一种基于二维拉格朗日连续水平集的图像分割方法

在图像分割领域中，基于离散水平集的图像分割方法不但对低信噪比图像难以实现正确地分割，而且分割速度较慢。针对这一问题，该文提出了一个基于连续水平集的图像分割方法。利用2维拉格朗日基函数的线性组合把水平集函数表示成连续函数。最小化实现图像分割的能量函数，建立基函数系数演化的微分方程。因此能量函数的最小值可直接根据拉格朗日的系数值获得。利用简单有限差分法对系数演化微分方程求解，实现了低信噪比图像的快速分割。实验结果表明该方法具有理想的分割结果。

An Image Segmentation Approach Based on Two-Dimension Lagrange Continuous Level Set

In the field of image segmentation, the image segmentation approach based on discrete level set can not accurately segment an image with low SNR value, and the speed of image segmentation is lower. In order to solve these problems, an alternative approach is proposed based on continuous level-set. The level-set function is modeled as a continuous parametric function using the line combination of two-dimension Lagrange basis. The difference equation is derived by minimizing the energy formulation for image segmentation. As a consequence, the minimization of the energy formulation is directly obtained in term of the Lagrange coefficient. The fast segmentation of image with low SNR value is implemented by the numerical solution of the coefficient difference equation that is solved by simple finite-difference methods. Experimental results demonstrate that the proposed approach can gain better perfect effect.