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Soft X-ray Tomography: Techniques and Applications
Published in Paolo Russo, Handbook of X-ray Imaging, 2017
Axel A. Ekman, Tia E. Plautz, Jian-Hua Chen, Gerry McDermott, Mark A. Le Gros, Carolyn A. Larabell
Although, in simple cases, thresholding can be an effective technique, it is inadequate in the circumstances of missing information, occlusions, and especially poor SNR. Furthermore, when organelles possess similar LAC, classification by thresholding is intractable. A number of more advanced techniques for semi-automatic segmentation have been proposed, including but not limited to, variational methods based on Mumford–Shah functionals (Vese and Chan 2002), hierarchical MRFs (Abend et al. 1965), topological derivative methods (Hintermüller and Laurain 2009), support vector machines (Cortes and Vapnik 1995), and geometric active contours (Sethian 1999), which can be assisted by shape priors (Cremers et al. 2002). Some of these methods have been applied to problems involving the segmentation of individual cells and cell nuclei in fields such as light microscopy, confocal microscopy, and fluorescence microscopy, for example, Ortiz De Solórzano et al. (1999), Lin et al. (2003), Würflinger et al. (2004), Dufour et al. (2005), and Jones et al. (2005). In electron microscopy, there have been a few attempts at automatic segmentation of individual organelles which have resulted in varying degrees of success (Keuper et al. 2011, Perez et al. 2014, Lucchi et al. 2015).
Cardiac Image Segmentation Using Generalized Polynomial Chaos Expansion and Level Set Function
Published in Ayman El-Baz, Jasjit S. Suri, Level Set Method in Medical Imaging Segmentation, 2019
Further, we integrate the gPC approximation of uncertainty in pixel values with the Chan-Vese model for image segmentation. Following the gPC approximation, Galerkin projection can be used to solve the gPC coefficients of level set function by substituting (9.19) and (9.21) into (9.29) and by solving the partial differential equations through numerical discretization. The minimization of Chan-Vese model can be solved using different optimization techniques, such as semi-implicit gradient descent method [18], topological derivative [34], and multigrid method [35]. For brevity, the details of each optimization technique are not discussed for brevity.
On the Kohn–Vogelius formulation for solving an inverse source problem
Published in Inverse Problems in Science and Engineering, 2021
P. Menoret, M. Hrizi, A. A. Novotny
The topological derivative measures the sensitivity of a given shape function with respect to infinitesimal geometry perturbations such as the creation of inclusions, cracks, cavities, inhomogeneities, or source-terms. Theoretically, the topological sensitivity concept is the first term of the asymptotic expansion of such shape functions with respect to the small parameter that measures the size of the introduced perturbation. This idea was first developed by Schumacher [12] under the name of bubble method in the context of compliance minimization in linear elasticity, followed by Sokołowski and Żochowski [13] and Céa et al. [14]. Since then, this concept has been successfully applied to many relevant scientific and engineering problems such as inverse problems [15–20], topology optimization [21–24], image processing [25–28], damage [29,30] and fracture [31,32] evolution modelling, and many other applications.
Topology optimization of heat and mass transfer problems in two fluids—one solid domains
Published in Numerical Heat Transfer, Part B: Fundamentals, 2019
Rony Tawk, Boutros Ghannam, Maroun Nemer
Beside density method, level set technique gained attention in applying topology optimization on fluid flow problems. Zhou and Li [13] conducted 2D and 3D numerical experiments in topological design using level set method, and proved a relatively good agreement of their results with those obtained by density methods. Duan et al. [14] considered the bend pipe and diffuser cases in level set method, which were solved in density method by various authors [3, 9] for low Reynolds number. However, even if for some specific configurations level set method showed agreement with density method, the performance of this technique is still significantly limited by its incapacity of creating new holes in the design domain, which make the method highly dependent on the initial guess. Incorporating topological derivative method into level set method to reduce its dependency on the initial guess was considered in mechanical structure problems [15], then in mechanical fluid problems [16, 17]. Topological derivative indicates the location in the optimization domain where new holes should be nucleated using two different strategies: by including topological sensitivity information in the evolution equation of level set method, or using this information at discrete places in the optimization algorithm [17]. However results showed that the combined method of level set and topological derivatives still depend strongly on the starting guess, as discussed in [18].
Evolutionary topology optimization for acoustic-structure interaction problems using a mixed u/p formulation
Published in Mechanics Based Design of Structures and Machines, 2019
Different types of topology optimization methods exist, such as density-based methods, including homogenization and solid isotropic material with penalization (SIMP), discrete methods, which include bi-directional evolutionary structural optimization (BESO) (Kim, Ramana, and Mark 2006; Huang and Xie 2010a, 2010b; Xia et al. 2016), boundary variation methods, such as the level-set method (Van Dijk et al. 2013; Noguchi et al. 2017), and topological derivative-based methods (Kim, Ha, and Cho 2009). Although numerous attempts have been made to compare the various topology optimization approaches, the best optimization approaches are still controversial, due to their strengths and weaknesses in relation to different optimization problems (Sigmund and Maute 2013).