Fast Fixed-point Algorithm for Image Segmentation
Funds:
The National Natural Science Foundation of China (11172314)
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摘要: 該文在去除背景便能獲得目標的分割思想之上，提出了一個凸的無約束最小化問題。證明了問題提出過程中添加懲罰項的合理性，并通過實驗驗證了證明結(jié)果。在最小化求解方面，應(yīng)用次微分和近似算子的相關(guān)理論，構(gòu)造了求解的不動點算子，進而結(jié)合Opial -averaged定理，給出了求解所提凸優(yōu)化問題的不動點算法，并理論推導(dǎo)出了收斂條件，證明了算法的收斂性。與經(jīng)典文獻方法的對比實驗表明所提方法分割結(jié)果更精確。同時實驗顯示該文算法比梯度下降法和分裂Bregman方法更快速。另外，所提算法對初始曲線和噪聲有較好的魯棒性。
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關(guān)鍵詞:
- 圖像處理 /
- 圖像分割 /
- 凸優(yōu)化問題 /
- 不動點算法
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.-
Key words:
- Image processing /
- Image segmentation /
- Convex optimization /
- Fixed-point algorithm
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