[Algebra and Analysis Seminar]
Xue-Cheng Tai (Hong Kong Baptist University)
Fast Algorithms for Euler´s Elastica energy minimization and applications
This talk is divided into three parts.
In the first part, we will introduce the essential ideas in using Augmented Lagrangian/operator-splitting techniques for fast numerical algorithms for minimizing Euler's Elastica energy.
In the 2nd part, we consider an Euler's elastica based image segmentation model. An interesting feature of this model lies in its preference of convex segmentation contour. However, due to the high order and non-differentiable term, it is often nontrivial to minimize the associated functional. In this work, we propose using augmented Lagrangian method to tackle the minimization problem. Especially, we design a novel augmented Lagrangian functional that deals with the mean curvature term differently as those ones in the previous works. The new treatment reduces the number of Lagrange multipliers employed, and more importantly, it helps represent the curvature more effectively and faithfully. Numerical experiments validate the efficiency of the proposed augmented Lagrangian method and also demonstrate new features of this particular segmentation model, such as shape driven and data driven properties.
In the 3rd part, we will introduce some recent fast algorithms for minimizing Euler's elastica energy for interface problems. The method combine level set and binary representations of interfaces. The algorithm only needs to solve an Rodin-Osher-Fatemi problem and a re-distance of the level set function to minimize the elastica energy. The algorithm is easy to implement and fast with efficiency.
The content of this talk is based joint works with Egil Bae, Tony Chan, Jinming Duan and Wei Zhu.