数字图像中丝状目标的快速渐近检测
Fast and Asymptotically Powerful Detection for Filamentary Objects in Digital Images
摘要：
给定一个嵌入在噪声图像中的非均匀链，我们考虑这样的嵌入链是可检测的条件。许多应用，如运动目标检测、船舶航迹检测等，都可以抽象为链的存在性检测。在这项工作中，我们提供了检测算法的计算复杂度低的顺序来检测链和最佳的理论检测能力的SNR（信噪比）下的正态分布模型。具体来说，我们推导出一个分析阈值，指定什么是可检测的。我们设计了一个最长有效链检测算法，其计算复杂度为$O(n\log n)$数量级。我们还证明了我们提出的算法是渐近强大的，这意味着，作为维度$n \rightarrow \infty$，错误检测的概率为零。最后给出了一些模拟算例和一个实际数据算例，验证了理论的正确性.
英文摘要：
Given an inhomogeneous chain embedded in a noisy image, we consider the conditions under which such an embedded chain is detectable. Many applications, such as detecting moving objects, detecting ship wakes, can be abstracted as the detection on the existence of chains. In this work, we provide the detection algorithm with low order of computation complexity to detect the chain and the optimal theoretical detectability regarding SNR (signal to noise ratio) under the normal distribution model. Specifically, we derive an analytical threshold that specifies what is detectable. We design a longest significant chain detection algorithm, with computation complexity in the order of $O(n\log n)$. We also prove that our proposed algorithm is asymptotically powerful, which means, as the dimension $n \rightarrow \infty$, the probability of false detection vanishes. We further provide some simulated examples and a real data example, which validate our theory.
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