PLP: Point-Line Minimal Problems under Partial Visibility in Three Views

Timothy Duff, Kathlén Kohn, Anton Leykin, Tomás Pajdla

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.