On optimal linear filtering for edge detection
On optimal linear filtering for edge detection
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DOI：
10.1109/tip.2002.800887
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发表时间：
2002-07
期刊：
影响因子：
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通讯作者：
D. Demigny
中科院分区：
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作者：
D. Demigny
在本文中，我们将重新讨论Canny边缘检测质量的三个标准的解析表达式：良好的检测，良好的定位和低错误检测的多重性。我们的工作与Canny的工作在两个关键点上有所不同。这里给出的准则适用于离散采样信号，也就是说，适用于实际实现的滤波器。我们使用不同宽度的脉冲作为输入信号，而不是单步边缘。其他边缘的接近程度会影响检测过程的质量。这些标准的新表述考虑到了这一点。我们为每个标准和它们的任何组合推导出最优过滤器。特别地，我们定义了一个最大限度地检测和定位的原始滤波器，以及同时最大化三个标准的最优滤波器的简单近似。计算标准的上界，允许用户测量任何滤波器的绝对和相对性能（指数，德里希和高斯滤波器的一阶导数进行评估）。当检测分辨率固定时，我们的准则也可用于计算给定滤波器的尺度参数的最优值。
In this paper, we will revisit the analytical expressions of the three Canny's criteria for edge detection quality: good detection, good localization, and low multiplicity of false detections. Our work differs from Canny's work on two essential points. Here, the criteria are given for discrete sampled signals, i.e., for the real, implemented filters. Instead of a single-step edge as input signal, we use pulses of various width. The proximity of other edges affects the quality of the detection process. This is taken into account in the new expressions of these criteria. We derive optimal filters for each of the criteria and for any combination of them. In particular, we define an original filter which maximizes detection and localization and a simple approximation of the optimal filter for the simultaneous maximization of the three criteria. The upper bounds of the criteria are computed which allow users to measure the absolute and relative performance of any filter (exponential, Deriche, and first derivative of Gaussian filters are evaluated). Our criteria can also be used to compute the optimal value of the scale parameter of a given filter when the resolution of the detection is fixed.