Laplacian Coordinates: Theory and Methods for Seeded Image Segmentation
Laplacian Coordinates: Theory and Methods for Seeded Image Segmentation
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DOI：
10.1109/tpami.2020.2974475
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发表时间：
2020-02
影响因子：
23.6
通讯作者：
Wallace Casaca;J. P. Gois;H. C. Batagelo;G. Taubin;L. G. Nonato
中科院分区：
文献类型：
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作者：
Wallace Casaca;J. P. Gois;H. C. Batagelo;G. Taubin;L. G. Nonato
种子分割方法由于其在分割复杂图像方面的良好性能、易于使用以及与基于图表示的协同作用而受到了广泛的关注。这些方法通常依赖于复杂的计算工具，其性能在很大程度上取决于训练数据反映所寻求的图像模式的程度。此外，对图像轮廓的粘附性差、缺乏唯一解以及计算成本高是大多数种子分割方法中存在的其他常见问题。在这项工作中，我们介绍了拉普拉斯坐标，一个二次能量最小化框架，以有效和数学上合理的方式解决了上述问题。所提出的配方建立在图拉普拉斯算子，二次能量函数，和快速最小化方案，以产生高度准确的分割。此外，所提出的能量函数不倾向于局部最小值，即，该解决方案保证是全局最优的，这是大多数图像分割方法中不存在的特性。另一个关键的属性是，最小化过程导致一个受约束的稀疏线性方程组，使分割的高分辨率图像在交互式的速度。拉普拉斯坐标的有效性是证明了一套全面的比较，涉及九个国家的最先进的方法和几个基准广泛使用的图像分割文献。
Seeded segmentation methods have gained a lot of attention due to their good performance in fragmenting complex images, easy usability and synergism with graph-based representations. These methods usually rely on sophisticated computational tools whose performance strongly depends on how good the training data reflect a sought image pattern. Moreover, poor adherence to the image contours, lack of unique solution, and high computational cost are other common issues present in most seeded segmentation methods. In this work we introduce Laplacian Coordinates, a quadratic energy minimization framework that tackles the issues above in an effective and mathematically sound manner. The proposed formulation builds upon graph Laplacian operators, quadratic energy functions, and fast minimization schemes to produce highly accurate segmentations. Moreover, the presented energy functions are not prone to local minima, i.e., the solution is guaranteed to be globally optimal, a trait not present in most image segmentation methods. Another key property is that the minimization procedure leads to a constrained sparse linear system of equations, enabling the segmentation of high-resolution images at interactive rates. The effectiveness of Laplacian Coordinates is attested by a comprehensive set of comparisons involving nine state-of-the-art methods and several benchmarks extensively used in the image segmentation literature.