Knowledge-based tensor anisotropic diffusion of cardiac magnetic resonance images

We present a general formulation for a new knowledge-based approach to anisotropic diffusion of multi-valued and multi-dimensional images, with an illustrative application for the enhancement and segmentation of cardiac magnetic resonance (MR) images. In the proposed method all available information is incorporated through a new definition of the conductance function which differs from previous approaches in two aspects. First, we model the conductance as an explicit function of time and position, and not only of the differential structure 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 function to vary depending on the location in the spatial and temporal coordinate space. Secondly, by defining the conductance as a second-rank tensor, the non-homogeneous diffusion equation gains a truly anisotropic character which is essential to emulate and handle certain aspects of complex data systems. The method presented is suitable for image enhancement and segmentation of single- or multi-valued images. We demonstrate the efficiency of the proposed framework by applying it to anatomical and velocity-encoded cine volumetric (4-D) MR images of the left ventricle. Spatial and temporal a priori knowledge about the shape and dynamics of the heart is incorporated into the diffusion process. We compare our results to those obtained with other diffusion schemes and exhibit the improvement in regions of the image with low contrast and low signal-to-noise ratio.