Plane measurement method with monocular vision based on variable-height homography

Aiming at the measurement of variable-height plane with single non-metric camera in applications such as river surface imaging velocimetry (RSIV), a vision measurement method based on variable-height homography (VHH) is proposed. The VHH relation between image plane and water plane is established based on the 3-D perspective projection model and combining with the water surface elevation model described by the coefficients of water level and slopes. The difficulties of ground control point (GCP) deployment and water level variation remaining in existing methods based on planar homography are overcome. A distortion correction direct linear transform method is designed to solve the VHH, which efficiently improves the measurement accuracy of non-metric camera. The experiments emphatically analyze the sensitivities of GCP distribution, distortion aberration, water level error and tilt angle to the method under weakly controlled conditions. The results show that the coordinate calculation precision of the method can reach 5 mm under well deployed controlling field, which fulfills the requirement of RSIV for medium and small rivers.