High-resolution farmland image edge detection plays a key role in precision agriculture and ecological monitoring. However, the performance of existing methods relies heavily on large-scale, high-quality annotated datasets, which are costly and difficult to obtain in practice. At the same time, farmland imagery presents additional challenges since boundaries often suffer from low contrast, textures and structures introduce multi-scale interference, and limited annotations further amplify supervision noise in semi-supervised settings. To overcome these issues, we propose GLogSemiFNet, a semi-supervised contrastive learning framework that explicitly strengthens edge perception with frequency-domain priors. The framework introduces Gabor and Log-Gabor (G-Log) filters, where learnable Gabor and Log-Gabor filters are jointly optimized to extract direction-aware and scale-adaptive edge features. This design effectively captures fine-grained boundaries across multiple scales and improves edge representation under complex textures. In addition, a G-Log-ClassMix augmentation strategy leverages edge cues together with prediction confidence from dual branches to generate more reliable pseudo labels, thereby alleviating the impact of supervision noise. Furthermore, an edge-guided local dense contrastive learning module (G-LogC) enhances feature discrimination along edges, ensuring boundary coherence and robust segmentation in challenging farmland scenarios. Extensive experiments on the Guangdong and French farmland datasets demonstrate that GLogSemiFNet achieves IoU of 49.73% and 43.58% with only 20% labeled data, substantially outperforming state-of-the-art semi-supervised methods. Visualization results further confirm its robustness in handling curved boundaries, complex textures, and noisy backgrounds, ultimately providing reliable edge information for downstream tasks such as precise farmland edge detection and land parcel delineation. The code is available at: https://github.com/YuchunHuang/Farmland_GLogSemiFNet.