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Normal maps play an important role in computer 3D graphics to express pseudo roughness of the surface with a small amount of polygon data. In this paper, a highly efficient normal map compression algorithm is proposed based on an estimation model to predict the quality of the images rendered with the compressed normal maps. The optimal encoding is achieved by minimizing the predicted mean square error (MSE) employing vector quantization (VQ). In addition, encoding and decoding time is fast enough for practical usage. Experimental results demonstrate that the algorithm proposed in this paper yields better compression performance than the other algorithms in the literatures.