1：Experimental Design and Method Selection:

The methodology involves modifying the YOLOv2 network for parameter regression, incorporating an RNN for variable parameter prediction, and using a layered detection model inspired by hierarchical image analysis. A novel circular loss function is introduced for RNN training to handle variable control points in splines.

2：Sample Selection and Data Sources:

Synthetic datasets of 150,000 images (416x416 pixels) are generated with primitives like rectangles, triangles, ellipses, and closed spline curves, including variations with noise, textures, and affine transformations to test robustness.

3：List of Experimental Equipment and Materials:

Computational resources for deep learning training and testing, including GPUs for running PyTorch-based implementations. No specific hardware is detailed beyond software tools.

4：Experimental Procedures and Operational Workflow:

The backbone network (Darknet-19) processes images through convolutional layers and detection blocks. RoI pooling is used for layered detection, cropping feature maps based on bounding box predictions. Training is end-to-end with scheduled sampling for stability, and RNN decoder is pre-trained separately.

5：Data Analysis Methods:

Performance is evaluated using precision, recall, mean average precision (mAP), and reconstruction loss (pixel-wise RMSE). Comparisons are made with traditional methods (contour detection, Hough transform) and learning-based baselines (CSGNet, flat model, recursive model).