Abstract

We present a complete classification of minimal problems for generic arrangements of points and lines in space observed partially by three calibrated perspective cameras when each line is incident to at most one point. This is a large class of interesting minimal problems that allows missing observations in images due to occlusions and missed detections. There is an infinite number of such minimal problems; however, we show that they can be reduced to 140,616 equivalence classes by removing superfluous features and relabeling the cameras. We also introduce camera-minimal problems, which are practical for designing minimal solvers, and show how to pick a simplest camera-minimal problem for each minimal problem. This simplification results in 74,575 equivalence classes. Only 76 of these were known; the rest are new. To identify problems having potential for practical solving of image matching and 3D reconstruction, we present several natural subfamilies of camera-minimal problems as well as compute solution counts for all camera-minimal problems which have fewer than 300 solutions for generic data.

中文翻译：

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PL $${}_{1}$$ P：三视图部分可见下的点线最小问题

摘要

我们提出了一个完整的分类，用于空间中点和线的一般排列，当每条线最多入射到一个点时，由三个校准的透视相机部分观察到。这是一大类有趣的最小问题，允许由于遮挡和漏检而导致图像中缺少观察结果。这样的小问题有无数个；然而，我们表明，通过删除多余的特征并重新标记相机，可以将它们减少到 140,616 个等价类。我们还介绍了相机最小问题，这对于设计最小求解器非常实用，并展示了如何为每个最小问题选择最简单的相机最小问题。这种简化产生了 74,575 个等价类。其中只有 76 个是已知的；其余的都是新的。为了识别具有实际解决图像匹配和 3D 重建潜力的问题，我们提出了相机最小问题的几个自然子族，并计算了所有相机最小问题的解决方案计数，这些问题的通用数据解决方案少于 300 个。