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

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

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

Concept lattice: Example Context Université de la Rochelle

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

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

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

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)

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 ? Université de la Rochelle

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

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

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

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}

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