基于点云的球面三维逆向建模

3D Converse Modeling for Sphere Point Cloud

球面拟合是三维逆向建模中面临的亟待解决的复杂难题之一。它广泛应用于零件检测、建筑物结构恢复建模、医学血管和细胞模拟领域。论文改进了对三维球面点云进行直接拟合的方法,得到球面的相关几何参量,并在速度和精确度上都获得了提高。论文对拟合相关参数和噪声影响进行分析,并否定了对选定的数据集分组整合的算法。LM(Levenberg-Marquardt)算法是最广泛应用的最小二乘法二次曲面拟合的方法之一,本算法在与LM算法的对比中凸显了算法在时间和某些情况下精度的优越性,为进一步研究三维图形拟合重建恢复等工作打下了基础。

Sphere fitting is one of the complex and waiting prompt solution problems in the field of 3D Converse Modeling,which can be used for the parts detection,the recovery of the architecture,medicine and so on.The paper offers a method to directly fit sphere,called DF algorithm,and acquire the geometric parameters with improvement at speed and accuracy.The paper also pays attention to data analysis for the cause of the results and the comparison with the LM（Levenberg-Marquardt） algorithm,which is the one of the most widely used nonlinear least square methods,laying foundations for the rebuilding the parts and the gives of the further work.