Computer Vision and Graph-Based Representation

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Transcription:

Jean-Yves Ramel Romain Raveaux Laboratoire Informatique de Tours - FRANCE Computer Vision and Graph-Based Representation Presented by: Romain Raveaux

About me I

About me II

Recherche Partners ISRC 2011 LITIS Rouen LI Tours LORIA Nancy L3i La Rochelle Relations inter-laboratoires 3 séjours recherche 8 séminaires extérieurs Co-rédactions de projets ANR Co-encadrements de stagiaires Co-écritures d articles CVC Barcelona

Some colleagues

Content 1. Computer Vision and Graph-Based Representation 1. {pixel, interest point, region, primitive, shape} graph 2. Spatial relationship graph 2. Pattern Recognition problems 1. Classification 2. Indexing 3. Clustering

Aim of the talk - We want to illustrate the very particular graphs issued from computer vision techniques. - Noisy - Complex Attributes (continuous, numerical, symbolic, semantic, ) - Graph Size - What we won't talk about : - Graph for image segmentation (Normalized Cut Graph,...) - Graph for knowledge representation (Ontology, RDF,...)

Part 1 Computer Vision and Graph-Based Representation

Graph of pixels Pixels Edges The nodes of the graph The values (RGB, grey shades) [Morris, 1986] 0 255 0 0 255 0 255 255 0 128 0 Image 0 0 128 0 0 128 [Franco, 2003] Attributed graph Maximum spanning tree Expensive edge deletion Problem Graphs made of pixels are often too big to be analysed

Interest Point Graph

Region Adjacency Graph

Neighborghood graph

Region Adjacency Graph Impact of noise on Graph-Based Representation Herve Locteau : PhD 2008

Impact of noise on Graph-Based Representation =

Impact of noise on Graph-Based Representation

Region Adjacency Graph

Primitive, shape graphs Skeleton 3 0 Primitive 1 4 5 2 P 3 0 T P P T 4 1 5 2 T Shape Components composante occlusion voisinage inclusion 17

Skeleton Graph 18

Spatial relationship graph

Spatial relationship graph

Spatial relationship graph Bi dimensional Allen Algebra Egenhofer algebra

Visibility Graph Spatial relationship graph

Visibility Graph Spatial relationship graph

Image : Graph based respresentation Strongly attributed graphs Numerical vectors Symbolic information Complex structures From planar graph to complete graph Graph size From large to small : It depends on the description level Low level : One node = one pixel High level: One node = one object Graph corpus Large data set : one graph equal one image

IAM DB Please read the following paper : IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning

Pattern Recognition Classification (supervised) Clustering (Unsupervised) Indexing All these notions will be deeply explained by Nicolas Ragot in details.

What is pattern recognition? The assignment of a physical object or event to one of several prespecified categeries -- Duda & Hart A pattern is an object, process or event that can be given a name. A pattern class (or category) is a set of patterns sharing common attributes and usually originating from the same source. During recognition (or classification) given objects are assigned to prescribed classes. A classifier is a machine which performs classification.

Basic concepts Pattern y Hidden state y Y x x 1 2 x n - Cannot be directly measured. = x Feature vector - A vector of observations (measurements). - is a point in feature space. - Patterns with equal hidden state belong to the same class. x x X X Task - To design a classifer (decision rule) q : X Y which decides about a hidden state based on an onbservation.

Example height Task: jockey-hoopster recognition. weight x x 1 2 = x The set of hidden state is The feature space is Y X = { H, J} 2 = R Linear classifier: Training examples x 2 {( x, y1),,( x l, y 1 l y = H )} q( x) = H J if if ( w x) + b ( w x) + b < 0 0 y = J ( w x) + b = 0 x 1

Pattern Recognition

Pattern Recognition

Nearest Neighbor Search

Vector vs Graph Data structure Representational strength Fixed dimensionality Sensitivity to noise Efficient computational tools Pattern Recognition Structural Statistical symbolic data structure numeric feature vector Yes No No Yes Yes No No Yes

Graph recognition

Pattern Recognition When using graphs in pattern recognition the question turns often in a graph comparison problem? Are two graphs similar or not? How to compute a similarity measure for graphs? Any ideas?

Triangle inequality : Graph Comparison

Graph Comparison Distance (metric) : 1-2-3-4 Pseudo metric : 1-3-4 Similarity measure : s(x,y) = k d(x,y) Dissimilarity measure

Pattern Recognition When using graphs in pattern recognition the question turns often in a graph comparison problem? Are two graphs similar or not? How to compute a similarity measure for graphs? Any ideas? At least 2 solutions : Graph matching Graph embedding

Some clues : Graph Matching

Some clues : Graph Matching MCS : Stands for Maximum common subgraph

Bibliography Bibliography : IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning

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