论文标题
数字图像中对丝状物体的快速和渐近的功能检测
Fast and Asymptotically Powerful Detection for Filamentary Objects in Digital Images
论文作者
论文摘要
给定嵌入在嘈杂图像中的不均匀链，我们考虑可检测到这种嵌入式链的条件。许多应用程序，例如检测移动对象，检测船只唤醒，可以抽象为对链的存在的检测。在这项工作中，我们提供了具有低计算复杂性的检测算法，以检测链和正态分布模型下SNR（信号与噪声比）的最佳理论可检测性。具体而言，我们得出一个分析阈值，该阈值指定可检测到的阈值。我们设计了最长的链条检测算法，其计算复杂性按$ O（n \ log n）$为顺序。我们还证明，我们提出的算法在渐近强大的功能上，这意味着尺寸$ n \ rightarrow \ infty $，错误检测的可能性消失了。我们进一步提供了一些模拟示例和一个真实的数据示例，这些示例验证了我们的理论。
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.
