We describe a new approach to lossy compression of silhouette-like images. By a silhouette-like image we mean a bi-level image consisting of black and white regions divided by a small number of closed curves. We use a boundary detection algorithm to express the closed curves by chain codes, and we express the chains as one function of one variable. We compress this function using WFA over two letter alphabet. Finally, we use arithmetic coding to store the automaton. 1.) This work was supported by the National Science Foundation under Grant No. CCR-9417384. Preliminary version was presented in DCC 1997.