3D winding number: theory and application to medical imaging
Journal of Biomedical Imaging - Special issue on modern mathematics in biomedical imaging
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Motion estimation is an important topic in medical image analysis. The investigation and quantification of, e.g., the cardiac movement is important for assessment of cardiac abnormalities and to get an indication of response to therapy. In this paper we present a new aperture problem-free method to track cardiac motion from 2-dimensional MR tagged images and corresponding sine-phase images. Tracking is achieved by following the movement of scale-space critical points such as maxima, minima and saddles. Reconstruction of dense velocity field is carried out by minimizing an energy functional with regularization term influenced by covariant derivatives gauged by a prior assumption.MR tags deform along with the tissue, a combination of MR tagged images and sine-phase images was employed to produce a regular grid from which the scale-space critical points were retrieved. Experiments were carried out on real image data, and on artificial phantom data from which the ground truth is known. A comparison between our new method and a similar technique based on homogeneous diffusion regularization and standard derivatives shows increase in performance. Qualitative and quantitative evaluation emphasize the reliability of dense motion field allowing further analysis of deformation and torsion of the cardiac wall.