Simplex Mesh Diffusion Snakes: Integrating 2D and 3D Deformable Models and Statistical Shape Knowledge in a Variational Framework

In volumetric medical imaging the boundaries of structures are frequently blurred due to insufficient resolution. This artefact is particularly serious in structures such as articular joints, where different cartilage surfaces appear to be linked at the contact regions. Traditional image segmentation techniques fail to separate such erroneously linked structures, and a sensible approach has been the introduction of prior-knowledge to the segmentation process. Although several 3D prior-knowledge based techniques that could successfully segment these structures have been published, most of them are pixel-labelling schemes that generate pixellated images with serious geometric distortions. The Simplex Mesh Diffusion Snakes segmentation technique presented here is an extension of the two dimensional Diffusion Snakes, but without any restriction on the number of dimensions of the data set. This technique integrates a Simplex Mesh, a region-based deformable model and Statistical Shape Knowledge into a single energy functional, so that it takes into account both the image information available directly from the data set, and the shape statistics obtained from a training process. The resulting segmentations converge correctly to well defined boundaries and provide a feasible location for those removed boundaries. The algorithm has been evaluated using 2D and 3D data sets obtained with Magnetic Resonance Imaging (MRI) and has proved to be robust to most of the MRI artefacts, providing continuous and smooth curves or surfaces with sub-pixel resolution. Additionally, this novel technique opens a wide range of opportunities for segmentation and tracking time-dependent 3D structures or data sets with more than three dimensions, due to its non-restrictive mathematical formulation.