Clustering unorganized 3D point clouds

1
Clustering unorganized 3D point clouds for
robotic vision a study of different paradigms
François-Xavier Jollois and Nicolas Loménie UFR
Mathématiques et Informatique, CRIP5 Université
Paris Descartes Prenom.Nom_at_math-info.univ-paris5.f
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1. Context
3.c Method 3 Data Mining
Computer Vision and 3D scene understanding. 2
different types of acquisition considered
optical stereoscopic camera and laser range
camera.
A. Optical stereoscopic camera

• Home made outdoor scene database
• Data with no structure
• Object with no model

B. Laser Range Camera or Structured Light Camera
6. Preliminary Results
Method 1 Eps 0.1 Max_Iter 25
Method 2 Specific morphological heuristic set
Method 3
Method 1 Eps 0.1 Max_Iter 25
Method 2 Specific morphological heuristic set
Method 3
Database 1
Scene 020 9 350 pts
Scene 121 9 170 pts
3 objects / 2 s
5 objects / 3 s
20 objects
5 objects / 10 s
20 objects
Scene 022 7 115 pts
Scene 125 8 274 pts
2. Data
3 objects / 2 s
4 objects / 3 s
20 objects
20 objects
Scene 074 8 140 pts
Scene 174 7 662 pts

• A. Database 1 / Real Condition Stereoscopic
  Outdoor Scene
• Set of disparity map images 152x114 and 768x576
  (from Triclops camera, PointGray Inc. )
• We filtered out points farther than 7 meters from
  camera. For the 152x114 images, it results about
  10 000 points to process.

6 objects / 7 s
20 objects
6 objects / 4 s
20 objects
2 objects / 1 s
Scene 077 7413 pts
Scene 175 6 387 pts
Homemade database in collaboration with LAAS-CNRS
lab- Toulouse- France and EADS- Paris - France

• B. Database 2 / Laser Range Toy Indoor Scene with
  ground truth
• Set of disparity map images 512x512 (from Laser
  range device)
• For the full format 512x512 images, it results
  about 200 000 points to process. We process also
  with a decimation of 16, resulting with 128x128
  images and about 10 000 points to process.

5 objects / 5 s
20 objects
2 objects / 1 s
20 objects
Database 2
Method 1 Eps 0.1 Max_Iter 25
Method 1 Eps 0.1 Max_Iter 50
Method 3
Indoor toy USF Range Image Database
http//marathon.csee.usf.edu/range/DataBase.html
Low resolution
Scene 0 11 299 pts
3. Methods
We compared three different paradigms of
clustering method 1 and 2 are more inspired by
a pattern recognition and image analysis
background while method 3 is more inspired by
data mining methodologies. Various criteria and
strategies to choose the right number of classes
are also competing on the specific computer
vision issues described above.
4 objects /7 s
3 objects / 7 s
Scene 19 12 446 pts
2 objects / 2 s
2 objects / 2 s
3.a. Method 1 Exponential Fuzzy K-Means
BEZ81GAT89
Scene 21 13 208 pts
A. Principle  Nuées Dynamiques

• Algorithm
• ISODATA with convergence parameters
• number_of_iterations
• epsilon

7 objects / 35 s
7 objects / 39 s

• Implementation
• Fuzzy K-Means optimization of J(UV)) with
• Distance exponential de
• Prototypes centroids Vj andfuzzy covariance
  matrix Fj

High resolution
Method 1 Eps 0.1 Max_Iter 25
Method 1 Eps 0.1 Max_Iter 50
Method 3
Method 2 planarity test with RANSAC
Scene 0 182 246 pts
2 objects / 37 s
4 objects / 180 s
B. Choice of the number of classes K

• Incremental Partition from k2 tok20 classes
  with computation of the Average Density
  Partition Criterion ADP(k)?
• Stop as soon as the ADP(m) criterion decreases

Scene 19 199 790 pts
2 objects / 30 s
2 objects / 30 s
Scene 21 211 133 pts
4 objects / 108 s
4 objects / 110 s
3.b. Method 2 Expert Exponential Fuzzy K-Means
LOM01 LOM04
5. Conclusions and perspectives

• A. Declarative approach (see Expert Systems)
• inference engine EFKM algorithm of method 1
• knowledge base application-driven heuristic set
  (morphological, geometrical, metrical)
• fact base point set

Bibliography
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(ICPR'00), Barcelona, Spain, Septembre
2000 LOM04 N. Loménie, A generic methodology
for partitioning unorganised 3D point clouds for
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Banfield, J. D. and Raftery, A. E. (1993),
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• B. Various strategy (see Backward/ Forward sheme
  of Expert Systems) to apply the rules.
• One is proposed here
• Others have been tested for real-time application