Harmonic Active Contours

• Published in: IEEE transactions on image processing Vol. 23; no. 1; pp. 69 - 82
• Main Authors: Estellers, Virginia, Zosso, Dominique, Bresson, Xavier, Thiran, Jean-Philippe
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: active contours; Algorithms; Alignment; Applied sciences; Artificial Intelligence; Beltrami; Channels; Contours; edge detection; Exact sciences and technology; Fragmentation; Image edge detection; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image segmentation; Information Storage and Retrieval - methods; Information, signal and communications theory; Inhomogeneities; Level set; Manifolds; Measurement; Minimization; Pattern recognition; Pattern Recognition, Automated - methods; Radio frequency; Reproducibility of Results; Segmentation; Sensitivity and Specificity; Signal processing; Telecommunications and information theory; Harmonic; Image processing; Pattern recognition; Shape detection; Subjective evaluation; Geometrical model; Multiple image; Beltrami; Heterogeneity; Image segmentation; Riemann function; Geodesic; Integrator; Anisotropic scattering; active contours; Edge detection; Active contour
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2013.2286326

We propose a segmentation method based on the geometric representation of images as 2-D 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 results in a segmentation criterion that exploits the directional information of image gradients 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: 1) the natural coupling of image channels proposed for anisotropic diffusion and 2) the ability of subjective surfaces 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, the active contours without edges, and the robust edge integrator) to higher dimensional spaces, non-flat images, and feature spaces. Our experiments show that the proposed technique improves the segmentation of multi-channel images, images subject to inhomogeneities, and images characterized by geometric structures like ridges or valleys.