基于稳态偏微分方程的几何形状特征提取
Geometric Shape Features Extraction Using a Steady State Partial Differential Equation System
摘要：
本文提出了一种将稳态偏微分方程（PDE）系统作为边值问题来处理的从二值图像数据中提取几何形状特征的统一方法。偏微分方程和函数的制定，以提取厚度，方向，和骨架同时进行。所提出的方法的主要优点是，方向的定义没有衍生物和厚度的计算是不强加的拓扑约束的目标形状。一个一维的解析解提供了验证所提出的方法。此外，二维数值算例证实了所提出的方法的有效性。
英文摘要：
A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to extract the thickness, orientation, and skeleton simultaneously. The main advantages of the proposed method is that the orientation is defined without derivatives and thickness computation is not imposed a topological constraint on the target shape. A one-dimensional analytical solution is provided to validate the proposed method. In addition, two-dimensional numerical examples are presented to confirm the usefulness of the proposed method.
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