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Active surfaces acceleration methods
Published in João Manuel, R. S. Tavares, R. M. Natal Jorge, Computational Modelling of Objects Represented in Images, 2018
Julien Olivier, Julien Mille, Romuald Boné, J.-Jacques Rousselle
Conversely, implicit implementations, based on the level set framework (Malladi, Sethian, and Vemuri 1995), handle the surface as the zero level of a hypersurface, defined on the same domain as the image (for 3D images, the hypersurface is a R3 → R application). Level sets are often chosen for their natural handling of topological changes and adaptiveness to any dimension. Their algorithmic complexity is a function of the image resolution, making them time-consuming. Despite the development of accelerating methods (like the narrow band technique (Malladi, Sethian, and Vemuri 1995), the fast marching method (Adalsteinsson and Sethian 1995) and the recent fast level set (Shi and Karl 2005)), their computational cost remains high, preventing their use in time-critical applications. Moreover, mesh surfaces have several advantages over their implicit counterparts. Their representation is more intuitive, and thus allow easier modeling of a priori knowledge and user interaction. The main drawback is that meshes do not modify their topology naturally (techniques for detection of topological changes must be implemented beside the evolution algorithm).
Image Visualization
Published in Alexandru Telea, Data Visualization, 2014
Overall, all these methods are relatively simpler to implement than the Fast Marching Method presented in the previous section. However, as already explained, the Fast Marching Method has the important advantage that it allows one to specify the speed function, i.e., the gradient of the distance metric, differently at each point of the domain. This allows one to easily implement complex space-dependent and anisotropic distance metrics, a feature that is not supported in general by the other methods listed in this section. A second advantage of the Fast Marching Method is that it processes the image pixels in increasing distance order. This allows one to stop the distance computation when, e.g., a certain maximal distance has been reached. This feature is not supported by other methods such as the raster scanning class.
Level Set Methods for Cardiac Segmentation in MSCT Images
Published in Ayman El-Baz, Jasjit S. Suri, Level Set Method in Medical Imaging Segmentation, 2019
Ruben Medina, Sebastian Bautista, Villie Morocho, Alexandra La Cruz
The Fast Marching Method is an algorithm useful for monotonically advancing fronts using a computational efficient method as proposed by Sethian [29]. This approach can be used for segmentation by synthesizing an external speed term that is applied to the front for stopping it near the objects contours as explained in [30]. The Fast Marching algorithm is constructed based on the level set approach presented in section 7.2.1.
A simple iterative geometry-based interface-preserving reinitialization for the level set method
Published in International Journal of Computational Fluid Dynamics, 2019
Lanhao Zhao, Hairong Zhang, Jia Mao, Hanyue Zhu, Dawei Peng, Kailong Mu
Reinitialization techniques can be divided into explicit and implicit schemes. The explicit reinitialization requires the location of zero-level-set before reconstructing a SDF. The first attempt to reinitialize the level set function explicitly is the direct approach (Chopp 1993; Shakoor et al. 2015; Long and Choi 2017) introduced by Chopp. The direct method calculates the signed distance from each node to the interface but tends to produce irregular distribution of the level set especially at sharp corners. Hence, the direct method cannot provide a smooth description of the sharp interface. Another explicit scheme is the fast marching method (FMM) (Sethian 1996; Bockmann and Vartdal 2014; Yang and Stern 2017) proposed by Sethian. This method generates a SDF via the eikonal equation based on the appropriate construction of extension velocities, but the exact location of the interface must be represented explicitly to construct the expansion velocities in each pseudo time step. Moreover, FMM combined with parallel algorithms would be complicated and computationally expensive, which limits its extensive application in large-scale computing heavily (Yang and Stern 2017).