Curb detection is a key enabling functionality for the precise curb-following sanitation control of autonomous sanitation vehicles. The robust and efficient curb detection in complex environments is still a challenging issue. In this paper, we propose a novel semantic segmentation-based framework for curb detection using monocular bird's eye-view images. We employ a lightweight segmentation network based on HRNet to extract the drivable area. A zero-shot post-processing approach is proposed to extract a candidate point set from the segmented image for robust curve fitting. In addition, we propose a modified RANSAC fitting approach that accounts for outlier points to achieve dynamic order curve fitting and curb representation. Experimental results in complex sanitation scenarios demonstrate the efficiency, accuracy, and robustness of the proposed approach.