A Vision-Based Algorithm for Material Volume Estimation on Conveyor Belts Using Optical Flow and Vanishing Points

Laser Plane Laser triangulation, which is a vital non-contact measurement technique, plays an important role in dynamic volume measurement of conveyed objects on belt conveyors. In this process, cross-sectional area measurement, which constitutes the crucial step in volume determination, is carried out. However, the measurement process requires the laser plane to be perpendicular to the belt direction. Since the rotation of the laser plane significantly affects the cross-sectional area (which determines the accuracy of volume measurements for objects on the conveyor belt), precise alignment is crucial. We propose a method that employs the optical flow method to estimate vanishing points from the motion trajectories of objects on a conveyor belt, and simultaneously corrects the object area errors caused by the rotation of the laser plane based on the vanishing point method. First, determine the vanishing points based on the optical flow method and motion trajectory of the objects; then, derive the calibrated laser plane using the vanishing point algorithm; finally, obtain the cross-sectional area of the object based on the 3D point cloud acquired through laser triangulation method. Experimental results demonstrate that this method yields excellent results. When the angle of the laser plane is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1 0}^{\circ}$</tex> (yaw), 25° (yaw), 10° (pitch) and 25° (pitch), using this method the error in the object's cross-sectional area accounted for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.74 \%, 9.09 \%$</tex>, 0.95 % and 0.59 %, respectively. In experiments where different Gaussian noises were introduced and repeated 5000 times, the mean absolute error accounted for 0.75 % and 11.4113 % of the baseline cross-sectional area when the yaw angles were 10° and 25°, respectively. For pitch angles of 3.31° and 4.45°, the mean absolute error corresponded to 0.7047 % and 0.5138 % of the baseline area, respectively. In terms of motion trajectory correction, when the frame rates are stable, the error percentages in the cross-sectional area of objects between Video <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$A$</tex> and Video B are 0.0266 % and 0.0405 %, respectively. Experimental verification indicates that the proposed Material volume measurement algorithm demonstrates remarkable robustness and operational stability under varying environmental conditions.