1. Using the Concept Lattice for Graphic Understanding
Laboratoire d ’Informatique et d ’Imagerie Industrielle
Département Informatique - Pôle Sciences et Technologies - Université de La Rochelle
Using the Concept Lattice for Graphic Understanding
M. Al-hajj, K. Bertet, J. Gay, J-M. Ogier
L3I - University of La Rochelle - France
Université de la Rochelle

2. Description of the problem
Knowledge representation:
Prototypes basis
Concept lattice
Noisy object recognition:
Noisy object
one prototype
concept lattice
Université de la Rochelle

3. Concept lattice: Example
G (prototypes)
Concept:
(12,abd)
(123,bd)
(12,abd) C (123,bd)
M (attributes)
Université de la Rochelle

4. Concept lattice: Example
Context
Université de la Rochelle

5. Meaning of a concept (A,B)
Prototypes A
Attributes B
Concept (A,B)
validated attributes B’:
 (A,B): smallest concept containing B ’
 B \ B’: inferred attributes
 A: candidates prototypes
Université de la Rochelle

6. Relation between two concepts
Reduction:
validated attributes 
candidates prototypes 
Validation:
validated attributes
candidates prototypes
(A1,B1)
(A,B)
A  A1 et B  B1
Université de la Rochelle

7. Recognition steps (A’,B’ ) Final step: one candidate prototype
Basic step:
(un)validated attributes inferred attributes
(A1,B1 )
(A,B )
Initial step:
no validated attributes
G candidate prototypes
(G,)
Université de la Rochelle

8. 4 basic steps In: (A,B)  Out: (A1,B1)
Global validation : (A1,B1) > (A,B)
Local validation : (A1,B1)  (A,B)
Global reduction : (A1,B1) < (A,B)
Local reduction : (A1,B1)  (A,B)

9. Graphic recognition 1- Knowledge representation
by a concept lattice from a context
2- Noisy object recogntion
by a sequence of validation/reduction steps through the lattice
Which context ?
Which steps ?
How to select
attributes ?
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10. Fourrier-Melin Transform,
Image analysis
Two different image analysis techniques :
statistical analysis:
image x  signature (x1,…, xm)
structural analysis
Zernique moments,
Fourrier-Melin Transform,
……..
Université de la Rochelle

11. Knowledge representation
Set of prototypes
signatures
Sampling of the values in disjoint intervals
Context
Concept lattice
co-atomistique

12. Attributes selection function
 Iik (xi ) = membership degree of xi to Iik
Selection function (bound): to validate the interval Iik when  Iik (xi ) > bound
 Iik (xi )
Iik
bound xi
L3I - Pôle Sciences et Technologies - Université de La Rochelle

13. Graphic recogntion In: a signature (x1,…, xm) (A,B) = ( ,M)
seuil = 100
while |A|>2
(A,B) = global validation ((A,B))
seuil = seuil - 10
if |A| = 0
(A,B) = local reduction ((A,B))
Out: A={a}

14. Conclusion
Experimental study with the statistic descriptors in progress
Strutural approach to study
Agorithmical study: on-line generation of the basic steps through the lattice without generating the whole lattice (exponential)
 using an implicationnal system