Accurate localization of organ boundaries is critical in medical imaging for segmentation, registration, surgical planning, and radiotherapy. While deep convolutional networks (ConvNets) have advanced general-purpose edge detection to near-human performance on natural images, their outputs often lack precise localization, a limitation that is particularly harmful in medical applications where millimeter-level accuracy is required. Building on a systematic analysis of ConvNet edge outputs, we propose a medically focused crisp edge detector that adapts a novel top-down backward refinement architecture to medical images (2D and volumetric). Our method progressively upsamples and fuses high-level semantic features with fine-grained low-level cues through a backward refinement pathway, producing high-resolution, well-localized organ boundaries. We further extend the design to handle anisotropic volumes by combining 2D slice-wise refinement with light 3D context aggregation to retain computational efficiency. Evaluations on several CT and MRI organ datasets demonstrate substantially improved boundary localization under strict criteria (boundary F-measure, Hausdorff distance) compared to baseline ConvNet detectors and contemporary medical edge/contour methods. Importantly, integrating our crisp edge maps into downstream pipelines yields consistent gains in organ segmentation (higher Dice scores, lower boundary errors), more accurate image registration, and improved delineation of lesions near organ interfaces. The proposed approach produces clinically valuable, crisp organ edges that materially enhance common medical-imaging tasks.