A framework for object segmentation in vector-valued images is presented in this paper. The first scheme proposed is based on geometric active contours moving towards the objects to be detected in the vector-valved image. Objects boundaries are obtained as geodesics or minimal weighted distance curves in a Riemannian space. The metric in this space is given by a definition of edges in vector-valued images. The curve flow corresponding to the proposed active contours holds formal existence, uniqueness, stability, and correctness results. The techniques is applicable for example to color and texture images. The scheme automatically handles changes in the deforming curve topology. We conclude the paper presenting an extension of the color active contours which leads to a possible image flow for vector-valued image segmentation. The algorithm is based on moving each one of the image level-sets according to the proposed color active contours. This extension also shows the relation of the color geodesic active contours with a number of partial-differential-equations based image processing algorithms as anisotropic diffusion and shock filters.