The document presents an algorithm for covering 3D objects with a set of camera views at a specified precision level. The algorithm first computes an initial set of camera views to cover the object's triangles. It then selects a subset of cameras that maximally covers the object and attempts to add cameras to cover remaining triangles. Experiments show the algorithm can cover test objects like a dinosaur and dog with 30-35 views at 99-99.8% coverage. The algorithm is also applicable to illumination, camera placement, range data validation, and compression.

1. Frank Nielsen and Nicolas de Mauroy
On the Precision of Textures
MVA 2000: 31-34
IEICE 2001 (Special issue)
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20 Kb data

2. Camera model
（probing device)
Two models of pinhole perspective cameras.
Other projection models may be simulated by the computer :
( orthographic, scaled orthographic )

3. Precision
Intuitive meaning : the size of the
projection of a pixel of the camera on
the objet

4. Cover an object with a precision
• All the triangles must be entirely
covered.
• The pictures must have a guaranteed
minimum precision.

5. 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.

6. 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%

7. Other applications of the
camera selection algorithm
• illumination of a scene.
• position of supervision cameras.
• validation of data obtained by range
finding.
• compression.

8. 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.

9. 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.

10. Object simplification

11. Triangle simplification
• must guarantee a bound on the error.
• can change the topology.
Modified edge collapsing
[[ Garland Heckbert SIGGRAPH 97 ] ]

12. Checking the vertices and edges of
each triangle

13. 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 )

14. A simplification
Original object
( 8251 triangles 200 Kb of texture )
Simplification
( 2238 triangles 71 Kb of texture )

15. 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

16. 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.

17. 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="", }