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We present a new approach for generating thumbnail images from H.264/AVC coded bit streams. We have verified analytically that mismatch errors between the encoder and decoder prevent the direct generation of thumbnail images from H.264/AVC transform coefficients. Based on this analysis, we have devised a method that exploits both the spatial and transform domains. What distinguishes our algorithm from previous works is that it determines the thumbnail image pixels by summing the residual and estimate block averages. The residual block averages are directly acquired in the transform domain and the estimate block averages are calculated in the spatial domain. The proposed method produces thumbnail images that are indistinguishable to the ones produced by the method that decodes the H.264/AVC-I slice bit streams and then scales them down, while, for most of images, it executes almost 3 times faster than the down-scaling method at frequently used bandwidths. [ABSTRACT FROM AUTHOR]