概率霍夫变换（Progressive Probabilistic Hough Transform）原理详解

概率霍夫变换（Progressive Probabilistic Hough Transform）的原理很简单，如下所述：

1.随机获取边缘图像上的前景点，映射到极坐标系画曲线；

2.当极坐标系里面有交点达到最小投票数，将该点对应x-y坐标系的直线L找出来；

3.搜索边缘图像上前景点，在直线L上的点（且点与点之间距离小于maxLineGap的）连成线段，然后这些点全部删除，并且记录该线段的参数（起始点和终止点），当然线段长度要满足最小长度；

4.重复1. 2. 3.。

In "A real-time lane marking localization, tracking and communication system":

Hough transform (HT) was proposed in [30] and is usually used to detect lines and circles; it has been used as the core method of lane marking detection in [3] and [31]. The core formula of HT is:

λ=xcos(θ)+ysin(θ)

λ is the length between the origin and the pedal of detected line and θ is the angle of its perpendicular line.

In [32], Matas et al. proposed the PPHT, which has been commonly accepted as one of the best line detection methods based on Hought transform theory. The algorithm PPHT proceeds as follows:

1. Randomly, select a new point for voting in the accumulator array, with contributions to all available bins (as referenced in [32], bin stands for a pair of (λ, θ)). Then remove the selected pixel from the input image.

2. Check if the highest peak (the pair of (λ, θ) with the most voting points) in the updated accumulator is greater than a pre-defined threshold th(N). If not then go to Step 1.

3. Find all lines with the parameter (λ, θ) which was specified by the peak in Step 2. Choose the longest segment (which can be denoted by starting point Pt0 and ending point Pt1) of all lines.

4. Remove all the points of the longest line from the input image.

5. Remove all the points of the selected line in Step 3 (Pt0−Pt1) from the accumulator, which means those points do not attend any other voting process.

6. If the selected segment is longer than a pre-defined minimum length, then take the segment (Pt0−Pt1) as one of the output results.

7. Go to Step 1.

References:

[3] D.O. Cualain, C. Hughes, M. Glavin, E. Jones. Automotive standards-grade lane departure warning system. IET Intell. Transp. Syst., 6 (1) (2012), pp. 44–57

[30] P.V.C. Hough, A method and means for recognizing complex patterns, US Patent: 3,069,654 (1962).

[31] K. Zu. Realtime lane tracking of curved local road. Proceedings of the IEEE Intelligent Transportation Systems (2006), pp. 1149–1155

[32] J. Matas, C. Galambos, J. Kittler. Robust detection of lines using the progressive probabilistic hough transform. Comput. Vision Image Underst., 78 (1) (2000), pp. 119–137