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By layering regions filled with linear gradients, complex appearances can be created. We propose an automatic method to convert a raster image into layered regions of linear gradients. Given an input raster image segmented into regions, our approach decomposes the resulting regions into opaque and semi-transparent linear gradient fills. Our approach is fully automatic (e.g., users do not identify a background as in previous approaches) and exhaustively considers all possible decompositions that satisfy perceptual cues. 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