Graphical models and point set matching

Point pattern matching in Euclidean Spaces is one of the fundamental problems in Pattern Recognition, having applications ranging from Computer Vision to Computational Chemistry. Whenever two complex patterns are encoded by two sets of points identifying their key features, their comparison can be seen as a point pattern matching problem. This work proposes a single approach to both exact and inexact point set matching in Euclidean Spaces of arbitrary dimension. In the case of exact matching, it is assured to find an optimal solution. For inexact matching (when noise is involved), experimental results confirm the validity of the approach. We start by regarding point pattern matching as a weighted graph matching problem. We then formulate the weighted graph matching problem as one of Bayesian inference in a probabilistic graphical model. By exploiting the existence of fundamental constraints in patterns embedded in Euclidean Spaces, we prove that for exact point set matching a simple graphical model is equivalent to the full model. It is possible to show that exact probabilistic inference in this simple model has polynomial time complexity with respect to the number of elements in the patterns to be matched. This gives rise to a technique that for exact matching provably finds a global optimum in polynomial time for any dimensionality of the underlying Euclidean Space. Computational experiments comparing this technique with well-known probabilistic relaxation labeling show significant performance improvement for inexact matching. The proposed approach is significantly more robust under augmentation of the sizes of the involved patterns. In the absence of noise, the results are always perfect.

Ontology-based metadata for e-learning content

Nowadays, the popularity of the Web encourages the development of Hypermedia Systems dedicated to e-learning. Nevertheless, most of the available Web teaching systems apply the traditional paper-based learning resources presented as HTML pages making no use of the new capabilities provided by the Web. There is a challenge to develop educative systems that adapt the educative content to the style of learning, context and background of each student. Another research issue is the capacity to interoperate on the Web reusing learning objects. This work presents an approach to address these two issues by using the technologies of the Semantic Web. The approach presented here models the knowledge of the educative content and the learner’s profile with ontologies whose vocabularies are a refinement of those defined on standards situated on the Web as reference points to provide semantics. Ontologies enable the representation of metadata concerning simple learning objects and the rules that define the way that they can feasibly be assembled to configure more complex ones. These complex learning objects could be created dynamically according to the learners’ profile by intelligent agents that use the ontologies as the source of their beliefs. Interoperability issues were addressed by using an application profile of the IEEE LOM- Learning Object Metadata standard.