Pointillist Halftoning Alejo Hausner CS Department University of New Hampshire

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Pointillist HalftoningAlejo HausnerCS
DepartmentUniversity of New Hampshire
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Color Reduction Problem

• Print continuous-tone images
• image colors gtgt device colors
• eg laser printer colors 2

Continuous tone
Fixed threshold
Random threshold
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Halftoning

• Spatial vs Color Resolution
• eye fuses dot patterns, sees color tones
• Ordered dither
• Bayer, Clustered-dot
• Error diffusion
• Floyd-Steinberg

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Halftoning
greyscale
ordered
clustered
Error diffusion
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Closest Color
R-G-B-W ramp
Closest Color
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Random Threshold
R-G-B-W ramp
Random Threshold
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Our Algorithm
R-G-B-W ramp
25 BFS 75 DFS
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Artists Halftone Random Dots

• BW dotsstippling

• Colored dotspointillism

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Outline

• Motivation why random-point halftone?
• Problem Statement
• Approach non-grid error diffusion
• Results
• Conclusion

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Why?

• Alias-free display devices
• scanned color prints moiré patterns
• CRT displays need antialising
• Poisson-disc dots noise replaces aliasing
• High-saturation printing
• CMYK color separation regular dot grid
• ink dots overlap

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Color Separation
Black
Cyan
Magenta
Yellow
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Commercial offset printing
Ink dots overlap ? loss of saturation
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Simulated Pointillism

• Pointillist art
• unmixed paint richer colors
• scintillatingeffect
• Seurat, Signac
• NPR filter

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Mosaics with Few Colors

• commercial tiles
• limited palette
• nearest-color alg?
• color banding!

Desired mosaic
Using only 27 colors
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Outline

• Motivation why random-point halftone?
• Problem Statement
• Approach non-grid error diffusion
• Results
• Conclusion

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The Challenge

• No regular grid
• Stippling random ink strokes
• Pointillism hand-placed paint dots
• Halftoning algs assume regular grid
• ordered dither dither matrix
• error diffusion scanline processing
• How to halftone random-point images?

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Problem Statement

• Given
• 1 dot (or stroke) positions
• 2 underlying image
• 3 discrete set of colors
• Output
• color for each dot
• Goal
• colored dots look like underlying image

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Outline

• Motivation why random-point halftone?
• Problem Statement
• Approach non-grid error diffusion
• Results
• Conclusion

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The Approach

• eg Floyd-Steinberg error diffusion
• well-researched
• random-looking dither
• Algorithm
• set pixel to nearest color
• add error to neighbors
• visit pixels in scanline order

spread error
7/16
5/16
1/16
3/16
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The Approach (2)

• Random-dot F-S
• nearest dot neighbors
• in what order?

• Floyd-Steinberg (F-S)
• pixel neighbors
• scanline order

• Dot-processing orders investigated
• get nearest-neighbor graph, traverse
• depth-first
• breadth first
• error-driven (choose from frontier dots)
• hybrids

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Original Dots
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Points (dot centers)
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Dots and Neighbors (Delaunay Triangulation)
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Pixel Graphs
(Pixels have neighbors too)
4-neighbors
diagonal neighbors
8-neighbors
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The Algorithm

• Visit Dots in some order
• for each dot
• set to closest color in set
• (color changed ? error)
• add error to neighbors

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Visit dots in What order?

• dots nodes in graph
• visit dots traverse graph
• depth-first graph traversal?
• breadth-first?
• other?

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Depth-first graph traversal

• Stack stores advancing front
• push node on stack
• while (stack not empty) node ? top of
  stack process node (color it) for each
  neighbor of node push neighbor on
  stack

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Breadth-first graph traversal

• Queue stores advancing front
• push node on queue
• while (queue not empty) node lt head of
  queue process node for each neighbor of
  node append neighbor on queue

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Error-driven traversal

• Front set of candidate dots
• add node to front
• while (front not empty) choose node from
  front (min, max, or median error)
  process node for each neighbor of node
  add neighbor to front

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Gray Ramp Test (8-neighbor graph)
Gray ramp
Depth-first(DFS)
Breadth-first(BFS)
25 BFS 75 DFS
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Use Hybrid Traversal

• Error-driven traversal looks horrible!
• too ugly to show
• Breadth-first and Depth-first show artifacts
• Hybrid
• queue of pixels, random variable x (0 ? x ?
  1)
• if (x ? 1/4) get pixel from head of queue
• if (x gt 1/4) get pixel from tail of queue

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Outline

• Motivation why random-point halftone?
• Problem Statement
• Approach non-grid error diffusion
• Results
• Conclusion

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Pointillism simulation

• Restricted set of colors
• Dots are paint strokes
• Assume dot positions are known

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Seurats Pointillism
Original
Simulation
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Luces Pointillism
Original
Simulation
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Color Stippling
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Application Color Printing

• 4-color offset printing
• dots overlap
• loss of saturation
• random-dot halftoning color stippling
• dots dont overlap
• brighter colors

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Comparison
Standard 4-color printing
Error diffusion on adjacency graph
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Comparison
Sharper, more saturated
4-color printing
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Restricted Mosaic

• Simulated tiles
• tile color underlying image
• many colors possible
• Actual tiles
• limited color choice
• must use halftone
• Dots are square!
• use area voronoi diagram to get graph

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Restricted-color Mosaic
Continuous color
27 tile colors
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Better-chosen colors
2000 tile colors
8 tile colors
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Conclusion

• Random-dot halftone
• error diffusion on adjacency graph
• Applications
• simulated pointillism
• improved offset printing
• arbitrary dot shapes

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Future Work

• Pointillism
• better paint stroke placement
• artists didnt place them randomly
• Color printing
• edge emphasis non-round dots
• Ordered dither?
• what is the Bayer matrix for a graph?