Determination of Moment Invariants and Their Application to Visual Servoing

Moment invariants are important shape descriptors in computer vision. In this paper, we give a general and systematic method to derive moment invariants of any order and for k-dimensional space (invariants to scale, to orthogonal transformation and to translation). This result is applied to the selection of adequate features for visual servoing. To elaborate the control law, we also determine the analytical form of the interaction matrix of any image moment. This matrix relates the variation of the image moments to the 3D motions of the camera. We nally presents some visual servoing experimental results using very simple images. These results allow to validate the theoretical developments proposed in this paper. Moments invariants : m ethodes de calcul et application a l'asservissement visuel R esum e : Dans cet article, on pr esente une nouvelle m ethode de calcul des moments invariants. Nous utiliserons ces invariants pour minimiser les non lin earit es de la matrice d'interaction des primitives choisies et pour obtenir un asservissement visuel 2D d ecoupl e. Des r esultats exp erimentaux utilisant une cam era embarqu ee sur un robot 6 ddl pour se positionner parall element un objet plan de forme complexe sont pr esent es pour d emontrer l'eecacit e de la m ethode propos ee.