This study introduces a novel and efficient least squares based method for rectangle fitting, using a continuous fitness function that approximates a unit square accurately. The proposed method is compared with the existing method in the literature using both simulated data and real data. The real data is derived from aerial photogrammetry point clouds of a rectangular building. The simulated tests show that the proposed method performs better than the reference method, reducing the root-mean-square error by about 93% and 14% for clean datasets and noisy point clouds, respectively. The proposed method also improves the fitting of the real dataset by about 81%, achieving centimetre level accuracy. Furthermore, the test results show that the proposed method converges in fewer than 10 iterations.

翻译：本研究提出一种新颖且高效的基于最小二乘的矩形拟合方法，采用连续适应度函数精确逼近单位正方形。通过与文献中现有方法进行模拟数据和实测数据的对比，验证了该方法的性能。实测数据来源于航空摄影测量点云中矩形建筑的数据。模拟实验表明，所提方法优于参考方法：对于纯净数据集和含噪声点云，均方根误差分别降低约93%和14%。在处理真实数据集时，该方法拟合精度提升约81%，达到厘米级精度。此外，测试结果显示该方法可在少于10次迭代内收敛。