Distance transforms (DTs) are standard tools in image analysis, with applications in image registration and segmentation. The DT is based on extremal (minimal) distance values and is therefore highly sensitive to noise. We present a stochastic distance transform (SDT) based on discrete random sets, in which a model of element-wise probability is utilized and the SDT is computed as the first moment of the distance distribution to the random set. We present two methods for computing the SDT and analyze them w.r.t. accuracy and complexity. Further, we propose a method, utilizing kernel density estimation, for estimating probability functions and associated random sets to use with the SDT. We evaluate the accuracy of the SDT and the proposed framework on images of thin line structures and disks corrupted by salt and pepper noise and observe excellent performance. We also insert the SDT into a segmentation framework and apply it to overlapping objects, where it provides substantially improved performance over previous methods. Finally, we evaluate the SDT and observe very good performance, on simulated images from localization microscopy, a state-of-the-art super-resolution microscopy technique which yields highly spatially localized but noisy point-clouds.

中文翻译：

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随机距离变换：理论，算法和应用

距离变换（DT）是图像分析中的标准工具，并在图像配准和分割中得到应用。DT基于极值（最小）距离值，因此对噪声高度敏感。我们提出基于离散随机集的随机距离变换（SDT），其中利用了逐元素概率模型，并且计算了SDT作为到随机集的距离分布的第一时刻。我们提出了两种计算SDT的方法，并分析了它们的准确性和复杂性。此外，我们提出了一种利用核密度估计来估计与SDT一起使用的概率函数和相关随机集的方法。我们评估了SDT和所提出的框架在细线结构和被盐和胡椒噪声破坏的磁盘上的图像的准确性，并观察了出色的性能。我们还将SDT插入分段框架，并将其应用于重叠的对象，与以前的方法相比，它可以显着提高性能。最后，我们在定位显微镜的模拟图像上评估了SDT并观察到了非常好的性能，