Error analysis of precision measurement with monocular vision

Abstract To systematically study the measurement error of the calibration coefficient method when the camera’s optical axis is not perpendicular to the measurement plane, this paper first discusses the principle of error measurement with 2D imaging model, and then derives the distribution relationship of physical points corresponding to evenly distributed pixels in the pixel coordinate system based on the projection transformation matrix of the vision system. Theoretical analysis reveals an equivariance series in the expression of physical point intervals. Considering rotational symmetry of the coordinate axis, this paper analyzes the geometric relationship when the calibration plane rotates around the X axis and derives the mathematical expression for dimensional measurement. Finally, an experimental platform with both industrial and telecentric lenses is proposed and designed. Experimental results demonstrate that the measurement results of the expression derived in this paper are consistent with the traditional coordinate transformation method and the maximum deviation of the measurement is less than 0.06 mm, validating the theoretical analysis presented in this paper and providing theoretical guidance for subsequent practical application.