We propose a technique that uses a proximity metric for delineating partially or fully bounded regions of a scanned bitmap that depicts a building floor plan. A proximity field is defined over the bitmap, which is used both to identify the centers of subjective regions in the image and to assign pixels to regions by proximity. The region boundaries generated by the method tend to match well the subjective boundaries of regions in the image. We discuss incorporation of the technique in a semi-automated interactive system for region identification in floor plans. In contrast to area-filling techniques for delineating areal regions of images, our approach works robustly for partially bounded regions. Furthermore, the frailties of the method that do remain, unlike those of alternative techniques, are well-moderated by simple human intervention.