Abstract: Shape representation and registration are two important problems in computer vision and graphics. Representing the given cloud of points through an implicit function provides a higher level information describing the data. This representation can be more compact more robust to noise and outliers, hence it can be exploited in different computer vision application. In the first part of this thesis implicit shape representations, including both implicit B-spline and polynomial, are tackled. First, an approximation of a geometric distance is proposed to measure the closeness of the given cloud of points and the implicit surface. The analysis of the proposed distance shows an accurate estimation with smooth behavior. The distance by itself is used in a RANSAC based quadratic fitting method. Moreover, since the gradient information of the distance with respect to the surface parameters can be analytically computed, it is used in Levenberg-Marquadt algorithm to refine the surface parameters. In a different approach, an algebraic fitting method is used to represent an object through implicit B-splines. The outcome is a smooth flexible surface and can be represented in different levels from coarse to fine. This property has been exploited to solve the registration problem in the second part of the thesis. In the proposed registration technique the model set is replaced with an implicit representation provided in the first part; then, the point-to-point registration is converted to a point-to-model one in a higher level. This registration error can benefit from different distance estimations to speed up the registration process even without need of correspondence search. Finally, the non-rigid registration problem is tackled through a quadratic distance approximation that is based on the curvature information of the model set. This approximation is used in a free form deformation model to update its control lattice. Then it is shown how an accurate distance approximation can benefit non-rigid registration problems.