Local Spacing-Aware Hungarian Matching for Stable Point-Supervised Crowd Counting

Point-supervised crowd counting and localization enable end-to-end training by casting prediction as set matching with one-to-oneHungarian assignment. However, point annotations provide no explicitscale information, making distance-based assignment prone to neighbor-induced ambiguity in congested regions, where nearby ground-truth pointscompete for similar proposals and corrupt supervision. We propose LocalSpacing-Aware Hungarian Matching (SAH-matcher), a drop-in replace-ment that derives a local spacing prior from k-nearest-neighbor distancesand performs per-target rescaling of the geometric cost, inducing a moreselective effective matching region in dense areas while remaining toler-ant in sparse ones. To quantify assignment behavior, we introduce Com-petitive Ambiguity Score (CAS) and Hijacking Rate (HR) for within-epoch ambiguity and severe hijacking failures, and combine them withInstability Rate (IR) to measure cross-epoch consistency. Experiments onmultiple benchmarks show improved assignment reliability and trainingstability, with particularly clear counting and localization gains in denseor locally ambiguous settings, modest overhead, and favorable transfer-ability across the evaluated point-based frameworks. Code is available athttps://github.com/kaijiang77/SAHCC.