一种图像分割的快速不动点算法

李伟斌; 易贤; 宋松和

doi:10.11999/JEIT150112

一种图像分割的快速不动点算法

doi: 10.11999/JEIT150112

基金项目:

国家自然科学基金(11172314)

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- 被引次数: 0
出版历程
- 收稿日期: 2015-01-20
- 修回日期: 2015-05-11
- 刊出日期: 2015-10-19

Fast Fixed-point Algorithm for Image Segmentation

Funds:

The National Natural Science Foundation of China (11172314)

摘要

摘要: 该文在去除背景便能获得目标的分割思想之上，提出了一个凸的无约束最小化问题。证明了问题提出过程中添加惩罚项的合理性，并通过实验验证了证明结果。在最小化求解方面，应用次微分和近似算子的相关理论，构造了求解的不动点算子，进而结合Opial -averaged定理，给出了求解所提凸优化问题的不动点算法，并理论推导出了收敛条件，证明了算法的收敛性。与经典文献方法的对比实验表明所提方法分割结果更精确。同时实验显示该文算法比梯度下降法和分裂Bregman方法更快速。另外，所提算法对初始曲线和噪声有较好的鲁棒性。
- 图像处理 /
- 图像分割 /
- 凸优化问题 /
- 不动点算法
Abstract: Based on the idea that objects in a given image can be segmented by removing the background part, an unconstrained convex minimization problem is proposed. The penalization term added in the construction procedure of the proposed problem is proven to be viable, which is demonstrated by the experiment. At the computational level, a fixed-point operator and the corresponding algorithm are proposed by applying the theory of subdifferential and proximity operators, and Opial -averaged theorem. And then the convergence proof of the algorithm is given. Comparisons with other classical models show that the proposed segmentation model is more accurate. And the experiments also demonstrate that the fixed-point algorithm is faster than the gradient descent method and the split Bregman method. Moreover, the algorithm is robust to the initial curve and noise.
- Image processing /
- Image segmentation /
- Convex optimization /
- Fixed-point algorithm

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参考文献(19)

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