Estimation of apple flower bud growth position during bud stage based on deep learning and geometric constraints

Apple thinning is often demand to precisely estimate the flower bud positions at the bud stage. Complex canopy environments have posed great challenges in orchard, including flower bud detection, branch topology reconstruction, and flower bud-branch affiliation determination. This study aimed to estimate the growth position of flower bud using deep learning and geometric constraints. An improved YOLOv8 model (YOLO-Bud) was developed with Deformable Convolution version 4 (DCNv4) to enhance morphological adaptability for irregular targets. A lightweight downsampling module (DSampleLite) was designed to balance computational efficiency and feature expression. 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. Branch segment affiliation relationships were determined using dual geometric constraints with the growth direction consistency (first principal component PCA1 angle ≤20°) and spatial distribution correlation (centroid connection line with PCA1 angle ≤15°). B-spline curves were utilized to fit and reconstruct fractured branch contours under severe occlusion. Flower bud growth positions were located using the midpoint of the intersection line between flower stem and branch contours. Affiliation relationship was determined to minimum Euclidean distance from flower bud or flower stem centroids to branch polygon boundaries. The YOLO-Bud model was achieved in a mean average precision (mAP50) of 81.70% after segmentation on complex orchard image. 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%. The accuracy of branch segment classification reached 96.10% under dual geometric constraints. The IoU between reconstructed branch edges and ground truth annotations was 0.82. The Dice coefficient was 0.90 for the branch reconstruction. 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 were 90.81% and 95.58%, respectively, for the flower buds and flower stems. 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 and 2.93 pixels, respectively. 90% of all experimental samples shared the estimation errors within 4.2 pixels. 95% of samples had estimation errors within 5.1 pixels. The real-time inference speed of 38.20 frames per second. The parameter count was 20.34 million. Floating point operations (FLOPs) were 105.40 G. The superior performance was achieved to compare with Mask R-CNN, MaskLab, YOLACT, FastInst, YOLOv9c, and YOLOv11m models. The hybrid framework with deep learning and geometric constraints can be expected for the multi-object segmentation, fractured branch reconstruction, and flower bud positioning in complex orchard environments. The position of flower bud growth was accurately estimated with pixel-level precision suitable for robotic thinning applications. This finding can provide the reliable spatial support to apple thinning robots for precision visual perception in agricultural orchards.