In this paper we consider the multiple geometrical object detection problem. On the basis of the set \(\mathcal {A}\) containing data points coming from and scattered among a number of geometrical objects not known in advance, we should reconstruct or detect those geometrical objects. A new efficient method for solving this problem based on the popular RANSAC method using parameters from the DBSCAN method is proposed. Thereby, instead of using classical indexes for recognizing the most appropriate partition, we use parameters from the DBSCAN method which define the necessary conditions proven to be far more efficient. Especially, the method is applied to solving multiple circle detection problem. In this case, we give both the conditions for the existence of the best circle as a representative of the data set and the explicit formulas for the parameters of the best circle. In the illustrative example, we consider the multiple circle detection problem for the data point set \(\mathcal {A}\) coming from 5 intersected circles not known in advance. The method is tested on numerous artificial data sets and it has shown high efficiency. The comparison of the proposed method with other well-known methods of circle detection in real-world images also indicates a significant advantage of our method.

在本文中，我们考虑了多个几何物体检测问题。基于包含来自和散布在许多事先未知的几何对象中的数据点的\（\ mathcal {A} \）集合，我们应该重构或检测这些几何对象。提出了一种新的有效方法，该方法基于流行的RANSAC方法，使用DBSCAN方法中的参数进行求解。因此，我们不是使用经典索引来识别最合适的分区，而是使用来自DBSCAN的参数定义必要条件的方法被证明是更加有效的。特别地，该方法用于解决多圆检测问题。在这种情况下，我们既给出了代表数据集的最佳圆的存在条件，又给出了最佳圆的参数的明确公式。在说明性示例中，我们考虑来自5个事先未知的相交圆的数据点集\（\ mathcal {A} \）的多圆检测问题。该方法在大量的人工数据集上进行了测试，并且显示出很高的效率。所提出的方法与现实世界图像中其他众所周知的圆圈检测方法的比较也表明了我们方法的显着优势。