This paper presents a comprehensive computer vision framework for automated detection and analysis of linear patterns in palm imagery. While hand lines have been studied in traditional contexts, this research approaches them purely as geometric features for pattern recognition and biometric analysis. Our method employs four specialized SeqNet models derived from UNet architecture, combined with MediaPipe for hand landmark detection, to achieve robust line segmentation. Through systematic image processing including skeletonization, curve fitting, and broken line connection algorithms, we extract quantifiable geometric features including line curvature, endpoints, and morphological characteristics. Experimental evaluation on 500 hand images demonstrates mean Intersection over Union (IoU) of 0.865, representing a 9.6% improvement over standard UNet baselines. The proposed system achieves feature classification accuracies ranging from 87.4% to 94.7% across different geometric analysis tasks. This research contributes to computer vision, pattern recognition, and biometric analysis by providing a robust framework for automated geometric feature extraction from hand imagery.