Flange docking and positioning are crucial steps in the unloading process of liquefied natural gas (LNG). The precise extraction of the inner diameter and elliptical contour of a flange is a prerequisite for achieving the pose positioning of the flange, based on the elliptical feature curve. Given that current ellipse extraction methods struggle to accurately extract the inner diameters of flanges in the presence of localized bright spots, a robust ellipse extraction method that is tailored for flange inner diameters is proposed. First, the flange region in the image is localized using YOLOv4 to narrow the target scope. Subsequently, the fast ellipse detection based on the arc adjacency matrix (AAMED) is employed to preliminarily extract the elliptical contour of the flange inner diameter. Finally, geometric constraints are established to gradually approximate the edge of the flange inner diameter. For the highlight regions present on the edge of the flange, the extracted elliptical arc segments are further optimized through the curvature characteristics of arcs and slope variation characteristics between line segments segmented from arcs. These optimized arc segments are then used to fit the ellipse. Experiments are conducted using large caliber LNG unloading flanges to verify the accuracy and robustness of this method in ellipse extraction. The proposed method ensures ellipse extraction error within 1 pixel and localizes the centers of flanges via monocular vision based on ellipse feature curves. The proposed method achieves a maximum error of 1.93 mm, compared with the measurement results of the total station, and satisfies complex industrial measurement requirements.