diffusion curves
Download
Skip this Video
Download Presentation
Diffusion Curves

Loading in 2 Seconds...

play fullscreen
1 / 49

Diffusion Curves - PowerPoint PPT Presentation


  • 161 Views
  • Uploaded on

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”.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Diffusion Curves' - hao


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
diffusion curves

Diffusion Curves

Dr. Scott Schaefer

diffusion curves1
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
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
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
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 simplified1
Implementation (Simplified)
  • Colored pixels are constraints
  • Find a harmonic function satisfying constraints
    • Harmonic function has Laplacian zero everywhere
implementation simplified2
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 simplified3
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 simplified4
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
problem1
Problem

Final Result

problem2
Problem

100 Iterations

problem3
Problem

200 Iterations

problem4
Problem

400 Iterations

problem5
Problem

800 Iterations

problem6
Problem

1600 Iterations

problem7
Problem

6400 Iterations

problem8
Problem

Infinity Iterations

simple multi grid
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
Example

Original 512x512

example1
Example

Down-sampled 256x256

example2
Example

Down-sampled 128x128

example3
Example

Down-sampled 64x64

example4
Example

Down-sampled 32x32

example5
Example

Down-sampled 16x16

example6
Example

Down-sampled 8x8

example7
Example

Down-sampled 4x4

example8
Example

Down-sampled 2x2

example9
Example

Down-sampled 1x1

example10
Example

Up-sampled

example11
Example

Smoothed

example12
Example

Up-sampled

example13
Example

Smoothed

example14
Example

Up-sampled

example15
Example

Smoothed

example16
Example

Up-sampled

example17
Example

Smoothed

example18
Example

Up-sampled

example19
Example

Smoothed

example20
Example

Up-sampled

example21
Example

Smoothed

example22
Example

Up-sampled

example23
Example

Smoothed

example24
Example

Up-sampled

example25
Example

Smoothed

example26
Example

Up-sampled

example27
Example

Smoothed

ad