IEEE Trans Image Process. 2013 Dec;22(12):5322-35. doi: 10.1109/TIP.2013.2279952.
This paper presents the first framework capable of performing active contour segmentation using Earth Mover's Distance (EMD) to measure dissimilarity between multidimensional feature distributions. EMD is the best known and understood cross-bin histogram distance measure, and as such it allows for meaningful comparisons between distributions, unlike bin-to-bin measures that only account for discrepancies on a bin-to-bin basis. Because EMD is obtained with linear programming techniques, its differential structure with respect to variations in bin weights as the active contour evolves is expressed through sensitivity analysis. Euler-Lagrange equations are then derived from the computed sensitivity at every iteration to produce gradient descent flows. We validate our approach with color image segmentation, in comparison with state-of-the-art Bhattacharyya (bin-to-bin) and 1D EMD (cross-bin) active contours. Some unique advantages of cross-bin comparison are highlighted in our segmentation results: better perceptual value and increased robustness with respect to the initialization.
本文提出了第一个使用基于距离的主动轮廓分割框架，该框架使用基于 Earth Mover's Distance (EMD) 的多维特征分布之间的差异来测量。EMD 是最著名和最被理解的跨箱直方图距离度量，因此它允许在分布之间进行有意义的比较，而不像仅在箱到箱的基础上考虑差异的箱到箱度量。由于 EMD 是通过线性规划技术获得的，因此它在主动轮廓演变过程中关于箱权重变化的微分结构是通过敏感性分析来表示的。然后，从每次迭代计算的灵敏度推导出欧拉-拉格朗日方程，以产生梯度下降流。我们通过与基于贝叶斯（箱到箱）和一维 EMD（跨箱）主动轮廓的彩色图像分割进行比较，验证了我们的方法。在我们的分割结果中，突出了跨箱比较的一些独特优势：更好的感知价值和对初始化的更高鲁棒性。
