• CN:11-2187/TH
  • ISSN:0577-6686

›› 2012, Vol. 48 ›› Issue (14): 17-24.

• 论文 • 上一篇    下一篇



  1. 沈阳航空航天大学航空宇航工程学院
  • 发布日期:2012-07-20

3D Shape Measurement Method Based on New System Mathematic Model

QU Xuejun;SONG Yuewen;WANG Yong;HAN Zhiren;ZHANG Lingyun   

  1. School of Astronautics, Shenyang Aerospace University
  • Published:2012-07-20

摘要: 提出新的测量系统数学模型,将投影仪投射光场视为由相位值唯一标识的光投射面的集合所形成的空间,将摄像机成像模型视为一种由成像点图像坐标确定的成像射线形成的集合,将被测点视为所对应的投射面与成像射线的交点。以此为理论基础,采用逆向求解法建立投影仪的数学模型,避免显示标定投影仪的复杂操作过程。将离心畸变与径向畸变分解为两个独立的过程顺序求解,再使用小孔成像模型建立消除畸变后的摄像机数学模型。采用平面靶标自由移动法采集足够多的标定数据,对标定靶的尺寸与位置要求不严,并且在不要求标定数据充满整个视场空间的情况下仍可获得完整的标定结果。本标定过程对系统位置无任何严格要求,同时摆脱对精密位移装置的需求,并有效地消除摄像机与投影仪镜头畸变所产生的标定误差。

关键词: 镜头畸变, 三维重构, 系统标定, 相位测量轮廓术

Abstract: A new measurement model is proposed to solve this problem, in which the projector light field is regarded as the space swept by projection planes marked by their phase values, and the camera model is regarded as the collection of rays marked by their image coordinates, then the point on the measured part can be determined as the intersection point of corresponding projection plane and the image ray. Based on above analysis, the reverse method for solving the mathematic model of the projector is proposed, which has the benefit of avoiding calibrating projector explicitly. The radical and tangential lens distortion coefficients of the camera are solved by two separately separate steps, and then the camera model can be set up according to the pinhole image model. Enough calibration foundation data is collected by the planar target free location method, so the location and size of the target is no longer been restricted strictly, and the complete calibration result can still be fulfilled while the calibration data is not cover the entire view space. Benefits of our calibration method are that strict construction assembly requirement and accurate displacement device are no longer being needed, and the calibration error caused by lens distortion of both the projector and the camera can be eliminated effectively.

Key words: 3D reconstruction, Lens distortion, Phase measurement profilometry (PMP), System calibration