Edge detection has been a fundamental and important task in computer vision for many years, but it is still a challenging problem in real-time applications, especially for unsupervised edge detection, where ground truth is not available. Typical fast edge detection approaches, such as the single threshold method, are expensive to achieve in unsupervised edge detection. This study proposes a Genetic Programming (GP) based algorithm to quickly and automatically extract binary edges in an unsupervised manner. We investigate how GP can effectively evolve an edge detector from a single image without ground truth, and whether the evolved edge detector can be directly applied to other unseen/test images. The proposed method is examined and compared with a recent GP method and the Canny method on the Berkeley segmentation dataset. The results show that the proposed GP method has the ability to effectively evolve edge detectors by using only a single image as the whole training set, and significantly outperforms the two methods it is compared to. Furthermore, the binary edges detected by the evolved edge detectors have a good balance between recall and precision.