Active Vision Reconstruction Based on Ratio Invariability of Triangle Areas Generated from Triangle Array in Affine Space

An active-vision process is presented by the affine invariability of the ratio of triangle areas to reconstruct the 3D object. Firstly, a plate with the triangle array is designed in the same plane of the planar laser. The image of the plate is rectified from the projection space to the affine space by the image of the line at infinity. Then the laser point and the centroids of the triangles constitute a new triangle that bridges the affine space and the original Euclidean space. The object coordinates are solved by the invariant of the triangle area ratio before and after the affine transformation. Finally, the reconstruction accuracy under various measurement conditions is verified by experiments. The influence analyses of the number of line pairs and the accuracy of the extracted point pixels are provided in the experimental results. The average reconstruction errors are 1.54, 1.79, 1.90, and 2.46 mm for the test distance of 550, 600, 650, and 700 mm, which demonstrates the application potential of the approach in the 3D measurement.