The medial axis transform (MAT) is a sparse representation of shape, which, being reversible, has potential for binary image compression. The MAT also provides structural information not accessible with alternative binary image codes. This structural information is often used for line extraction and pattern recognition. Therefore, the MAT occupies an interesting middle ground between lower-level, compressible image codes and higher-level, meaningful image representations. In an attempt to realize this middle ground, a MAT-based coding scheme which respects its structural properties is developed. The MAT-based coding method is applied to the CCITT facsimile test images. The resulting compression is comparable to that of known coding schemes for textual and somewhat better for graphical data. Some simple modifications to improve skeleton coding performance are suggested. To substantiate the claim that the MAT is effective for higher-level processing, the representation is extended to perform line segment and curve extraction. The extraction takes place under the control of a global error tolerance parameter and thus provides a new method to trade off data compression with distortion for binary images.