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arXiv · 2505.08957

Even Faster Algorithm for the Chamfer Distance

Ying Feng·Piotr Indyk
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Abstract

For two d-dimensional point sets A, B of size up to n, the Chamfer distance from A to B is defined as CH(A,B) = \sum_{a \in A} \min_{b \in B} \|a-b\|. The Chamfer distance is a widely used measure for quantifying dissimilarity between sets of points, used in many machine learning and computer vision applications. A recent work of Bakshi et al, NeuriPS'23, gave the first near-linear time (1+eps)-approximate algorithm, with a running time of O(ndlog(n)/eps^2). In this paper we improve the running time further, to O(nd(loglog(n)+log(1/eps))/eps^2). When eps is a constant, this reduces the gap between the upper bound and the trivial Omega(dn) lower bound significantly, from O(log n) to O(loglog n).

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Ying Feng, Piotr Indyk. 2025-05-13. Even Faster Algorithm for the Chamfer Distance. https://arxiv.org/abs/2505.08957

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