Abstract 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.

中文翻译：

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基于仿射空间三角形阵列生成三角形面积比不变性的主动视觉重建

摘要 利用三角形面积比的仿射不变性提出了一种主动视觉重建3D对象的过程。首先，在平面激光器的同一平面上设计一个具有三角形阵列的板。板的图像通过无穷远线的图像从投影空间校正到仿射空间。然后激光点和三角形的质心构成一个新的三角形，连接仿射空间和原始欧几里得空间。对象坐标通过仿射变换前后三角形面积比的不变量求解。最后通过实验验证了各种测量条件下的重建精度。实验结果中给出了线对数和提取点像素精度的影响分析。