Multi-Class Blue Noise SamplingMulti-Class Blue Noise Sampling

Li-Yi Wei

魏立一

Microsoft Research

Blue noise distributionBlue noise distribution

random & uniform

applicationssampling

stippling

meshing

texturing

object placement[Turk 1992][Balzer et al. 2009][Ostromoukhov et al. 2004]

Previous workPrevious work

half-toning[Ulichney 1986; Wang and Parker 1999; Ostromoukhov 2001; Zhou and Fang 2003; Pang et al.

2008; Chang et al. 2009]

dart throwing[Cook 1986; Mitchell 1987; McCool and Fiume 1992; Jones 2006; Dunbar and Humphreys 2006;

White et al. 2007; Wei 2008; Fu and Zhou 2008; Cline et al. 2009; Gamito and Maddock 2010]

relaxation[Lloyd 1982; Turk 1992; Balzer et al. 2009; Tung et al. 2010; Liu et al. 2010; Levy and Liu 2010]

tiling[Cohen et al. 2003; Ostromoukhov et al. 2004; Kopf et al. 2006; Lagae and Dutre 2006;

Ostromoukhov 2007]

Prior art mostly for 1 sample class Prior art mostly for 1 sample class

scenarios with multi-class samples

sampling(retina cells)

stippling(pointillism)

texturing(flowers)

Apply 1 class blue noise to > 1 classUniform per classApply 1 class blue noise to > 1 classUniform per class

class 0 class 1total set

O OX

Apply 1 class blue noise to > 1 classUniform total setApply 1 class blue noise to > 1 classUniform total set

total set class 0 class 1

X XO

Multi-class blue noise samplingMulti-class blue noise sampling

uniform & random for each class & their unions

class 0 class 1total set

O OO

Background of blue noiseBackground of blue noise

random & uniform

controlled by spacing r r

r

1

r -1

power spectrum

anisotropy

r -1

radial mean

r

Dart throwing [Dippe and Wold 1985; Cook 1986]Dart throwing [Dippe and Wold 1985; Cook 1986]

loop:

random sample

conflict check

indirectly specify r through sample count N

given a set of N sample

loop:

Voronoi for each sample

move sample to centroid

Relaxation[Lloyd 1982]Relaxation[Lloyd 1982]

Core idea for multi-class blue noiseCore idea for multi-class blue noise

replace scalar spacing r by a matrix r

r00 r01 r02

r10 r11 r12

r20 r21 r22

c0 c1 c2

c0

c1

c2

r00

r11

r01

Generating multi-class blue noiseGenerating multi-class blue noise

hard disk sampling

control sample spacing r

(like dart throwing)

soft disk sampling

control sample count N

(like Lloyd relaxation)

Multi-class hard disk samplingMulti-class hard disk sampling

like 1-class dart throwing, but

r matrix for conflict check

consistent fill rate 1:4:16

0 1 2 2 1 2 2 0 1 2 2 1 2 2

may kill existing samples

c0 c1 c2c0

c1

c2

0.40 0.18 0.090.18 0.20 0.090.09 0.09 0.10

Soft disk: single classSoft disk: single class

Gaussian blob per sample

minimize max(E) → uniform distribution

Ss

s ssE'

,' )()( r

Soft disk: multi classSoft disk: multi class

minimize max(E) → uniform distribution

Ss

sss ssE'

)',(,' )()(

R/G/B: E(c0 /c1 /c2)

)',()',( ssrss

Multi-class soft disk samplingMulti-class soft disk sampling

~ best candidate dart throwing [Mitchell 1987]

loop for each trial:

random k samples

pick one with min max(E)

X Lloyd relaxation

stuck in multi-class setting

Build r matrixBuild r matrix

diagonal entries {rii}i=0:c-1 given

how to compute off-diagonal entries {rij}i≠j?

(symmetry: rij = rji )

see paperr00 r01 r02 r03

r10 r11 r12 r13

r20 r21 r22 r23

r30 r31 r32 r33

Analysis [Lagae and Dutre 2008]Analysis [Lagae and Dutre 2008]

spatial uniformity σ

ideal σ in [0.65 0.85]; our σ in [0.65 0.70]

soft disk sampling has larger σ

total set

class 1

class 0

class 2

Analysis [Lagae and Dutre 2008]Analysis [Lagae and Dutre 2008]

spectral analysis

(good quality; radial mean diff from 1-class)

power spectrum radial mean anisotropy

- 1-class- multi-class

Object placement: uniformObject placement: uniform

Object placement: uniformObject placement: uniform

Object placement: more classesObject placement: more classes

Object placement: adaptiveObject placement: adaptive

Color stipplingColor stippling

RGBCMYB dots

input

zoneplatesin(x2+y2)

Sensor layoutSensor layout

Bayer mosaic Penrose pixel our method

Discrete layoutDiscrete layout

Bayer mosaic random soft disk

noisy

TradeoffTradeoff

Hard disk sampling

O control sample spacing

X control sample count

O continuous space

X discrete space

X less uniform

O faster

Soft disk sampling

X control sample spacing

O control sample count

O continuous space

O discrete space

O more uniform

X slower

Future workFuture work

applications & extensions

3D or higher dimensions

surfaces or other non-Euclidean domains

anisotropy

acceleration

tiling

parallelization

[Bowers et al. 2010]aniso [Li et al. 2010]isotropic

AcknowledgementAcknowledgement

Yin Li

Kun Zhou

Xin Tong

Eric Stollnitz

Jason Fondran

http://www.gif-favicon.com/

Brandon Lloyd

Bill Baxter

Naga Govindaraju

John Manferdelli

Reviewers

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