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
http://store.got3d.com/
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