Key-words: parametric surfaces, meshes, discrete objets, shape analysis, information extraction, constraint modeling

The activities of G-Mod can be divided into three main topics that are obviously not independent and involve the development of a broad but coherent activity in geometric modeling.

Geometrical and Topological Analysis – Information extraction

Initiated on continuous surfaces, the work has been enlarged on polyhedral surfaces. The analysis of local and global characteristics of geometric data is one basis of modeling methods, matching, or multi-resolution approaches. While differential geometry provides an essential tool for the study of continuous surfaces (local property of tangency, normal vectors, curvatures, …), the extension of these concepts to discrete surfaces (especially triangulated surfaces) is a sensitive issue.

The applications are numerous and varied: tumor detection on organs, recognition of tree trunks in forest LIDAR acquisitions, analysis of digitized monuments, construction of mean models of cornea, information extraction for biometrics, crater detection on small bodies in the solar system, representation of 3D objects by homotopy spanning trees for the study of internal structures (porous bones or rocks, holes, tunnels, cavities).

Modeling – Reconstruction

Mathematical models considered in geometric modeling are well controlled. Tools for modeling objects with a high level of abstraction from the underlying model are in opposition poorly developed. The objective of the work is to enrich the geometric model with semantic knowledge. This can come from properties provided by the designer to create the object (declarative modeling), or extracted from a scanned object (extraction of characteristics, learning). Wealth thus obtained provides various advantages: « high-level » design, automatic selection of algorithms based on the properties, indexing and comparison … This approach naturally leads to the establishment of a set of constraints from various levels (from data to application expertise), which then requires specific techniques and stable specific resolution.

Reconstruction (in particular the modeling of objects from a point cloud) is the starting point for many applications in various fields. Acquisition processes are numerous, but still lead to the same characteristics: important volume of data, significant noise, and in some cases, missing data (holes) or area of over or sub-sampling, lost of topology and of neighborhood. Links with polyhedral surfaces and characteristic extraction of the first topic obviously exist. The objective is usually to produce a surface mesh, but studies have been launched to handle point clouds. An important application is the binary volumes in particular in the case of medical images (CT, MRI) data. Reconstruction is usually surfacic because it is difficult to obtain information other than the outer envelope: the notion of volume is obtained by considering the object homogeneous, or by setting an offset of the outer shell.

Our algorithms are suitable for various application domains: building, GIS, industrial design…

Data Fusion and Modeling for Simulation

We propose to develop a new methodology for data fusion and graphic simulation, in which modeling, and especially geometrical modeling, is the core part. It is an up-to-date question, because data amounts are very huge now, and they carry a very high level of redundancy. Thus, using important means to extract and register information from this data is not sufficient: we need to introduce knowledge in the fusion process and this can be performed though the use of a model. Graphic simulation quality not only depends on visualizing realistic images: it mainly requires to display efficiently the relevant information so that the end user can easily catch it, and this also can be performed through semantic attributes related to a model. For these two reasons (image and cloud of points registration, and efficient simulation), we think that our methodology needs to be centered on the use of a model, and on its geometrical component.