Abstract

We propose a multi-stage approach to curve extraction where the curve fragment search space is iteratively reduced by removing un- likely candidates using geometric constrains, but without affecting recall, to a point where the application of an ob jective functional becomes ap- propriate. The motivation in using multiple stages is to avoid the draw- back 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 frag- ment candidates, (v ) merging curve fragments based on a learned pho- tometric and geometric cues as well a novel lateral edge sparsity cue, and (vi ) the application of a learned ob jective functional to get a final selection of curve fragments. The resulting curve fragments are typically visually salient and have been evaluated in two ways. First, we measure the stability of curve fragments when images undergo visual transfor- mations such as change in viewpoints, illumination, and noise, a critical factor for curve fragments to be useful to later visual processes but one often ignored in evaluation. Second, we use a more traditional compari- son against human annotation, but using the CFGD dataset and CFGD evaluation strategy rather than the standard BSDS counterpart, which is shown to be not appropriate for evaluating curve fragments. Under both evaluation schemes our results are significantly better than those state of the art algorithms whose implementations are publicly available.