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We propose a multi-stage approach to curve extraction where the curve fragment search space is iteratively reduced by removing unlikely candidates using geometric constrains, but without affecting recall, to a point where the application of an objective functional becomes appropriate. The motivation in using multiple stages is to avoid the drawback of using a global functional directly on edges, which can result in non-salient but high scoring curve fragments, which arise from non-uniformly distributed edge evidence. The process progresses in stages from local to global: (i) edges, (ii) curvelets, (iii) unambiguous curve fragments, (iv) resolving ambiguities to generate a full set of curve fragment candidates, (v) merging curve fragments based on a learned photometric and geometric cues as well a novel lateral edge sparsity cue, and (vi) the application of a learned objective functional to get a final selection of …