CTIC 2008

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Easychair

CTIC 2008

Workshop on Computational Topology in Image Context

Poitiers - France - 16,17 June 2008

CTIC 2008 will offer three invited lectures:

Isabelle BLOCH from ENST, Paris, France

A few topological aspects in medical imaging

Abstract: In this talk, an overview of various models taking topology into account will be presented, for applications in medical imaging. Preserving topology is often an important constraint in segmentation and this will be addressed in the first part of the talk. We will show that such constraints can be modeled on different digital 3D representations (voxels, cellular complexes, tetrahedral meshes). This will be illustrated with examples in brain segmentation from 3D images. In the second part of the talk, the modeling of topological spatial relations will be addressed, in the framework of fuzzy sets. The interest of these models will be illustrated on model-based recognition problems, in particular for anatomical structures.

Pedro REAL from DAM, Sevilla, Spain

Digital Volume Homological Processing

Abstract: In this talk, digital volumes are seen and analysed from an algebraic-topological point of view . A polyhedral continuous analogous $K(V)$ is uniquely associated to a digital volume $V$ (with $26$-adjacency relation for neighbors voxels) and a "gradient" cellular field $\phi$ over this complex can be obtained using different classical homological techniques (incremental, matrix, local contractibility, Morse-based-method,....) In fact, the map $\phi$ determines an especial homotopy equivalence algebraically connecting $K(V)$ and its homology, working on a field as a ground ring. From this datum and a property of local simplicialization for $K(V)$, it is possible to deduce advanced homological information for $V$: representative cycles of homology generators, homological classification of cycles, homological operations, ....). This idea of describing homology in terms of chain homotopies is not new and comes back to Eilenberg-MacLane work on Algebraic Topology and it has been developed later in algebraic-topological methods like Effective Homology and Homological Perturbation Theory and in discrete settings as Discrete Morse and AT-model theories.

Francis SERGERAERT from UJF, Grenoble, France

Constructive Algebraic Topology

Abstract: "Standard" Algebraic Topology is not appropriately designed for computations, for example the usual spectral sequences are most often *not* computable from the data usually available. From a theoretical point of view, standard Algebraic Topology is *not* constructive. To make it constructive, according to the methods of the so-called *Effective_Homology*, two main ingredients are to be used: 1) Functional programming allows to partially implement infinite objects as "locally effective" objects on a theoretical or concrete computer. 2) The Basic Perturbation Lemma becomes the main mathematical tool to process the necessary connections between ordinary homology groups and the corresponding locally effective objects. Plan: 1) Description of the main ideas of Effective Homology. 2) Results so obtained. 3) Open problems.