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Étienne Le Quentrec
Locally Turn-Bounded Curves and their Applications to Digital Geometry
21 novembre 2024 - 09:00Salle de conférences IRMA
When an object is photographed, the resulting image is pixelated. The position of a point in such an image is described by integer coordinates, unlike that of a point on the original object, which is described by real coordinates. This transition from the usual Euclidean geometry describing the original object to the discrete geometry describing the obtained image, called digitization, causes significant information loss. If the resolution of the discrete image is too low compared to the level of detail of the original object, topological information and geometric quantities can be lost. It then becomes necessary to impose certain assumptions on this real object to allow the reconstruction of this information.
By modeling the digitization process, it is possible to ensure the reconstruction of the topology and geometric quantities of objects that meet certain assumptions. However, currently in digital geometry, the assumptions on real objects that guarantee the reconstruction of all this information are quite restrictive and do not allow the simultaneous inclusion of shapes whose boundary is a smooth curve and those whose boundary is a polygon.
To simultaneously address these two families of shapes, we propose a new assumption based on the concept of total curvature introduced by Milnor in 1950. This consists of locally limiting this total curvature on the boundary of the real object. This assumption, which includes shapes with smooth or polygonal boundaries, guarantees the reconstruction of topology and allows for bounding the errors of discrete estimators of geometric quantities.
About the speaker: Étienne Le Quentrec is assistant professor (maître de conférences) at ICube, member of IMAGeS team since September 2022. He defended his PhD thesis in 2021 on digital Geometry at ICube. He was also student at UFR in mathematics where he obtained his "agrégation" in 2016. His main research interests are digital topology and discrete estimation.