Abstract Circle detection is a critical issue in pattern recognition and image analysis. Conventional geometry-based methods such as tangent or symmetry are sensitive to noise or occlusion. Area computation is more robust against noise, because it avoids differential calculations. Inspired by this characteristic, we present a novel method for fast circle detection using inscribed triangles. The proposed algorithm, which is robust to noise and resistant to occlusion, first extracts circular arcs by approximating line segments and identifying inflection points and sharp corners. To speed up the computation, irrelevant segments are filtered out through the triangle inequality. Arcs that belong to the same circle are then combined according to the position constraint and the inscribed triangle constraint. The circle parameters are further estimated by inscribed triangles based upon the Theil-Sen estimator and linear error refinement without the dependence of least-square fitting but still with the equivalent accuracy. Finally, candidate circles are verified to prune false positives through an inlier ratio rule, which jointly considers both distance and angle deviations. Extensive experiments are conducted on synthetic images including overlapping circles, and real images from four diverse datasets (three publicly available and one we built). Results are compared with those of representative state-of-the-art methods, and the proposed method is demonstrated to embraces several advantages: resistant to occlusion, more robust to noise, and better performance and efficiency.

中文翻译：

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使用内接三角形的抗遮挡圆检测器

摘要 圆检测是模式识别和图像分析中的一个关键问题。传统的基于几何的方法（例如切线或对称）对噪声或遮挡敏感。面积计算对噪声更稳健，因为它避免了差分计算。受此特性的启发，我们提出了一种使用内接三角形进行快速圆检测的新方法。所提出的算法对噪声具有鲁棒性并且抗遮挡，首先通过近似线段和识别拐点和尖角来提取圆弧。为了加快计算速度，通过三角不等式过滤掉不相关的部分。然后根据位置约束和内接三角形约束组合属于同一圆的弧。圆参数通过基于 Theil-Sen 估计器和线性误差细化的内接三角形进一步估计，而不依赖于最小二乘拟合，但仍具有等效精度。最后，通过联合考虑距离和角度偏差的内点比率规则验证候选圆以修剪误报。对合成图像进行了广泛的实验，包括重叠圆圈和来自四个不同数据集（三个公开可用的一个我们构建的一个）的真实图像。结果与具有代表性的最先进方法的结果进行了比较，并且证明了所提出的方法具有几个优点：抗遮挡、对噪声更鲁棒以及更好的性能和效率。