Abstract: To improve the objectivity, in situ non-destructive applicability, and field robustness of angle phenotyping for crop slender organs, a growth angle measurement method based on fast segment anything model with skeleton-geometric constraints (FS-SGC) was developed. Angle measurement of stems and other slender crop organs in field environments is often constrained by three practical problems: strong dependence on manual judgment, difficulty in obtaining non-destructive measurements under natural conditions, and unstable performance caused by cluttered backgrounds, irregular organ boundaries, local curvature, and multi-view projection distortion. To address these limitations, a task-oriented workflow was constructed by integrating zero-shot instance segmentation, global-topology-guided geometric feature extraction, and vector-based angle estimation. First, fast segment anything model (FastSAM) was adopted as the front-end segmentation model to isolate target organs from complex scenes without task-specific dense annotation training. A multi-scale region-of-interest cascade strategy was then introduced to progressively refine local target regions, suppress redundant background interference, and generate high-quality binary masks for individual target organs. Second, a topology-constrained skeleton extraction procedure was designed to preserve continuity and endpoint integrity during thinning, and the extracted skeleton was further used to construct a global geometric envelope representing the dominant structural extent and directional trend of the target organ. To complement the global description, local ridge-like geometric features were extracted in multi-scale space by using a Hessian-matrix-based strategy, so that subtle structural information along slender organs could be retained and local directional deviations could be corrected. Third, key feature points were vectorized by least-squares edge updating, and organ growth angle was estimated from the fitted directional structure under the guidance of the global geometric envelope. For field deployment, a calibration-board-assisted geometric correction procedure was further incorporated to reduce projection distortion caused by non-orthogonal image acquisition and to improve geometric fidelity under multi-view imaging conditions.The proposed method was evaluated on a self-constructed rapeseed stem dataset containing 330 images collected from different growth stages and structural forms, and was further validated on a public wheat flag leaf dataset to examine cross-organ generalization performance. On the rapeseed stem dataset, the proposed method achieved a coefficient of determination (R²) of 0.9282 and a root mean square error (RMSE) of 2.078°, indicating strong agreement with manual measurements. Comparative experiments were conducted against representative geometry-based, edge-based, contour-based, and segmentation-assisted methods. Results showed that the proposed method outperformed the reference methods in mean absolute error (MAE), RMSE, R², Pearson correlation coefficient (r), and agronomic tolerance compliance rate (ATCR), while maintaining an acceptable complete-pipeline processing time of 0.3660 s per sample. In particular, the proposed workflow was more effective for organs with slender morphology, irregular boundaries, local bending, or background interference, where conventional methods were more likely to produce biased direction estimation. Ablation experiments further demonstrated that each core module contributed positively to the final performance. High-quality target isolation was essential for reliable angle estimation; topology-constrained skeleton extraction improved structural continuity and directional stability; and local Hessian-based geometric features effectively compensated for directional deviations that could not be fully resolved by coarse global envelopes alone. On the wheat flag leaf dataset, the method achieved an R² of 0.9932, demonstrating good adaptability across different crops, organs, and image characteristics. In addition, the calibration-board-assisted geometric correction significantly improved field measurement reliability under non-orthogonal imaging, reducing the average angular error caused by perspective distortion to within 1.8°. Overall, the proposed FS-SGC method provides an effective solution for automatic angle measurement of crop slender organs by combining zero-shot segmentation, topology-preserving skeleton analysis, local geometric enhancement, and least-squares vector fitting within a unified workflow. The method achieved high accuracy on both self-constructed and public datasets, showed robust adaptability to slender and irregular plant structures, and maintained practical applicability under field imaging conditions after geometric correction. It can provide technical support for fine-scale characterization of crop slender-organ architecture, lodging-related phenotyping, and non-destructive monitoring in smart agriculture, and also offers a feasible technical pathway for high-throughput extraction of structural traits in field-based crop phenomics.