Geometric Correction for Line-Scan Imaging: A 1D Projective–Polar Mapping for Highly Reflective Cylindrical Surfaces

Optical inspection of highly reflective cylindrical components—such as stainless-steel vessels featuring both planar and curvilinear surfaces—presents significant challenges due to complex geometric distortions in single-pass imaging. This study proposes a line-scan imaging framework that integrates synchronized kinematic control with geometry-aware distortion correction. The system addresses shape deformations through three coordinated modules: (1) parametric synchronization between rotational motion and image acquisition ensures full-surface coverage; (2) scanline-specific 1D projective transformations correct perspective distortions on toroidal sidewalls; and (3) adaptive polar coordinate remapping restores radial symmetry on circular bases. Experimental results demonstrate subpixel-level geometric correction accuracy, validating the proposed framework’s effectiveness in eliminating geometric aberrations with low computational complexity and without reliance on data-driven training, while maintaining compatibility with defect detection and quantitative surface analysis of specular cylindrical specimens.