Fig. 1. Geometric model of line structured light perspective projection

Fig. 2. Schematic diagram of rail profile measurement with line structured light

Fig. 3. Target coordinate system and rail longitudinal direction. (a) Target coordinate system; (b) Z-axis (Z_tcs) of target coordinate system is vertical to rail longitudinal direction

Fig. 4. Schematic diagrams of plane target moving on rail surface. (a) Longitudinal rotation around rail; (b) longitudinal translation along rail; (c) rotate around the Z-axis of target coordinate system tcs

Fig. 5. Diagrams of nine typical plane target poses

Fig. 6. Flow chart of rail longitudinal calibration

Fig. 7. Rail profile measurement device with structured light. (a) Rail profile measurement device; (b) flat target is closely attached to top surface of rail; (c) flat target is closely attached to side of rail

Fig. 8. Plane target images under different postures

Fig. 9. Distribution of vectors V_i and the normal of fitting plane

Fig. 10. Schematic diagrams of rail rotation position. (a) Axonometric view; (b) top view

Fig. 11. Rail longitudinal calibration results for 9 rotating positions

Fig. 12. Relationship between rail longitudinal calibration error and number of target images