摘要
二值图像的直线检测过程中 ,标准霍夫变换算法的计算量为 O(N3) .该文提出一种快速霍夫变换算法 ,其计算量仅为 O(N2 log2 N) .该快速算法可以并行实现 ;处理器阵列规模为 O(N2 )时 ,计算量为 O(log2 N) .文中还分析得到快速算法的误差上界 ,并提出一种改进的快速霍夫变换算法以获得更高的计算精度 .最后 ,给出算法的数值算例 .理论分析及数值算例都表明 ,该文的快速霍夫变换算法在直线检测过程中有着更高的计算效率 ,并且具有良好的计算精度 .
Since Hough publicized the method and means of recognizing complex patterns in his patent (1962), the Hough Transform is applied widely in the fields of pattern recognition and computer vision, and the properties of Hough Transform have been studied by many people. The Fast Hough Transform (FHT) algorithm and the Modified Fast Hough Transform (MFHT) algorithm designed in this paper aim at reducing the algorithm complexity and improving the computing efficiency in the line detection for the binary image. On the computational problem of FHT, many forerunners such as R E Cypher, C Guerra, Y Pan and J F Jenq et al. took parallel processing strategies and got some valuable results. In the paper, we design the FHT and MFHT methods as serial algorithms, but they can be implemented by parallel processing.It is well known that the standard Hough Transform algorithm (SHT) requires time O(N 3). But, the FHT algorithm proposed in this paper requires computational time O(N 2log 2N). The algorithm can be implemented by parallel processing, and it requires time O(log 2N) for O(N 2) processors. In section 2, we give the fundamental principle of our method, and then describe the FHT and analyze its complexity. In section 3, based on some definition we introduced, the error bound of the FHT algorithm is analyzed, and the result is shown in Theorem 1. In section 4, we design the MFHT algorithm in order to get better precision in the computation. The compare of computational complexity and error bound between SHT, FHT and MFHT methods are illustrated. In section 5, some numerical examples are presented. Our research results about fast Hough Transform are summarized in section 6.The theoretical analysis and the numerical examples in the paper indicate that algorithms designed in the paper have better properties for the computing efficiency and the computing precision in the line detection procedure.
出处
《计算机学报》
EI
CSCD
北大核心
2001年第10期1102-1109,共8页
Chinese Journal of Computers
