Self-consistent gradient flow for shape optimization.
Optim Methods Softw
; 32(4): 790-812, 2017 Jul 04.
Article
em En
| MEDLINE
| ID: mdl-28670104
ABSTRACT
We present a model for image segmentation and describe a gradient-descent method for level-set based shape optimization. It is commonly known that gradient-descent methods converge slowly due to zig-zag movement. This can also be observed for our problem, especially when sharp edges are present in the image. We interpret this in our specific context to gain a better understanding of the involved difficulties. One way to overcome slow convergence is the use of second-order methods. For our situation, they require derivatives of the potentially noisy image data and are thus undesirable. Hence, we propose a new method that can be interpreted as a self-consistent gradient flow and does not need any derivatives of the image data. It works very well in practice and leads to a far more efficient optimization algorithm. A related idea can also be used to describe the mean-curvature flow of a mean-convex surface. For this, we formulate a mean-curvature Eikonal equation, which allows a numerical propagation of the mean-curvature flow of a surface without explicit time stepping.
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Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Optim Methods Softw
Ano de publicação:
2017
Tipo de documento:
Article
País de afiliação:
Áustria