Frank Nielsen and Nicolas de Mauroy

On the Precision of Textures

MVA 2000: 31-34

IEICE 2001 (Special issue)

500 Kb data 20 Kb data

Camera model

（probing device)

Two models of pinhole perspective cameras.

Other projection models may be simulated by the computer :

( orthographic, scaled orthographic )

Precision

Intuitive meaning : the size of the

projection of a pixel of the camera on

the objet

Cover an object with a precision

• All the triangles must be entirely

covered.

• The pictures must have a guaranteed

minimum precision.

Object covering algorithm (heuristics)

• compute a set of cameras.

• compute the triangles visible from each

camera within the given precision.

• select a subset of cameras that covers the

largest possible part of the object.

• try to find a camera for the not yet covered

triangles.

experiments

• naïve choice of the original set of

cameras usually covers around 98% of

an object.

• an object is usually covered in around

30 pictures.

dinosaur : 4300 triangles, 31pictures, 99.8%

dog: 4707 triangles, 32 pictures, 99.1%

Other applications of the

camera selection algorithm

• illumination of a scene.

• position of supervision cameras.

• validation of data obtained by range

finding.

• compression.

Previous methods of

object simplification [ Cohen Olano Manocha Siggraph 98 ]

• separation of the object into different

patches.

• simplification of the geometry and of the

texture INSIDE each patch.

Does not allow topological changes.

Important restrictions on simplification.

Our algorithm

• simplify the geometry without

topological restrictions within the given

precision.

• find a set of cameras that cover the

simplified objet within the given

precision.

• take pictures of the original object with

this set of cameras.

Object simplification

Triangle simplification

• must guarantee a bound on the error.

• can change the topology.

Modified edge collapsing [[ Garland Heckbert SIGGRAPH 97 ] ]

Checking the vertices and edges of

each triangle

Precision of the simplification

• simplify the geometry within a precision.

• capture the texture with the same

precision ( with constraints on the incidence angle ).

range of use of the simplification

equivalence with the original model

( related to perception )

A simplification Original object

( 8251 triangles 200 Kb of texture )

Simplification

( 2238 triangles 71 Kb of texture )

Level-of-details hierarchy

From up-left to down-right

8251 triangles 200 Kb of texture

2925 triangles 120 Kb of texture

2238 triangles 71 Kb of texture

1567 triangles 33 Kb of texture

1034 triangles 18 Kb of texture

425 triangles 6 Kb texture

Conclusions

precision

• investigated both theoretical and heuristic

aspects of implementation.

• controls the quantity of information required for a

given range.

object simplification algorithm

• possibility of various inputs.

• no topological constraint on the geometry

simplification.

http://www.sonycsl.co.jp/person/nielsen/PT/precisiontexture

s/precisiontextures.html

@article{NIELSENFrank:2001-12-01,

author="NIELSEN, Frank and MAUROY, Nicolas De",

title="On the Precision of Textures(Special Issue on Machine Vision Applications)",

journal="IEICE transactions on information and systems", ISSN="09168532",

publisher="The Institute of Electronics, Information and Communication Engineers",

year="2001",

month="dec",

volume="84",

number="12",

pages="1684-1689",

URL="http://ci.nii.ac.jp/naid/110003210451/en/", DOI="", }