3D Winding Number: Theory and Application to Medical Imaging

We develop a new formulation, mathematically elegant, to detect critical points of 3D scalar images. It is based on a topological number, which is the generalization to three dimensions of the 2D winding number. We illustrate our method by considering three different biomedical applications, namely, detection and counting of ovarian follicles and neuronal cells and estimation of cardiac motion from tagged MR images. Qualitative and quantitative evaluation emphasizes the reliability of the results

Extraction of cardiac motion using scale-space features points and gauged reconstruction

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

Extraction of cardiac motion using scale-space features points and gauged reconstruction

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