In recent years, the field of active contour based image segmentation has seen the emergence of two competing approaches. The first and oldest approach represents active contours in an explicit (or parametric) manner corresponding to the Lagrangian formulation. The second approach represents active contours in an implicit manner corresponding to the Eulerian framework. After comparing these two approaches, we describe several new topological and geometrical constraints applied to parametric active contours in order to combine the advantages of these two contour representations. This paper proposes a framework for handling parametric active contours shape and topology in a more intuitive manner. More precisely, the following three algorithms are introduced: - Metric and Shape Control : a new internal force expression allows to regularize both vertex spacing and vertex smoothness. The smoothness constraint is enforced without producing any shrinkage. - Contour Resolution Control : the total number of contour vertices is periodically updated in order to constrain the distance between vertices. This approach is more efficient than performing any global reparameterization. - Topology Control : the connected components of a contour are automatically created or merged based on the detection of edge intersections. Our algorithm can handle opened and closed contours.