This paper offers a computational study of finger localization on 2D curved objects using tactile data which builds on efficient numerical processing of curves. Our first algorithm localizes one rolling finger on a stationary object. It finds all boundary segments with the same arc length and total curvature computed from tactile data. The algorithm slides an imaginary segment along the object boundary by alternatively marching its two endpoints forward, stretching or contracting the segment if necessary. Through a curvature-based analysis we establish the global convergence of the algorithm to every location of such a segment and also derive the local convergence rate. The algorithm runs in time linear in the size of the discretized boundary curve domain. Based on these results, we present a global algorithm to localize two fingers rolling on a free object. The algorithm partitions the object boundary into segments over which related total curvature functions are monotonic. Then it combines bisection with forward marching to search for possible locations of the fingers within every pair of such segments.
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