Clustering de nuages de points stroscopiques : une comparaison de diffrents paradigmes

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Clustering de nuages de points stéréoscopiques
une comparaison de différents paradigmes
François-Xavier Jollois and Nicolas Loménie UFR
Mathématiques et Informatique, CRIP5 Université
Paris Descartes francois-xavier.jollois_at_univ-paris
5.fr nicolas.lomenie_at_math-info.univ-paris5.fr
François-Xavier Jollois and Nicolas Loménie UFR
Mathématiques et Informatique, CRIP5 Université
Paris Descartes francois-xavier.jollois_at_univ-paris
5.fr nicolas.lomenie_at_math-info.univ-paris5.fr
François-Xavier Jollois and Nicolas Loménie UFR
Mathématiques et Informatique, CRIP5 Université
Paris Descartes francois-xavier.jollois_at_univ-pari
s5.fr nicolas.lomenie_at_math-info.univ-paris5.fr
SFC 2007 7 Septembre - Paris
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Context

• No structure
• No model

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Context
Global strategy
Focus on
Statistical Global Clustering

• Structural Local Analysis of Clusters
• Heuristic Set

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Context
Database 1 Optical stereoscopic camera Outdoor
scene data set of disparity map images 152x114
and 768x576 (from Triclops camera, PointGray Inc.
) -gt We filter out points farther than 7
meters from camera. For the 152x114 images, it
results about 10 000 points to process.
Homemade database in collaboration with LAAS-CNRS
lab- Toulouse- France and EADS- Paris - France
Database 2 Laser Range Camera or Structured
Light Camera Indoor toy scene data set of
disparity map images 512x512 (from Laser range
device) -gt 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.
Indoor toy USF Range Image Database
http//marathon.csee.usf.edu/range/DataBase.htm
Homemade database in collaboration with LAAS-CNRS
lab- Toulouse- France and EADS- Paris - France
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Objective
Pattern recognition and computer vision paradigms
(N. Loménie's world)
Method 1 - Exponential Fuzzy K-Means
GathGeva89 Lom0104 Average Density
Partition Criteria by stopping at the first local
maximum from 2 objects to 15 objects. - Basic
Language C on a Linux OS, 2Go RAM, Intel(R)
Pentium(R) 4 CPU 3.40GHz - No optimization
either in Code, or Initialization or Partitioning
Strategy - C time_t function (returns only
seconds) for time consumption
Method 2 - Method 1 Application-driven
Morphological Criteria to carry on the
decomposition scheme of method 1
Clustering community paradigms (F.X. Jollois's
world)
Method 3 - Gaussian Mixture Model
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Methods
Method 1 Exponential Fuzzy K-Means
Nuées Dynamiques (Diday)
ISODATAAlgorithm
Fuzzy K-means
- number of points - density of the cluster -
shape of the cluster
GathGeva89
- convergence property
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Methods
Exponential Fuzzy K-Means (EFKM)
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Methods
Optimal number K of classes ?
Numerical criterion Average Density
Partition (ADP) ?
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Methods
Method 1
Method 2
Numerical criterion ADP(K)
KK1
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Methods
Final point of view of Pattern Recognition and
Computer Vision design of a declarative
approach of the problem with a statistical
classification inference engine (method 1) and a
morphological rule base controlling this engine
(method 2)
Data base / Point sets
Rule base / Morphological heuristics
Inference Engine / EFKM algorithm
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Methods
Method 3 Mixture Model approach

• Classical and powerful approach
• Maximizing the likelihood of the model in respect
  to the data
• Gaussian mixture model with continuous data
• Parameters
• Proportion
• Mean vector
• Variance-covariance matrix

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Methods
Algorithm

• Use of EM algorithm with two steps
• Expectation
• Maximisation
• Very popular for parameters estimations
• Algorithm
• Parameters initialisation
• Expectation step compute the posterior
  probabilities
• Maximisation step compute the parameters for
  each cluster.
• Repeat E-step and M-step until convergence
• Partition infered from parameters with MAP
  principle
• Use of MIXMOD

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Methods
Number of clusters

• Bayesian framework
• Different existing information criteria
• AIC (Akaike Information Criterion), AIC3, ICL
• BIC (Bayesian Information Criterion)
• Choose of BIC
• Based on an approximation of the integrated
  likelihood
• Penalizes the model with its complexity
• Number of free parameters
• Defined by

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Method 2 Specific morphological heuristic set
Method 3 Gaussian mixture model
Results
Results
Method 1 Eps 0.1 Max_Iter 25
Database 1
Scene 020 9 350 pts
14 objects
3 objects / 2 s
5 objects / 3 s
Scene 022 7 115 pts
3 objects / 2 s
5 objects
Scene 074 8 140 pts
6 objects / 7 s
4 objects
Scene 077 7413 pts
12 objects
5 objects / 5 s
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Method 2 Specific morphological heuristic set
Method 3 Gaussian mixture model
Results
Method 1 Eps 0.1 Max_Iter 25
Scene 121 9 170 pts
5 objects / 10 s
3 objects
Scene 125 8 274 pts
4 objects / 3 s
9 objects
Scene 174 7 662 pts
2 objects / 1 s
6 objects / 4 s
8 objects
Scene 175 6 387 pts
6 objects
2 objects / 1 s
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Method 1 Eps 0.1 Max_Iter 25
Method 1 Eps 0.1 Max_Iter 50
Method 3 Gaussian mixture model
Results
Database 2
Low resolution
Scene 0 11 299 pts
4 objects /7 s
3 objects / 7 s
16 objects
Scene 19 12 446 pts
2 objects / 2 s
2 objects / 2 s
5 objects
Scene 21 13 208 pts
7 objects / 35 s
7 objects / 39 s
12 objects
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Results
Method 2 planarity test with RANSAC
Method 3
Method 1 Eps 0.1 Max_Iter 25
Method 1 Eps 0.1 Max_Iter 50
High resolution
Scene 0 182 246 pts
2 objects / 37 s
4 objects / 180 s
6 objects
Scene 19 199 790 pts
2 objects / 30 s
2 objects / 30 s
12 objects
Scene 21 211 133 pts
4 objects / 108 s
4 objects / 110 s
3 objects
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Conclusions Perspectives

• Applied perspective Exploratory mode for
  real-time autonomous robotic vision

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