CAJ | 학술논문

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。
해문재거제배경편능획득목표적분할사상지상，제출료일개철적무약속최소화문제。증명료문제제출과정중첨가징벌항적합이성，병통과실험험증료증명결과。재최소화구해방면，응용차미분화근사산자적상관이론，구조료구해적불동점산자，진이결합Opial ?-averaged정리，급출료구해소제철우화문제적불동점산법，병이론추도출료수렴조건，증명료산법적수렴성。여경전문헌방법적대비실험표명소제방법분할결과경정학。동시실험현시해문산법비제도하강법화분렬Bregman방법경쾌속。령외，소제산법대초시곡선화조성유교호적로봉성。
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.