Une description topo-géométrique pour les formes 2D en utilisant la théorie de taille

Abstract

The objective of this work is to design and develop a shape descriptor for describing and matching of 2D shapes, more robust and e cient than other existing descriptors. The proposed approach introduces a new topological descriptor called the size function (or SFD) based on the representation of contour points distributed in annular curves according to sublevels calculated by the radial measurement function, which allows to represent and characterize the shape in a simple and more reduced way. The size function describes the shape based on the characteristics of the real functions de ned on the objects of the shape. These functions allow to quantify the geometric and topological properties of the shapes, thus providing powerful descriptors for their characterization. Thanks to the topological information contained in this new descriptor, it is more e cient to match shapes that are not strictly similar. In this regard, a matching algorithm is designed to compare a query shape with a collection of target shapes. The similarity score of the matching is evaluated according to the normalized distance interval [0..1]. We have validated the proposed approach using a standard 2D shape database. The obtained test results are favorable and promising and show the success and e ciency of this approach. These results also show that the new descriptor model is competitive with other descriptors for description and matching tasks and is more robust to noise, occlusions and invariant to geometric transformations. In the future, this descriptor may be a good candidate to successfully apply it to various classi cation and recognition problems