T. Preußer and M. Rumpf.
Extracting motion velocities from 3D image sequences.
In SPIE Conference on Visualization and Data Analysis, 2003.
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Recent image machinery delivers sequences of large scale three-dimensional (3D) images with a considerably small sampling width in time. In medical as well as in engineering applications the interest lies in underlying deformation, growth or motion phenomena. A robust method is presented to extract motion velocities from such image sequences. To avoid an ill-posedness of the problem one has to restrict the study to certain motion types, which are related to the concrete application. The derived formulas for the motion velocities clearly reflect the geometry of the motion. Robustness of the presented implementation is based on local regularizations in space-time. Thereby geometric quantities on the image sequences are evaluated on the local regularizations. Examples outline the potential of the proposed method in medical applications (3D ultrasound sequences) and experimental fluid dynamics (3D flow in porous media). As an improved regularization approach an effective denoising method based on anisotropic geometric diffusion for 3D data sets is discussed, which respects important features on levelsets such as edges and corners and accelerated motions and preserves them during the smoothing process. Its application as a pre-processing step turns out to be especially advisable for image sequences with a considerably small signal to noise ratio.