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In this paper, the multilevel pattern matching (MPM) code for compression of one-dimensional (1D) sequences is first generalized to compress two-dimensional (2D) images, resulting in a 2D multilevel pattern matching (MPM) code. It is shown that among all images of n pixels, the worst case redundancy of the 2D MPM code against any finite-template-based arithmetic code is O(1/√logn). This result contrasts unfavorably with the fact that among all 1D sequences of length n, the MPM code has a worst case redundancy of O(1/logn) against any finite-state arithmetic code; this is caused by the so-called 2D boundary effect. To alleviate the 2D boundary effect, we extend the 2D MPM code to the case of context modeling, yielding a context-dependent 2D MPM code. It is shown that among all images of n pixels, the context-dependent 2D MPM code has an O(1/logn) worst case redundancy against any finite-template-based arithmetic code satisfying a mild condition; this redundancy is better than that of the 2D MPM code without context models. Experimental results demonstrate that the context-dependent 2D MPM code significantly outperforms the 2D MPM code without context models for bi-level images. It is also demonstrated that, in terms of compression rates, the context-dependent 2D MPM code performs significantly better than the progressive coding mode of JBIG1 for both textual and bi-level images, and better than or comparably to the sequential coding mode of JBIG1 and JBIG2. In addition to its excellent compression performance, the context-dependent 2D MPM code allows progressive transmission of images.