The supercover of an m-flat is a discrete analytical object

International audienc

Discrete linear objects in dimension n: the standard model

International audienceA new analytical description model, called the standard model, for the discretization of Euclidean linear objects (point, m-flat, m-simplex) in dimension n is proposed. The objects are defined analytically by inequalities. This allows a global definition independent of the number of discrete points. A method is provided to compute the analytical description for a given linear object. A discrete standard model has many properties in common with the supercover model from which it derives. However, contrary to supercover objects, a standard object does not have bubbles. A standard object is (n-1)-connected, tunnel-free and bubble-free. The standard model is geometrically consistent. The standard model is well suited for modelling applications

Topological segmentation of discrete surfaces

International audienceThis article proposes a new approach to segment a discrete 3-D object into a structure of characteristic topological primitives with attached qualitative features. This structure can be seen itself as a qualitative description of the object, because : - it is intrinsic to the 3-D object, which means it is stable to rigid transformations (rotations and translations); - it is locally defined, and therefore stable to partial occlusions and local modifications of the object structure; - it is robust to noise and small deformations, as confirmed by our experimental results. Our approach concentrates on topological properties of discrete surfaces. These surfaces may correspond to the external surface of the objects extracted by a 3-D edge detector, or to the skeleton surface obtained by a new thinning algorithm. Our labeling algorithm is based on very local computations, allowing massively parallel computations and real-time computations. An indirect result of these topological properties is a new characterization of simple points. We present a realistic experiment to characterize and locate spatially a complex 3-D medical object using the proposed segmentation of its skeleton