This thesis is devoted to explore the potentialities of the Deformable Simplicial Complex (DSC) method for solving various problems. The DSC is an explicit interface tracking method that relies on meshes, triangle in 2D and tetrahedra in 3D, to represent piecewise constant functions. One can consider the DSC as the potential alternative for the popular level set method with additional explicit-geometric-information. In particular, the goals of this thesis include: the applications of the DSC in image segmentation, ﬂuid simulation, and a method for DSC eﬃciency optimization. Image segmentation faces many diﬃculties in dealing with volume data sets that represent multiple materials (phases) such as CT and MRI scans. In this thesis, we propose a novel method for 2D and 3D image segmentation using the DSC. The most important advantage of the method is multi-phase support with accurately deﬁned boundaries. Besides, this method is robust to noise because we distinguish the image space (the ﬁxed grid) and feature space (segmentation represented by the DSC meshes). Additionally, the outputs of our method, which are meshes, are useful for simulation and analysis. Simulation of ﬂuid is important for understanding ﬂuid properties and visualization, but it is challenging due to a massive amount of topological changes (surface splits and merges). With the DSC, handling the topology becomes trivial. We show that the DSC can be used for multi-phase ﬂuid tracking with complex topology. The DSC is primarily designed for memory eﬃciency and accuracy. In many cases, including image segmentation and ﬂuid tracking problem, performance is highly concerning. Our last contribution is a caching scheme that stores computed mesh data for later retrievals. The proposed method helps improving the DSC performance up to ﬁve times and enabling parallel mesh processing.
|Number of pages||160|
|Publication status||Published - 2018|
|Series||DTU Compute PHD-2018|