We present RibPull, a methodology that utilizes implicit occupancy fields to bridge computational geometry and medical imaging. Implicit 3D representations use continuous functions that handle sparse and noisy data more effectively than discrete methods. While voxel grids are standard for medical imaging, they suffer from resolution limitations, topological information loss, and inefficient handling of sparsity. Coordinate functions preserve complex geometrical information and represent a better solution for sparse data representation, while allowing for further morphological operations. Implicit scene representations enable neural networks to encode entire 3D scenes within their weights. The result is a continuous function that can implicitly compesate for sparse signals and infer further information about the 3D scene by passing any combination of 3D coordinates as input to the model. In this work, we use neural occupancy fields that predict whether a 3D point lies inside or outside an object to represent CT-scanned ribcages. We also apply a Laplacian-based contraction to extract the medial axis of the ribcage, thus demonstrating a geometrical operation that benefits greatly from continuous coordinate-based 3D scene representations versus voxel-based representations. We evaluate our methodology on 20 medical scans from the RibSeg dataset, which is itself an extension of the RibFrac dataset. We will release our code upon publication.