作为最小成本森林计算的标记分水岭算法的实现和复杂性
Implementation and complexity of the watershed-from-markers algorithm computed as a minimal cost forest
摘要：
分水岭算法属于数学形态学中的经典算法。Lotufo等人通过图像森林变换（IFT）发布了分水岭计算的原理，该变换从给定的标记计算最短路径森林。该算法本身是针对2D情况（图像）描述的，而没有详细讨论其对真实数据集的计算和内存需求。由于IFT巧妙地解决了高原问题，并且当必须分割薄对象时它给出了精确的结果，因此很明显，将该算法用于3D数据集，考虑到最小化3D情况下的较高内存消耗，而不会损失O（m+C）的低渐近时间复杂度（以及实际计算速度）。本文的主要目标是实现IFT算法的优先级队列桶和仔细调整这个实现，以达到尽可能最小的内存消耗。本文提出了五种可能的修改和方法的IFT算法的实施。所有提出的实现都保持了具有桶的标准优先级队列的时间复杂度，但是最好的实现最小化了昂贵的存储器分配，并且对于典型的3D医学成像数据集仅需要19-45%的存储器。通过IFT算法的简化实现了内存节省，该算法在临时结构中存储更多的元素，但这些元素更简单，因此需要更少的内存。最佳呈现的修改允许在当前可用的基于PC的工作站上以每体素12位或16位分割大型3D医学数据集（高达512 x512 x680体素）。
英文摘要：
The watershed algorithm belongs to classical algorithms in mathematical morphology. Lotufo et al. published a principle of the watershed computation by means of an Image Foresting Transform (IFT), which computes a shortest path forest from given markers. The algorithm itself was described for a 2D case (image) without a detailed discussion of its computation and memory demands for real datasets. As IFT cleverly solves the problem of plateaus and as it gives precise results when thin objects have to be segmented, it is obvious to use this algorithm for 3D datasets taking in mind the minimizing of a higher memory consumption for the 3D case without loosing low asymptotical time complexity of O(m+C) (and also the real computation speed). The main goal of this paper is an implementation of the IFT algorithm with a priority queue with buckets and careful tuning of this implementation to reach as minimal memory consumption as possible. The paper presents five possible modifications and methods of implementation of the IFT algorithm. All presented implementations keep the time complexity of the standard priority queue with buckets but the best one minimizes the costly memory allocation and needs only 19-45% of memory for typical 3D medical imaging datasets. Memory saving was reached by an IFT algorithm simplification, which stores more elements in temporary structures but these elements are simpler and thus need less memory. The best presented modification allows segmentation of large 3D medical datasets (up to 512x512x680 voxels) with 12-or 16-bits per voxel on currently available PC based workstations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
