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3D point cloud has been widely applied in virtual reality and augmented reality. A complex 3D scene always needs a large number of the point cloud to represent and demands a lot of space to store. Thus, point cloud compression becomes a crucial issue to research. In this paper, we propose a novel lossy geometric compression method of autoencoder based on DCGAN optimization. This method can reconstruct a high-quality point cloud and solves a large area of missing points in the process of compression and decompression. To improve the point cloud codec performance, we propose a multi-scale 3D deconvolution hopping connection structure to obtain a better-quality reconstructed point cloud under low bit rates. Our approach is the first GAN-based point cloud compression algorithm to our knowledge. Compared with state-of-the-art methods on the MVUB dataset, our approach achieves a better rate-distortion performance and visual quality.

A word $x$ that is absent from a word $y$ is called minimal if all its proper factors occur in $y$. Given a collection of $k$ words $y_1,y_2,\ldots,y_k$ over an alphabet $\Sigma$, we are asked to compute the set $\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{k}}$ of minimal absent words of length at most $\ell$ of word $y=y_1\#y_2\#\ldots\#y_k$, $\#\notin\Sigma$. In data compression, this corresponds to computing the antidictionary of $k$ documents. In bioinformatics, it corresponds to computing words that are absent from a genome of $k$ chromosomes. This computation generally requires $\Omega(n)$ space for $n=|y|$ using any of the plenty available $\mathcal{O}(n)$-time algorithms. This is because an $\Omega(n)$-sized text index is constructed over $y$ which can be impractical for large $n$. We do the identical computation incrementally using output-sensitive space. This goal is reasonable when $||\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{N}}||=o(n)$, for all $N\in[1,k]$. For instance, in the human genome, $n \approx 3\times 10^9$ but $||\mathrm{M}^{12}_{y_{1}\#\ldots\#y_{k}}|| \approx 10^6$. We consider a constant-sized alphabet for stating our results. We show that all $\mathrm{M}^{\ell}_{y_{1}},\ldots,\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{k}}$ can be computed in $\mathcal{O}(kn+\sum^{k}_{N=1}||\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{N}}||)$ total time using $\mathcal{O}(\mathrm{MaxIn}+\mathrm{MaxOut})$ space, where $\mathrm{MaxIn}$ is the length of the longest word in $\{y_1,\ldots,y_{k}\}$ and $\mathrm{MaxOut}=\max\{||\mathrm{M}^{\ell}_{y_{1}\#\ldots\#y_{N}}||:N\in[1,k]\}$. Proof-of-concept experimental results are also provided confirming our theoretical findings and justifying our contribution., Comment: Version accepted to DCC 2019

We consider a fixed-rate zero-delay source coding problem where a stationary vector-valued Gauss-Markov source is compressed subject to an average mean-squared error (MSE) distortion constraint. We address the problem by considering the Gaussian nonanticipative rate distortion function (NRDF) which is a lower bound to the zero-delay Gaussian RDF. Then, we use its corresponding optimal “test-channel” to characterize the stationary Gaussian NRDF and evaluate the corresponding information rates. We show that the Gaussian NRDF can be achieved by p-parallel fixed-rate scalar uniform quantizers of finite support with dithering signal up to a multiplicative distortion factor and a constant rate penalty. We demonstrate our framework with a numerical example. QC 20180108. QC 20191025