摘要翻译：
在基于区域的图像分割和修复中，我们提出了第一种处理曲率规律性的方法，该方法与初始化无关。为此，我们从基于曲面延拓约束的基于长度的优化方案出发，讨论了与现有方案的联系。该公式以a\emph{cell复合体}为基础，考虑了基本区域和边界单元。将相应的优化问题转换为整数线性规划。然后我们展示了如何将该方法扩展到包括曲率正则性，再次转换为整数线性规划。这里，我们考虑的是反映曲率的边界元对。此外，还导出了一个约束集，以确保边界变量确实反映区域变量所描述的区域的边界。结果表明，通过求解线性规划松弛法，曲率正则比标准长度正则更适合于细长物体的存在。
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英文标题：
《A linear framework for region-based image segmentation and inpainting
  involving curvature penalization》
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作者：
Thomas Schoenemann, Fredrik Kahl, Simon Masnou and Daniel Cremers
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最新提交年份：
2011
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Computer Vision and Pattern Recognition        计算机视觉与模式识别
分类描述：Covers image processing, computer vision, pattern recognition, and scene understanding. Roughly includes material in ACM Subject Classes I.2.10, I.4, and I.5.
涵盖图像处理、计算机视觉、模式识别和场景理解。大致包括ACM课程I.2.10、I.4和I.5中的材料。
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一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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英文摘要：
  We present the first method to handle curvature regularity in region-based image segmentation and inpainting that is independent of initialization.   To this end we start from a new formulation of length-based optimization schemes, based on surface continuation constraints, and discuss the connections to existing schemes. The formulation is based on a \emph{cell complex} and considers basic regions and boundary elements. The corresponding optimization problem is cast as an integer linear program.   We then show how the method can be extended to include curvature regularity, again cast as an integer linear program. Here, we are considering pairs of boundary elements to reflect curvature. Moreover, a constraint set is derived to ensure that the boundary variables indeed reflect the boundary of the regions described by the region variables.   We show that by solving the linear programming relaxation one gets quite close to the global optimum, and that curvature regularity is indeed much better suited in the presence of long and thin objects compared to standard length regularity.
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PDF链接：
https://arxiv.org/pdf/1102.3830