digital bas-relief from 3d scenes 何 会 珍 2008-11-13
TRANSCRIPT
![Page 1: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/1.jpg)
Digital Bas-Relief from 3D Scenes
何 会 珍 2008-11-13
![Page 2: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/2.jpg)
Tim Weyrich Assistant Professor
Dept. of Computer Science University College London
Connelly Barnes Graduate Student
Princeton Graphics Group Princeton University
![Page 3: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/3.jpg)
Szymon Rusinkiewicz Associate Professor
Department of Computer Science Princeton University
Adam Finkelstein Associate Professor
Department of Computer Science Princeton University
Jia Deng Ph.D. Student Computer Science Department Princeton University
![Page 4: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/4.jpg)
Examples of bas-relief
Top: Ancient Greek, Assyrian relief. Below: Modern examples
![Page 5: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/5.jpg)
Examples of high relief
high-relief of the cloister and a rotated view of it
![Page 6: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/6.jpg)
Motivation
1.Given: Height-Data as Z = h(x,y)2.Want: Relief3.Need: Compressing Height-Range
original 3D model generated relief
![Page 7: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/7.jpg)
Related Work
Automatic Generation Of Bas- And High-Reliefs;Cignoni, Montani, Scopigno; Journal of Graphics Tools;1997.
Gradient Domain High Dynamic Range CompressionFattal, R., Lischinski, D., Werman, M. 2002ACM Transactions on Graphics (SIGGRAPH ’02)
Numerous Works On HDR Image Compression
![Page 8: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/8.jpg)
Bas-Relief
1. Depth : achieved by perspective foreshortening2. Object Order: preserve depth order of overlapping objects3. Compression: the background are flatter than those in the foreground4. Discontinuities: depth discontinuities in the relief become smaller5. Steps: small step along the object outline6. Materials: wood, clay, stucco, metal, stone, ivory, bone, ice
![Page 9: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/9.jpg)
Main Idea
• Transforms the input 3D scene into a regularly sampled height field• Compression takes place in Gradient Domain• Integration to recover a height field• Cignoni : Linear Scaling important Features are lost
origin Linear Scaling Our algorithm
![Page 10: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/10.jpg)
Algorithm Workflow
GradientGradient
ExtractionExtraction
Fix the Fix the gradient gradient directiondirection
Extracting Extracting silhouettessilhouettes
CompressCompressGradient Gradient magtitudemagtitude
IntegrationIntegration
( , )h x yxh
yh
'( , )s x y'( , )h x y
( , )V x y
vsil
![Page 11: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/11.jpg)
1.Retrieving depth values: perspective foreshortening
2.Gradient Extraction: forward difference to extract gradients
3.Why Fix the gradient direction? preserve shapes visible
4. silhouettes: contribute as overly large gradients
5. How to extract silhouettes || ( , ) ||h x y vsil
![Page 12: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/12.jpg)
bunny extracted silhouettes
sprrow extracted silhouettes
![Page 13: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/13.jpg)
6.Attenuate gradient magtitude nonlinear compression function C to the gradient magnitude
(|| ( , )||),0 || ( , )||0, || ( , )||( , ) {C h x y h x y VsilVsil h x ys x y
1( ) log(1 ), 0C x x
[0.5,10]a
![Page 14: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/14.jpg)
this algorithm linear algorithm
origin teapot silhouette
![Page 15: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/15.jpg)
7.Integration: optimization process
hh'(x,y) = argmin F( h,g') dxdy
2 2 2( , ') || h-g'|| ( ' ) ( ' )
'( , ) ( , )* ( , )
x y
h hF h g g g
x y
g x y s x y V x y
其中
Variational Principle
Euler-Lagrange equation
x y
F d F d F0
h dx h dx h
![Page 16: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/16.jpg)
Poisson equation:
2 'h divg
2 22
2 2h
h h
x y
其中
' yxGG
divgx y
![Page 17: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/17.jpg)
1 10
Results about different
![Page 18: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/18.jpg)
8.Artistic Controls: decompose the gradient field '( , )g x y
1
1
~'
01
( )
, {1,... },
* , '
k k k
k k k
n
k k nk
l D l
d l l k n
g a d l l g
![Page 19: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/19.jpg)
Left : Increasing low frequencies. Right : Amplify high frequencies
Results:
![Page 20: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/20.jpg)
Results:
Left: unmodified version. Right: emphasize the teapot
![Page 21: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/21.jpg)
Results:
Original 3D model executed in wood
![Page 22: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/22.jpg)
Results:
executed in marble executed in silver
![Page 23: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/23.jpg)
Results:
Left: Scenes with high complexity Right: emphasizing depth discontinuities
![Page 24: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/24.jpg)
Future Work1.Other shapes: Creation of alto-relievo2.Explore material properties into the algorithm3. Using normal as input
Top: Photograph of a pine cone, and its normal field Bottom: Relief after converting normals to gradients
![Page 25: Digital Bas-Relief from 3D Scenes 何 会 珍 2008-11-13](https://reader038.vdocuments.pub/reader038/viewer/2022102718/56649d1f5503460f949f3557/html5/thumbnails/25.jpg)
Thank you!