Digital Bas-Relief from 3D Scenes

何 会 珍 2008-11-13

Tim Weyrich Assistant Professor

Dept. of Computer Science University College London

Connelly Barnes Graduate Student

Princeton Graphics Group Princeton University

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

Examples of bas-relief

Top: Ancient Greek, Assyrian relief. Below: Modern examples

Examples of high relief

high-relief of the cloister and a rotated view of it

Motivation

1.Given: Height-Data as Z = h(x,y)2.Want: Relief3.Need: Compressing Height-Range

original 3D model generated relief

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

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

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

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

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

bunny extracted silhouettes

sprrow extracted silhouettes

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

this algorithm linear algorithm

origin teapot silhouette

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

Poisson equation:

2 'h divg

2 22

2 2h

h h

x y

其中

' yxGG

divgx y

1 10

Results about different

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

Left : Increasing low frequencies. Right : Amplify high frequencies

Results:

Results:

Left: unmodified version. Right: emphasize the teapot

Results:

Original 3D model executed in wood

Results:

executed in marble executed in silver

Results:

Left: Scenes with high complexity Right: emphasizing depth discontinuities

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

Thank you!