基於魚眼投影幾何之物像對應模式鏡頭率定策略研擬

魚眼鏡頭因其超廣角之特性，故相較於一般廣角鏡頭更適用於需要一次性蒐集全景資訊之任務，如:環境監測、森林科學、顯露度測量、自駕車避障等相關應用需求。但伴隨而來的顯著影像變形，對於利用魚眼影像進行近景攝影測量高精度空間定位任務來說，鏡頭率定則為必要之。雖然類歸為光學鏡頭，但因應廣角取像，魚眼鏡頭設計之精確成像路徑並不適合以中心透視投影模式描述，故物像對應模式的適切性則成了決定空間定位品質的關鍵性因素，本研究為後續高精度(前方交會誤差毫米等級，或小於地面取樣距離)空間定位應用需求，故採用基於魚眼投影幾何所推導出的物像對應模式搭配附加參數吸納透鏡畸變差。為了精進魚眼鏡頭率定任務，本論文主要著眼於率定觀測資料蒐集面工作優化及最佳投影模式搜尋，並採取模擬實驗得到精確的率定策略，爾後即建立實際率定場並仿照模擬實驗之設計執行實際率定實驗，以定性及定量方式進行成果分析，檢視率定策略的有效性及實用性。根據以上所提方法所獲得研究成果顯示: 使用魚眼鏡頭幾何投影物像對應模式搭配附加參數之方法，經實驗證實可妥善地描述魚眼鏡頭之物像對應關係。除此之外，關於鏡頭率定策略，僅需於率定場中布設20個分布良好的率定標點以及位置適中的兩攝影站並採用自率光束法搭配次像元像點與毫米級控制點觀測量，即可獲得次像元後驗單位權標準差(0.24 pixels)與前方交會誤差毫米級(<5.6 mm，反投影約0.5pixels)之率定成果，具體展示本研究研議之方法及程序能有效及精準執行魚眼鏡頭率定，同時，物像對應品質亦足夠支援次像元等級的物空間定位應用。

關鍵字

魚眼鏡頭；透鏡畸變；單片後方交會；自適性自率光束法平差；自由網

並列摘要

Due to ultra wide-angle characteristics, fisheye lenses are widely used in artistic photography, surveillance application, forest science, self-driving obstacle avoidance, etc. Some applications that need to collect panoramic geo-information are especially suitable for using this kind of cameras. However, the imaging distortion of the fisheye image is significant, so the validity of fisheye lens calibration would largely depend on the correctness of geometric modelling between the image points and the object points. Since the fisheye lens has its own specific type of imaging formation, using collinearity equation attached by additional lens distortion parameters cannot set up a sufficient model. To achieve the relevant requirements of the metric measurement, this study adopts the rigorous object-image corresponding model to include geometric projection model for fisheye lens calibration. The discrepancy between the ideal image point and the actual image point is treated as the effect of lens distortion and modeled by additional parameters. This study aims to tackle effective implementation, including observation acquisition and optimal projection determination. Therefore, the contribution of this study is to support 3-D positioning with high precision under geometric projection models and to analyze, both quantitatively and qualitatively, the strategies of fisheye lens calibration. It is revealed from the experimental results that the object-to-image correspondence of fisheye lens based on the proposed model offers satisfactory geometric calibration quality. Strategically, the self-adatpive bundle adjustment with self-calibration for fisheye lens can be realized under sub-pixel image measurement quality at the expense of only 20 well-distributed coded targets and acquiring two images at appropriate locations to achieve the sub-pixel level of object point positioning. Thus, it is verified that the proposed methods and procedures can effectively and accurately implement the fisheye lens calibration. At the same time, the calibration result is also sufficient to support the mission of object point determination up to sub-pixel level quality.