIPT
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1
Dr. Scott Schaefer
Diffusion Curves
![Page 2: 1 Dr. Scott Schaefer Diffusion Curves. 2/38 Diffusion Curves Vector graphics-based representation for 2D images Images are piecewise smooth with discontinuities](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1add7f8b9ab05997570a/html5/thumbnails/2.jpg)
2/38
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”
![Page 3: 1 Dr. Scott Schaefer Diffusion Curves. 2/38 Diffusion Curves Vector graphics-based representation for 2D images Images are piecewise smooth with discontinuities](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1add7f8b9ab05997570a/html5/thumbnails/3.jpg)
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”
![Page 4: 1 Dr. Scott Schaefer Diffusion Curves. 2/38 Diffusion Curves Vector graphics-based representation for 2D images Images are piecewise smooth with discontinuities](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1add7f8b9ab05997570a/html5/thumbnails/4.jpg)
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”
![Page 5: 1 Dr. Scott Schaefer Diffusion Curves. 2/38 Diffusion Curves Vector graphics-based representation for 2D images Images are piecewise smooth with discontinuities](https://reader035.vdocuments.us/reader035/viewer/2022070605/5a4d1add7f8b9ab05997570a/html5/thumbnails/5.jpg)
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
5/49
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Implementation (Simplified)
Colored pixels are constraints Find a harmonic function satisfying
constraintsHarmonic function has Laplacian zero
everywhere
6/49
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Implementation (Simplified)
Colored pixels are constraints Find a harmonic function satisfying
constraintsHarmonic function has Laplacian zero
everywhere
7/49
-4
1
1
1
1
0 0
0 0
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Implementation (Simplified)
Colored pixels are constraints Find a harmonic function satisfying
constraintsHarmonic function has Laplacian zero
everywhereEach value is average of
its neighbors
8/49
-4
1
1
1
1
0 0
0 0
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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
9/49
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Problem
10/49
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Problem
11/49Final Result
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Problem
12/49100 Iterations
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Problem
13/49200 Iterations
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Problem
14/49400 Iterations
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Problem
15/49800 Iterations
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Problem
16/491600 Iterations
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Problem
17/496400 Iterations
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Problem
18/49Infinity Iterations
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Problem
19/49
256
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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
average of its neighbors from last iteration
20/49
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Example
21/49Original 512x512
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Example
22/49Down-sampled 256x256
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Example
23/49Down-sampled 128x128
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Example
24/49Down-sampled 64x64
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Example
25/49Down-sampled 32x32
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Example
26/49Down-sampled 16x16
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Example
27/49Down-sampled 8x8
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Example
28/49Down-sampled 4x4
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Example
29/49Down-sampled 2x2
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Example
30/49Down-sampled 1x1
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Example
31/49Up-sampled
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Example
32/49Smoothed
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Example
33/49Up-sampled
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Example
34/49Smoothed
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Example
35/49Up-sampled
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Example
36/49Smoothed
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Example
37/49Up-sampled
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Example
38/49Smoothed
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Example
39/49Up-sampled
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Example
40/49Smoothed
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Example
41/49Up-sampled
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Example
42/49Smoothed
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Example
43/49Up-sampled
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Example
44/49Smoothed
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Example
45/49Up-sampled
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Example
46/49Smoothed
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Example
47/49Up-sampled
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Example
48/49Smoothed
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Example
49/49