Shape representation as the intersection of n � k hypersurfaces

Shape representation as the intersection of n ? k hypersurfaces. Shape representation as the intersection of n ? k hypersurfaces. Abstract: We investigate the feasibility of representing implicitly a k-dimensional manifold embedded in the Euclidean space R n as the intersection of n ? k transverse hypersurfaces. From the analytical point of view, the embedded manifold is deened as the inverse image of a regular value of a vector function. This approach is a priori appealing since the corresponding function is diierentiable at any point of the embedded manifold. We focus on time-dependent manifolds and establish the link between the velocity eld of the evolving manifold and a Partial Diierential Equation (PDE) satissed by its describing function. Implicit representations of shape, Mean curvature motion in arbitrary codimension. Reprrsentation des formes par l'intersection de n ? k hypersurfaces. RRsumm : Nous tudions la possibilitt de reprrsenter implicitement une variitt de dimension k plongge dans l'espace Euclidien R n comme l'intersection de k hypersurfaces. Du point de vue analytique, cela revient dddnir la variitt plongge comme l'image rrciproque d'une valeur rguliire d'une fonction vectorielle. Cette approche est a priori ssduisante car, dans ce cas, la fonction vectorielle en question est diiirentiable en tout point de la variitt d'inttrrt. Nous nous inttressons plus particuliirement aux variitts se ddformant au cours du temps et mettons en vidence une quation aux DDrives Partielles vriiie par ladite fonction vectorielle.