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We develop a novel psychovisually motivated edge-based low-bit-rate image codec. It offers a compact description of scale-invariant second-order statistics of natural images, the preservation of which is crucial to the perceptual quality of coded images. Although being edge based, the codec does not explicitly code the edge geometry. To save bits on edge descriptions, a background layer of the image is first coded and transmitted, from which the decoder estimates the trajectories of significant edges. The edge regions are then refined by a residual coding technique based on edge dilation and sequential scanning in the edge direction. Experimental results show that the new image coding technique outperforms the existing ones in both objective and perceptual quality, particularly at low bit rates.