非接觸式三維輪廓量測空間映射函數演算法

A Novel Coordinate Mapping Algorithm for 3-D Profile Non-contact Measurement

林高輝(Kau-Hui Lin) ； 張維哲(Wei-Che Chang) ； 章明(Ming Chang)

《中原學報》 31卷3期 (2003/09) Pp. 181-187

https://doi.org/10.6358/JCYU.200309.0181

摘要

本研究提出一種新式的非接觸式三維座標量測技術及系統校正方式，可由數位影像直接求得空間中待測物體的三維座標。此簡單有效的校正技術是採用最小平方法的技巧，藉由在空間中一系列已知座標的三維空間校正網格特徵點與其對映成像於雙CCD攝影機二維影像平面之特徵點座標，即可建構出眞實空間與雙CCD影像空間的關係式，任何在CCD影像空間的待測物，均可透過此三維空間映射函數關係式的運算，找到其在眞實空間中的實際位置座標值，此演算法不僅有效減少三維尺寸量測時所需之龐大運算，更可提升量測的速度及精度。以目前的系統進行實測的結果，在80mm×60mm×60mm的量測空間中，其量測最大誤差量爲0.15mm、標準差爲0.061mm，顯示本量測法有潛力發展成爲一套快速且精確的非接觸式三次元座標量測系統。

關鍵字

三維座標量測 ； 映射函數 ； 立體視覺 ； 最小平方多項式

並列摘要

A novel approach to a measuring methodology and calibration method for 3-D coordinate non-contact measurement has been developed. This algorithm introduces variables that relate the output digital image directly to the viewed 3-D object. A simple and efficient calibration procedure is achieved using the least-squares technique. It takes advantage of a 2-D coordinate mapping relation along with dual CCD cameras and a 3-D calibration grid consisting of a series of characteristic points with known coordinates in real space. The space coordinates of these characteristic points are compared to their image coordinates in the CCDs. A 3-D mapping function between the actual space and its image planes in the dual CCD cameras is then constructed. The relationship between the two is determined accordingly and can be applied to extract 3-Dinformation from a tested object sitting in a specific space with satisfactory accuracy. This algorithm not only significantly reduces the 3-D measurement computations, but also increases the measurement precision and speed. Current experimental results show that the accuracy of measurement is 0.13mm and the standard deviation is 0.061 in a bounded space of 80mm×60mm×60mm. This result reveals that this measurement algorithm has the potential to be an effective positioning method for rapid and precise non-contact coordinate measuring systems.

並列關鍵字

3-D coordinate measurement ； mapping function ； stereo vision ； least-squares polynomial