Linear projections from \(\mathbb {P}^k\) to \(\mathbb {P}^h\) appear in computer vision as models of images of dynamic or segmented scenes. Given multiple projections of the same scene, the identification of sufficiently many correspondences between the images allows, in principle, to reconstruct the position of the projected objects. A critical locus for the reconstruction problem is a variety in \(\mathbb {P}^k\) containing the set of points for which the reconstruction fails. Critical loci turn out to be determinantal varieties. In this paper we determine and classify all the smooth critical loci, showing that they are classical projective varieties.

从\(\mathbb {P}^k\)到\(\mathbb {P}^h\) 的线性投影出现在计算机视觉中，作为动态或分段场景的图像模型。给定同一场景的多个投影，图像之间足够多的对应关系的识别原则上允许重建投影对象的位置。重建问题的一个关键轨迹是\(\mathbb {P}^k\)中的变体，其中包含重建失败的点集。结果证明，关键基因座是决定性变异。在本文中，我们对所有光滑临界位点进行了确定和分类，表明它们是经典的射影变种。