Closed or nearly closed regions are an important form of perceptual structure arising both in natural imagery and in many forms of human-created imagery including sketches, line art, graphics, and formal drawings. We present an effective algorithm especially suited for finding perceptually salient, compact closed region structure in hand-drawn sketches and line art. We start with a graph of curvilinear fragments whose proximal endpoints form junctions. The key problem is to manage the search of possible path continuations through junctions in an effort to find paths satisfying global criteria for closure and figural salience. We identify constraints particular to this domain for ranking path continuations through junctions, based on observations of the ways that junctions arise in line drawings. In particular, we delineate the roles of the principle of good continuation versus maximally turning paths. Best-first bidirectional search checks for the cleanest, most obvious paths first, then reverts to more exhaustive search to find paths cluttered by blind alleys. Results are demonstrated on line drawings from several sources including line art, engineering drawings, sketches on whiteboards, as well as contours from photographic imagery.