Triangulation Device Using Epipolar Polynomial Correction

The patent applies preliminary action by first obtaining initial three-dimensional coordinates through linear least squares method before performing bundle adjustment. This preliminary estimation provides a starting point that guides the nonlinear optimization process, reducing the search space and preventing convergence to local minima. The initial coordinates are calculated using epipolar geometry constraints, establishing a foundation that improves subsequent optimization convergence.

The patent changes parameters by transforming the optimization problem from unconstrained nonlinear optimization to a constrained problem using epipolar equations. By incorporating epipolar constraints as additional parameters and conditions, the search space is significantly reduced from infinite three-dimensional space to a constrained manifold, ensuring global optimality while maintaining measurement precision.

The patent segments the triangulation process into two distinct stages: first obtaining initial coordinates through linear least squares method for rapid computation, then refining these coordinates through bundle adjustment with epipolar constraints for high precision. This segmentation allows each method to operate in its optimal regime - speed for initialization, accuracy for refinement - resolving the contradiction between computation speed and measurement precision.

The patent uses bundle adjustment with epipolar constraints as an intermediary process between the rough initial estimation and the final precise coordinates. This intermediary step corrects the initial coordinates by minimizing reprojection error under epipolar constraints, effectively bridging the gap between fast but inaccurate linear least squares results and the desired high-precision coordinates.