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Comparing filtration functions on synthetic data. The binary ground truth road annotation (top-left in each table part) contains four loops, marked with cyan dashed lines. We synthesized a predicted class affinity map (bottom-left in each part) by extending one road to the left and interrupting another. In consequence, loop B and D from the ground truth are joined into B’ in the prediction, and A is split into A’ and E’. For each filtration method, we show binary masks resulting from filtration at different scales, pairs of persistence diagrams, and their optimal matches.

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