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CHIC

Object class invariants play a key role in computer imagery, and more specifically in image analysis and geometric modeling. Computing and representing topological information (neighborhood, connectedness, orientation, etc.) form an important part in applications such as image classification, indexing, shape description, shape recognition. Geometric modeling applications also take topological criteria into account to ensure the reliability of construction or to control the result of construction operations. Homology is an algorithmically computable topological invariant that characterizes an object by its "holes". The notion of "hole" is defined in any dimension. Informally “holes” of a 3D-object are its connected components in dimension 0, its tunnels in dimension 1, its cavities in dimension 2. This project deals with the computation of homological information (homology groups and their generators) of objects contained in images, and its use for image applications.

A donut: one connected component and one tunnelTorusSphere

Example 1: A donut with one connected component and one tunnel.

Example 2: A torus with one connected component, two tunnels and one cavitie.

Example 3; A sphere with one connected component and one cavitie.

This project deals with the computation of homological information (homology groups and their generators) of objects contained in images, and its use for image applications.

 

Bone

Example 4. Application of homological information in Medical Image (trabecular bone).

 

This research is based on the complementary scientific expertise of the partners. PRIP (Vienna, Austria), SIC (Poitiers, France), and LAIC (Clermont, France, please refer to the webpage of Prof. Rémy Malgouyres for the activity within CHIC) have already shown their interest and competences through publications dealing with the computation of topological invariants in digital imagery. Moreover the advanced theoretical background that is needed in this project belongs to the area of expertise of LMA (Poitiers, France). A joint project between the groups PRIP, SIC, LAIC and LMA is planned.

Project details