Linear Time Algorithms for Exact Distance Transform
Linear Time Algorithms for Exact Distance Transform
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DOI：
10.1007/s10851-010-0232-4
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发表时间：
2011-03-01
影响因子：
2
通讯作者：
Grevera, George J.
中科院分区：
文献类型：
--
作者：
Ciesielski, Krzysztof Chris;Chen, Xinjian;Grevera, George J.
2003年，Maurer et al.(IEEE传输。肛门图案。马赫。英特尔。25：265-270,2003)发表的一篇论文描述了一种算法，该算法计算k维空间a“e(K)中的矩形二进制图像在线性时间内的精确距离变换(相对于图像大小)和对于1a每千货币部分路标测量的距离，其中包括欧几里德距离L(2)。本文从理论和实践两个方面对该算法进行了讨论。在实际应用方面，我们集中讨论了它的欧几里德距离版本，讨论了将其实现为符号距离变换的可能方法，并对所实现的算法进行了实验比较。我们还描述了这些算法的并行化，并讨论了与它们相关的计算时间节约。所有这些实施将作为我们小组开发和维护的CAVASS软件系统的一部分提供(Grevera等人。在J.Digit。成像20：101-118,2007)。在理论方面，我们证明了我们的带符号距离变换算法GBDT返回到几何定义的对象边界的距离的精确值。我们提供了一个完整的证据(Maurer等人没有给出)。(IEEE传输。肛门图案。马赫。英特尔。25：265-270,2003)证明了这些算法对L(P)-度量1<；p<；a都是正确的。我们还指出了Maurer等人算法的精确形式。(IEEE传输。肛门图案。马赫。英特尔。25：265-270,2003)对于L(1)和L(A)的指标没有很好的定义。此外，我们还证明了该算法可以用来在线性时间内求出物体直径的精确值，即物体任意两个元素之间的最大可能距离。
In 2003, Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265-270, 2003) published a paper describing an algorithm that computes the exact distance transform in linear time (with respect to image size) for the rectangular binary images in the k-dimensional space a"e (k) and distance measured with respect to L (p) -metric for 1a parts per thousand currency signpa parts per thousand currency signa, which includes Euclidean distance L (2). In this paper we discuss this algorithm from theoretical and practical points of view. On the practical side, we concentrate on its Euclidean distance version, discuss the possible ways of implementing it as signed distance transform, and experimentally compare implemented algorithms. We also describe the parallelization of these algorithms and discuss the computational time savings associated with them. All these implementations will be made available as a part of the CAVASS software system developed and maintained in our group (Grevera et al. in J. Digit. Imaging 20:101-118, 2007). On the theoretical side, we prove that our version of the signed distance transform algorithm, GBDT, returns the exact value of the distance from the geometrically defined object boundary. We provide a complete proof (which was not given of Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265-270, 2003) that all these algorithms work correctly for L (p) -metric with 1 < p < a. We also point out that the precise form of the algorithm from Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265-270, 2003) is not well defined for L (1) and L (a) metrics. In addition, we show that the algorithm can be used to find, in linear time, the exact value of the diameter of an object, that is, the largest possible distance between any two of its elements.