Abstract: To address the critical demand for precise estimation of flower bud growth positions in automated apple thinning operations during the bud stage, this study aimed to solve persistent challenges in complex orchard canopy environments including flower bud detection difficulties, ambiguous branch topology reconstruction, and inaccurate flower bud-branch affiliation determination. A novel flower bud growth position estimation method integrating deep learning and geometric constraints was proposed. An improved YOLOv8 model (YOLO-Bud) was developed with Deformable Convolution version 4 (DCNv4) to enhance morphological adaptability for irregular agricultural targets. A lightweight downsampling module (DSampleLite) was designed to balance computational efficiency and feature expression capability. Shape-Intersection over Union (Shape-IoU) loss function was adopted to optimize boundary regression accuracy for precise instance segmentation of flower buds, branches, leaves, and flower stems. Principal component analysis (PCA) was employed to extract the main growth direction of individual branch segments. Dual geometric constraints combining growth direction consistency (first principal component PCA1 angle ≤20°) and spatial distribution correlation (centroid connection line with PCA1 angle ≤15°) were applied to determine branch segment affiliation relationships. B-spline curves were utilized to fit and reconstruct fractured branch contours caused by severe occlusion. Flower bud growth positions were located based on the midpoint of the intersection line between flower stem and branch contours. Affiliation was determined by minimum Euclidean distance from flower bud or flower stem centroids to branch polygon boundaries. The YOLO-Bud model achieved a mean average precision (mAP₅₀) of 81.70% in complex orchard image segmentation tasks. The intersection over union (IoU) reached 67.70%. The precision and recall were 85.60% and 76.40% respectively. The Dice coefficient reached 80.74%. Under dual geometric constraints, the branch segment classification accuracy reached 96.10%. The IoU between reconstructed branch edges and ground truth annotations was 0.82. The Dice coefficient for branch reconstruction was 0.90. The root mean square error (RMSE) of branch reconstruction was 2.62 pixels. The mean absolute error (MAE) was 1.79 pixels. The affiliation determination accuracies for flower buds and flower stems were 90.81% and 95.58% respectively. The RMSE of flower bud growth position estimation was 3.37 pixels in Euclidean distance measurement. The MAE was 2.72 pixels. The x-axis and y-axis RMSE were 3.21 pixels and 2.93 pixels respectively. 90% of all experimental samples had estimation errors within 4.2 pixels. 95% of samples had estimation errors within 5.1 pixels. The model maintained real-time inference speed of 38.20 frames per second. The parameter count was 20.34 million. The floating point operations (FLOPs) were 105.40 G. The proposed method demonstrated superior performance compared to Mask R-CNN, MaskLab, YOLACT, FastInst, YOLOv9c, and YOLOv11m models. The proposed hybrid technical framework combining deep learning and geometric constraints effectively resolved multi-object segmentation, fractured branch reconstruction, and flower bud positioning challenges in complex orchard environments. The method achieved the research objectives of accurate flower bud growth position estimation with pixel-level precision suitable for robotic thinning applications. This work provided reliable spatial decision support for apple thinning robots and enriched research methodologies for precision visual perception in agricultural orchards.