Abstract: Abstract: To address the strong subjectivity of growth angle measurement for crop slender organs, the difficulty in obtaining in situ non-destructive measurements, and the insufficient robustness of target segmentation and angle analysis in complex scenes, a growth angle measurement method based on the fast segment anything model with skeleton-geometric constraints (FS-SGC) was proposed. The study aimed to achieve stable target isolation, preserve the principal growth direction of slender structures, and improve the accuracy and adaptability of angle estimation under complex field imaging conditions. The method consisted of three modules: cascade perception-based instance segmentation, global topology-guided geometric feature extraction, and angle analysis based on least-squares edge updating. First, the zero-shot segmentation capability of the fast segment anything model (FastSAM) was combined with a multi-scale region of interest (ROI) cascade strategy to obtain high-quality binary masks of individual targets. Second, topology-constrained skeleton extraction was used to construct a global geometric envelope, while Hessian matrix-based local geometric features characterized the main growth direction and local structural details. Finally, local feature points were classified and fitted by least squares under the global geometric-envelope constraint, followed by edge updating for direction vector estimation and angle calculation. A calibration-board-assisted geometric correction preprocessing method was also designed for multi-view image acquisition. The proposed method was evaluated on a self-constructed rapeseed stem dataset and further validated on a public wheat flag leaf dataset. On the rapeseed stem dataset, FS-SGC achieved a mean absolute error (MAE) of 1.620°, a root mean square error (RMSE) of 2.078°, a coefficient of determination of 0.928 2, a Pearson correlation coefficient of 0.967, and an agronomic tolerance compliance rate (ATCR) of 84.38% within a 3° tolerance. Among the reference methods, the lowest MAE and RMSE were 2.319° and 3.110°, respectively, while the highest ATCR was 78.12%, confirming the superior accuracy of FS-SGC. The complete FS-SGC pipeline required an average processing time of 0.3660 s per sample. Ablation experiments further demonstrated the contributions of the three core modules. The baseline method produced an MAE of 3.532°, a coefficient of determination of 0.563 5, and an ATCR of 57.81%. After cascade perception-based instance segmentation, the global geometric envelope, and local geometric features were progressively incorporated, the MAE decreased to 1.620°, the coefficient of determination increased to 0.928 2, and the ATCR increased to 84.38%. These results indicated that high-quality target isolation reduced background interference, the global geometric envelope improved the stability of direction vector estimation, and Hessian matrix-based local geometric features further compensated for errors caused by minor bifurcations, local bending, and directional disturbances. On the public wheat flag leaf dataset, which contained leaf curling, folding, natural illumination variation, and local occlusion, the MAE, RMSE, coefficient of determination, and Pearson correlation coefficient were 3.30°, 4.11°, 0.993 2, and 0.998 1, respectively, demonstrating adaptability across different crops, organs, and image conditions. For multi-view field acquisition, the calibration-board-assisted geometric correction preprocessing method reduced the average angle measurement error from 5.3° to within 1.8°, improving geometric fidelity and measurement consistency. Field lodging-angle measurement examples further showed that FS-SGC could extract the principal stem direction and perform lodging-angle measurement under illumination variation, complex soil backgrounds, weed interference, adjacent-plant occlusion, and local stem deformation. The results indicated that FS-SGC could be applied to automatic angle measurement of crop organs characterized by a clear principal-axis direction and slender morphology. By integrating zero-shot segmentation, topology-constrained skeleton extraction, global geometric-envelope constraints, local geometric features, and least-squares edge updating, the method achieved relatively high measurement accuracy and maintained adaptability across different crop organs and field imaging conditions. The proposed method could provide technical support for the automatic acquisition of phenotypic parameters of crop slender organs and offer a reference for fine-grained, non-destructive structural phenotyping in complex field environments.