Transfinite interpolation

3D MRI reconstruction based on transfinite approximation

Our method, based on transfinite interpolation, aims at reconstructing high resolution isotropic volume from three anisotropic volumes with different orientations. The main idea is to register all data slices in the same space and use transfinite interpolation in convex cells to fill the output grid. The formula is based on projection on surrounding structures containing data and blend them taking into account the data geometries. In the general case, some projections belong to several slices which we manage to regularize data during the interpolation procedure. We manage to reconstruct volume high resolution isotropic volume improving resolution compared to raw data. Our reconstructed volume can serve as a basis for semi-automatic segmentation algorithms in the deep brain.

Fig. 1: Example of the spatial organisation of our data, each plane corresponding to a slice.

Fig. 2: Superior view of the reconstructed axial slice of TFI volume (left) and the reconstructed sagittal raw volume (right).