Knowledge-Based Anisotropic Diffusion of Vector-Valued 4-Dimensional Cardiac MR Images

We present a general formulation for a new knowledge-based approach to anisotropic diiusion of multi-feature and multi-dimensional images, with an illustrative application to cardiac MRI. We incorporate all available information through a more complete deenition of the conductance function which diiers from previous approaches in two aspects. First, we model the conductance as an explicit function of the position and not only of the diierential geometry of the image data. Inherent properties of the system (such as geometrical features or non-homogeneous data sampling) can therefore be taken into account by allowing the conductance values to depend on the location in the spatial and temporal coordinate space. Secondly, by deening the conductance as a second rank tensor, the non-homogeneous diiusion equation gains a truly anisotropic character which is essential to emulate and handle certain aspects of complex data systems. We demonstrate the eeciency of the proposed framework using density and velocity encoded cine volumetric MR images of the left ventricle. In this example we incorporate into the diiusion process spatial and temporal knowledge about the shape and dynamics of the heart. The method presented is suitable for image enhancement and also for segmentation. We compare our results to those obtained with other anisotropic diiusion methods.