A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Structural Matching by Discrete Relaxation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Structural Matching in Computer Vision Using Probabilistic Relaxation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Matching and Object Recognition Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shock-Based Indexing into Large Shape Databases
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
K-means clustering via principal component analysis
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Solving Markov Random Fields using Second Order Cone Programming Relaxations
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Skeletal Shape Abstraction from Examples
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiclass image labeling with semidefinite programming
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
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In this paper, we describe the use of concepts from structural and statistical pattern recognition for recovering a mapping which can be viewed as an operator on the graph attribute-set. This mapping can be used to embed graphs into spaces where tasks such as categorisation and relational matching can be effected. We depart from concepts in graph theory to introduce mappings as operators over graph spaces. This treatment leads to the recovery of a mapping based upon the graph attributes which is related to the edge-space of the graphs under study. As a result, this mapping is a linear operator over the attribute set which is associated with the graph topology. Here, we employ an optimisation approach whose cost function is related to the target function used in discrete Markov Random Field approaches. Thus, the proposed method provides a link between concepts in graph theory, statistical inference and linear operators. We illustrate the utility of the recovered embedding for shape matching and categorisation on MPEG7 CE-Shape-1 dataset. We also compare our results to those yielded by alternatives.