基于共形几何代数与Radon变换的圆检测方法

Circle Detection Algorithm Based on Conformal Geometric Algebra and Radon Transform

为解决图像中的目标检测问题,本文给出了一种基于共形几何代数与Radon变换的圆检测识别方法,从新的角度出发,讨论了运用共形几何代数概念来解决圆检测问题的可行性和简便性。该方法主要是通过共形几何代数理论,将欧氏空间中的圆用共形几何代数中的矢量表示,进而可以等效为平面,最后利用三维Radon变换,对空间中的平面进行检测,可以有效地检测识别图像中的圆形目标。实验结果表明该算法简洁明确,可以对图像中的多圆进行同时检测识别,对于算法的集成,提高效率有着很重要的意义。

To meet the need of object detection problem in images, a circle detection algorithm based on conformal geometric algebra and Radon transform is proposed. From a new point of view, the probability and simplicity for using the concept of conformal geometric algebra to solve circle detection problem is discussed in detail. Circles in Euclidean space can be represented as vectors by the conformal geometric algebra theory, a circle may be implemented as a plane in conformal space, and the plane in conformal space can be detected by 3D radon transform. This algorithm can detect circles in images effectively. The experimental results show that the proposed algorithm is compact and explicit, multi-circles in images can be detected by using this algorithm, and the integration of algorithm has an important significance in the improvement of efficiency.