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N-Point Hough transform for line detection

机译：N点霍夫变换用于线路检测

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In this paper, we introduce the N-point Hough transform for the detection of a large number of planar lines in a noisy image. The N-point Hough transform yields the randomized Hough transform and the three-point Hough transform if we set N = 2 and N = 3, respectively. From the viewpoint of the number of sample points required for the computation of lines, the N-point Hough transform is a generalization of the usual randomized Hough transform. The three-point Hough transform is introduced to increase the speed of the randomized Hough transform; the third point is used to avoid the selection of meaningless first and second sample points, which are used for the computation of the parameters of a line. This additional sample point guarantees the accuracy and robustness of a line detected using the first and second sample points. The N-point Hough transform evaluates the accuracy and robustness of a computed line using additional (N - 2) points for each line. The evaluation in the N-point Hough transform is achieved by counting the cardinality of sample points in the neighborhood of this line as the support of the sample points for the acceptance of this line. First, to define the neighborhood of a line mathematically, in this paper we clarify the relationship between a line and a set of parameters in the voting space using geometric duality. This relationship allows us to define a metric in the voting space. The metric is used for the clustering of bins in the spherical voting space to guarantee the accurate and robust computation of lines. Finally, we evaluate the performance of the N-point Hough transform by comparing it with the randomized Hough transform, which is the two-point Hough transform in our framework of the voting method. This comparative study shows the geometric and computational advantages of the N-point Hough transform.
机译：在本文中，我们介绍了用于检测噪声图像中大量平面线的N点霍夫变换。如果分别设置N = 2和N = 3，则N点霍夫变换将产生随机霍夫变换和三点霍夫变换。从计算线所需的采样点数的观点来看，N点霍夫变换是通常的随机霍夫变换的概括。引入三点霍夫变换以提高随机霍夫变换的速度。第三点用于避免选择无意义的第一和第二采样点，这些点用于计算线的参数。该附加采样点保证了使用第一和第二采样点检测到的直线的准确性和鲁棒性。 N点霍夫变换使用每条线的附加（N-2）点来评估计算线的准确性和鲁棒性。通过对这条线附近的采样点的基数进行计数，以此作为接受该线的采样点的支持，可以实现N点霍夫变换的评估。首先，在数学上定义一条直线的邻域，在本文中，我们使用几何对偶来阐明一条直线与投票空间中一组参数之间的关系。这种关系使我们可以在投票空间中定义指标。该度量标准用于球形投票空间中的bin聚类，以确保线的准确和鲁棒计算。最后，我们将N点霍夫变换与随机霍夫变换（在我们的投票方法框架中为两点霍夫变换）进行比较，从而评估其性能。这项比较研究显示了N点霍夫变换的几何和计算优势。

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