We propose a segmentation method based on the geometric representation of images as surfaces embedded in a higher dimensional space, handling naturally multichannel images. The segmentation is based on an active contour embedded in the image manifold, along with a set of image features. Hence, both data-fidelity and regularity terms of the active contour are jointly optimized minimizing a single Polaykov energy representing the hyper-surface of this manifold. Compared to previous methods, our approach is purely geometrical and does not require additional weighting of the energy functional to drive the segmentation to the image contours. The potential of such a geometric approach lies in the general definition of Riemannian manifolds, validating the proposed technique for scale-space methods, volumetric data or catadioptric images. We present here the segmentation technique called Harmonic Active Contours, give an implementation for multichannel images including gradient and region-based segmentation criteria and apply it to color images.