Search results for "Level set method"
showing 7 items of 7 documents
On a topology optimization problem governed by two-dimensional Helmholtz equation
2015
The paper deals with a class of shape/topology optimization problems governed by the Helmholtz equation in 2D. To guarantee the existence of minimizers, the relaxation is necessary. Two numerical methods for solving such problems are proposed and theoretically justified: a direct discretization of the relaxed formulation and a level set parametrization of shapes by means of radial basis functions. Numerical experiments are given.
The simulation of morphology of dissimilar copper–steel electron beam welds using level set method
2010
Abstract In present work, the simulation of morphology and velocity field in dissimilar electron beam welds formed between the metals with limited solubility is described by the example of copper–stainless steel couple. Finite element software COMSOL Multiphysics 3.5 has been employed due to its flexibility in solving of coupled multiphysical problems. The domination of horizontal flows allows reducing the model to two dimensions. Level set method has been used to determine the position of the interface between immiscible components basing on coupled heat transfer and fluid flow pseudo-stationary solution. The evolution of the shape, fluid flow and mixing pattern in function of operational …
Image boundaries detection: from thresholding to implicit curve evolution
2014
The development of high dimensional large-scale imaging devices increases the need of fast, robust and accurate image segmentation methods. Due to its intrinsic advantages such as the ability to extract complex boundaries, while handling topological changes automatically, the level set method (LSM) has been widely used in boundaries detection. Nevertheless, their computational complexity limits their use for real time systems. Furthermore, most of the LSMs share the limit of leading very often to a local minimum, while the effectiveness of many computer vision applications depends on the whole image boundaries. In this paper, using the image thresholding and the implicit curve evolution fra…
Architecture-Driven Level Set Optimization: From Clustering to Sub-pixel Image Segmentation
2016
Thanks to their effectiveness, active contour models (ACMs) are of great interest for computer vision scientists. The level set methods (LSMs) refer to the class of geometric active contours. Comparing with the other ACMs, in addition to subpixel accuracy, it has the intrinsic ability to automatically handle topological changes. Nevertheless, the LSMs are computationally expensive. A solution for their time consumption problem can be hardware acceleration using some massively parallel devices such as graphics processing units (GPUs). But the question is: which accuracy can we reach while still maintaining an adequate algorithm to massively parallel architecture? In this paper, we attempt to…
A local level set method for liver segmentation in functional MR imaging
2011
Functional Magnetic Resonance (fMR) is a medical image technique in which a contrast is injected in the vascular system so that blood diffusion along it can be observed as variations of the signal intensity. The uptake variations of the contrast agent are used in early detection of tumorous tissue. For the diagnostic to be accurate, successive volumes must be correctly registered. For binary registration prior segmentation of the 3D fMR data is required. Here we present a local 3D level-set segmentation method which preserves details and edges, along with its multi-scale version which has the advantage of a great acceleration with respect to the single-scale version. Results of liver segmen…
An Automatic Differentiation Based Approach to the Level Set Method
2015
This paper discusses an implementation of the parametric level set method. Adjoint approach is used to perform the sensitivity analysis, but contrary to standard implementations, the state problem is differentiated in its discretized form. The required partial derivatives are computed using tools of automatic differentiation, which avoids the need to derive the adjoint problem from the governing partial differential equation. The augmented Lagrangian approach is used to enforce volume constraints, and a gradient based optimization method is used to solve the subproblems. Applicability of the method is demonstrated by repeating well known compliance minimization studies of a cantilever beam …
On a topology optimization problem governed by two-dimensional Helmholtz equation
2015
The paper deals with a class of shape/topology optimization problems governed by the Helmholtz equation in 2D. To guarantee the existence of minimizers, the relaxation is necessary. Two numerical methods for solving such problems are proposed and theoretically justified: a direct discretization of the relaxed formulation and a level set parametrization of shapes by means of radial basis functions. Numerical experiments are given. peerReviewed