We study a local post-processing rule for maxmin (farthest-point) landmark selection in lazy witness persistence. Maxmin landmarks induce nearest-landmark cells. Within each cell, the landmark is moved toward a data point of maximum empirical halfspace depth, with smaller moves in sparsely populated cells, and is then projected back to a data point in the same cell. The resulting support-weighted rule preserves one landmark per original maxmin cell. We prove a convex-core guarantee for the depth target and explicit worst-case cover bounds for the recentered landmarks. Experiments on planar synthetic loops and 120 MPEG-7 (Moving Picture Experts Group 7) silhouettes separate average landmark fit from extremal coverage. On the synthetic benchmark, recentering reduces mean nearest-landmark distance in all 900 matched trials; after aggregation over landmark budgets, the mean change is $-0.0138$ across 300 dataset/noise/seed blocks, while maximum cover increases by $0.0067$ on average and a thresholded first homology ($H_1$) count is unchanged. On MPEG-7, the image-level mean distance decreases for all 120 silhouettes, while maximum cover increases for 118. Thus the correction consistently improves average landmark representativeness but does not improve worst-case coverage; on the controlled synthetic benchmark, this trade-off occurs without a detectable change in the coarse $H_1$ summary.

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