Harmonic Active Contours for multichannel image segmentation

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.

Harmonic Active Contours

Xavier Bresson, Virginia Estellers Casas, Jean-Philippe Thiran, Dominique Zosso

We propose a segmentation method based on the geometric representation of images as two-dimensional manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set function and the objective functional corresponds to the surface of the image manifold. In this geometric framework, both data-fidelity and regularity terms of the segmentation are represented by a single functional that intrinsically aligns the gradients of the level set function with the gradients of the image and exploits this directional information to overcome image inhomogeneities and fragmented contours. The proposed formulation combines this robust alignment of gradients with attractive properties of previous methods developed in the same geometric framework: the natural coupling of image channels proposed for anisotropic diffusion and the ability of the subjective surfaces of Sarti and Sethian to detect weak edges and close fragmented boundaries. The potential of such a geometric approach lies in the general definition of Riemannian manifolds, which naturally generalizes existing segmentation methods (the geodesic active contours of Caselles et al., the active contours without edges of Chan and Vese and the robust edge integrator of Kimmel and Bruckstein ) to higher dimensional spaces, non-flat images and feature spaces. Our experiments show that the proposed technique improves the segmentation of multichannel images, images subject to inhomogeneities, and images characterized by geometric structures like ridges or valleys.

Institute of Electrical and Electronics Engineers2014

Geodesic Active Fields - A Geometric Framework for Image Registration

Xavier Bresson, Jean-Philippe Thiran, Dominique Zosso

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including non-flat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Secondly, this method is, to the best of our knowledge, the first re-parametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.

Institute of Electrical and Electronics Engineers2011

Geodesic Active Fields - A Geometric Framework for Image Registration

Xavier Bresson, Jean-Philippe Thiran, Dominique Zosso

Institute of Electrical and Electronics Engineers2011