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Matched Queries for Curvature and Density at Branching Junctions

arXiv · AI, language, vision and robotics · article · Sep 1, 2026 · UTC

At a junction, a score field can reveal weighted tangent rays, yet these first-order quantities do not determine how individual branches bend or how their densities change away from the center. Recovering this missing information is necessary for describing local continuation beyond a single point, but finite observations must separate branchwise second-order effects while allowing error in the estimated center. We address this inverse problem using matched score queries at noise scales $σ$ and $λσ$. For a finite union of $C^{2,α}$ half-branches in $\mathbb{R}^D$, the normalized score has the

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