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A multiscale coder for curves and boundaries is presented. It utilizes a multiscale structure-beamlets-that is designed primarily for linear and curvilinear features. The coder is composed of three main components: 1) a rate-distortion optimized beamlet-based representation, 2) a tree-based coding from a beamlet representation to a symbol stream, and 3) an entropy coder. This coder is named "JBEAM". Taking advantage of its multiscale property, we utilized tree-based coding to make it progressive. The derived coder has a low order of computational complexity. Simulations demonstrate an advantage over the state-of-the-art industrial standard: JBIG 2. A software package, which includes an implementation of JBEAM, is made available. Variations and potential improvements of this method will be discussed. This work may inspire more activities in this line of research, improving curve coding.