Training-free interpretation of count-calibrated density maps for label-free cell localization

Abstract Density maps support object counting by integration, but their continuous outputs do not directly provide coordinates for cell-level analysis. We developed multi-scale density map interpretation (MSDMI), a training-free method that recovers cell-center coordinates from count-calibrated density maps. MSDMI calculates local density mass using two-dimensional moving sums, thresholds responses across window sizes, accumulates support maps, and returns regional maxima as coordinates. In a best-attainable analysis of 10 density maps, the median optimal sub-pattern assignment (OSPA) distance was 3.9046 pixels for MSDMI, versus 19.298 for Gaussian blur plus watershed and 19.501 for direct binarization. OSPA distances differed among methods (Friedman test, p = 4.54 × 10−5), and MSDMI outperformed both after Holm correction (adjusted p = 0.0039 each). Recovered coordinates also supported single-cell fluorescence measurement, extending density-map outputs from counting to localization and functional analysis.