Abstract Critical loci for projective reconstruction from three views in four dimensional projective space are defined by an ideal generated by maximal minors of suitable 4 × 3 matrices, N, of linear forms. Such loci are classified in this paper, in the case in which N drops rank in codimension one, giving rise to reducible varieties. This rests on the complete classification of matrices of size ( n + 1 ) × n for n ≤ 3 , which drop rank in codimension one. Instability of reconstruction near non-linear components of critical loci is explored experimentally. The classification of special matrices as above is also leveraged to study degenerate critical loci for suitable projections from P 3 .

中文翻译：

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计算机视觉中的关键位点和矩阵在第一个维度中的排名下降

摘要 从四维投影空间中的三个视图进行投影重建的关键轨迹由一个理想定义，该理想由线性形式的合适 4 × 3 矩阵 N 的最大次要生成。此类位点在本文中进行了分类，其中 N 在第 1 维中排名下降，从而产生可归约变体。这依赖于大小为 ( n + 1 ) × n 的矩阵的完整分类，其中 n ≤ 3 ，其在第一个维度中排名下降。实验探索了关键位点非线性分量附近重建的不稳定性。上述特殊矩阵的分类也被用来研究从 P 3 的合适投影的简并临界位点。