It has long been understood that precisely estimating the probabilistic structure of natural visual images is crucial for image compression. Despite remarkable success of recent end-toend optimized image compression, the latent code representation is assumed to be fully statistically factorized such that the entropy modeling is feasible. Here we describe context-based convolutional networks (CCNs) that exploit statistical redundancies in the codes for improved entropy modeling. We introduce a 3D zigzag coding order together with a 3D code dividing technique to define proper context and to achieve parallel entropy decoding, both of which boil down to place translation-invariant binary masks on convolution filters of CCNs. We demonstrate the power of CCNs for entropy modeling in both lossless and lossy image compression. For the former, we directly apply a CCN to binarized image planes for estimating the Bernoulli distribution of each code. For the latter, the categorical distribution of each code is represented by a discretized mixture of Gaussian distributions, whose parameters are estimated by three CCNs. We jointly optimize the CCN-based entropy model with analysis and synthesis transforms for rate-distortion performance. Experiments on two image datasets show that the proposed lossless and lossy image compression methods based on CCNs generally exhibit better compression performance than existing methods with a manageable computational complexity.

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