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We present a fast and efficient coding algorithm for compound images. Unlike popular mixture raster content (MRC) based approaches, we propose to attack compound image coding problem from the perspective of modeling location uncertainty of image singularities. We suggest that a computationally simple two-class segmentation strategy is sufficient for the coding of compound images. We argue that jointly exploiting topological properties of image source in classification and coding stages is beneficial to the robustness of compound image coding systems. Experiment results have justified effectiveness and robustness of the proposed topological coding algorithm.