以能量法觀點看影像中縮短物件邊界

Shortening on Boundary of Components in Image with Viewpoints from Energy Method

嚴炳欽(Ping-Chin Yen)

指導教授 ： 王藹農

國立臺灣大學/理學院/應用數學科學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201600512

摘要

能量法是一個藉由把相對應的能量泛函極小化，找出臨界點或臨界函數很好用的工具。在這篇論文當中，我們會介紹一些從偏微分方程式分析或泛函分析觀點而有的模型，用來把影像中某相對應的物件邊界極小化及將邊界設為零位集的問題。那些泛函的唯一性也會一同引入。最後，我們會加進一些分析的部份去看這些影像科學的模型的特性。

關鍵字

影像科學 ； 能量泛函 ； 能量法

並列摘要

Energy method is an applicable tool in finding critical points or functions by minimizing a respective functional. In this thesis we will introduce some models in perspectives of PDE analysis and functional analysis to minimize the boundaries of images and consider in case that boundaries are 0-level set for their respective component. Uniqueness of such functionals will also be introduced together with above. Eventually, analytical parts will be included in models to see some properties inside such models which work on imaging sciences.

並列關鍵字

Imaging Sciences ； Energy Functional ； Energy Method

參考文獻

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[2.] Oliver C. Schnürer, Felix Schulze, SELF-SIMILARLY EXPANDING NETWORKS TO CURVE SHORTENING FLOW (2007)

[3.] Selim Esedoglu, Yen-Hsi Richard Tsai, Threshold Dynamics for the Piecewise Constant Mumford–Shah Functional, Journal of Computational Physics 211 (2006) 367-384

[4.] Selim Esedoglu, Steven Ruuth, Richard Tsai, Diffusion Generated Motion Using Signed Distance Functions, Journal of Computational Physics 229 (2010) 1017-1042