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Description

How can we recover point locations from noisy directions between pairs of points, without knowing any distances? This problem arises in reconstructing camera positions from photographs. A longstanding practical problem is collapse: standard formulations can place many cameras at the same location when directions are corrupted.

I will present TriP, which starts from a simple geometric fact: the directions along a nondegenerate triangle determine the relative lengths of its edges. TriP combines overlapping triangles by synchronizing their unknown scales, then uses the recovered edge lengths to estimate camera locations. This intermediate step rules out zero-scale collapse and improves robustness to structured outliers. I will discuss exact recovery guarantees under bounded adversarial corruption and experiments on synthetic and real data, including graphs with more than one million cameras.

Joint work with Zhekai Fan, Wanze Li, and Jinxin Wang.