A denoising tool for the reconstruction of cortical geometries from MRI

The reconstruction of individual geometries from medical imaging is quite a standard in the framework of patient-specific medicine. A major drawback in such a context is represented by noise inherent to the data acquisition. Low signal-to-noise ratios can negatively impact extraction algorithms, and result in artefacts or poor quality of the reconstructed meshes. Direct application of numerical methods on such meshes can yield misleading results. Indeed, artefacts and badly shaped elements may corrupt numerical simulations or induce relevant errors in the computation of meaningful geometrical quantities, such as the curvature or the geodesic surface distance. In this paper, we propose a denoising procedure to remove artefacts from a triangular mesh of a three-dimensional closed surface which represents a brain cortex. For this purpose, we combine a smoothing technique (i.e., the Taubin or the HC-Laplacian smoothing) with an edge-flipping algorithm. To control the denoising procedure, we introduce a stopping criterion that takes into account both the improvement of the mesh quality and the loss of volume enclosed by the surface. On a brain cortical surface reconstructed from Magnetic Resonance Imaging (MRI) data, we first perform a tuning analysis of the parameters involved in the smoothing algorithm, then we investigate the effectiveness of the denoising procedure. Finally, as an example of relevant geometrical feature, we study the improvement generated by the proposed algorithm on the computation of the cortical curvature.