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Encoding the Region Of Interest (ROI) with better quality than the background has many applications including video conferencing systems, video surveillance and object-oriented vision tasks. In this paper, we propose a ROI-based image compression framework with Swin transformers as main building blocks for the autoencoder network. The binary ROI mask is integrated into different layers of the network to provide spatial information guidance. Based on the ROI mask, we can control the relative importance of the ROI and non-ROI by modifying the corresponding Lagrange multiplier $ \lambda $ for different regions. Experimental results show our model achieves higher ROI PSNR than other methods and modest average PSNR for human evaluation. When tested on models pre-trained with original images, it has superior object detection and instance segmentation performance on the COCO validation dataset., Comment: This paper has been accepted by ICASSP 2023

Recently, deep learning-based image compression has made signifcant progresses, and has achieved better ratedistortion (R-D) performance than the latest traditional method, H.266/VVC, in both subjective metric and the more challenging objective metric. However, a major problem is that many leading learned schemes cannot maintain a good trade-off between performance and complexity. In this paper, we propose an effcient and effective image coding framework, which achieves similar R-D performance with lower complexity than the state of the art. First, we develop an improved multi-scale residual block (MSRB) that can expand the receptive feld and is easier to obtain global information. It can further capture and reduce the spatial correlation of the latent representations. Second, a more advanced importance map network is introduced to adaptively allocate bits to different regions of the image. Third, we apply a 2D post-quantization flter (PQF) to reduce the quantization error, motivated by the Sample Adaptive Offset (SAO) flter in video coding. Moreover, We fnd that the complexity of encoder and decoder have different effects on image compression performance. Based on this observation, we design an asymmetric paradigm, in which the encoder employs three stages of MSRBs to improve the learning capacity, whereas the decoder only needs one stage of MSRB to yield satisfactory reconstruction, thereby reducing the decoding complexity without sacrifcing performance. Experimental results show that compared to the state-of-the-art method, the encoding and decoding time of the proposed method are about 17 times faster, and the R-D performance is only reduced by less than 1% on both Kodak and Tecnick datasets, which is still better than H.266/VVC(4:4:4) and other recent learning-based methods. Our source code is publicly available at https://github.com/fengyurenpingsheng., Comment: IEEE TRANSACTIONS ON MULTIMEDIA

Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of the geometry of the data. A common geometrical understanding of compositional data is via a regular simplex. Majority of existing approaches rely on a log-ratio or power transformations to overcome the innate simplicial geometry. In this work, based on the key observation that a compositional data are projective in nature, and on the intrinsic connection between projective and spherical geometry, we re-interpret the compositional domain as the quotient topology of a sphere modded out by a group action. This re-interpretation allows us to understand the function space on compositional domains in terms of that on spheres and to use spherical harmonics theory along with reflection group actions for constructing a compositional Reproducing Kernel Hilbert Space (RKHS). This construction of RKHS for compositional data will widely open research avenues for future methodology developments. In particular, well-developed kernel embedding methods can be now introduced to compositional data analysis. The polynomial nature of compositional RKHS has both theoretical and computational benefits. The wide applicability of the proposed theoretical framework is exemplified with nonparametric density estimation and kernel exponential family for compositional data.

Recently, skeleton-based approaches have achieved rapid progress on the basis of great success in skeleton representation. Plenty of researches focus on solving specific problems according to skeleton features. Some skeleton-based approaches have been mentioned in several overviews on object detection as a non-essential part. Nevertheless, there has not been any thorough analysis of skeleton-based approaches attentively. Instead of describing these techniques in terms of theoretical constructs, we devote to summarizing skeleton-based approaches with regard to application fields and given tasks as comprehensively as possible. This paper is conducive to further understanding of skeleton-based application and dealing with particular issues., Comment: 10 pages, 1 figures

Let $k$ be an arbitrary field, $P = P_k^{m_1} \times_k \cdots \times_k P_k^{m_p}$ be a multiprojective space over $k$, and $X \subseteq P$ be a closed subscheme of $P$. We provide necessary and sufficient conditions for the positivity of the multidegrees of $X$. As a consequence of our methods, we show that when $X$ is irreducible, the support of multidegrees forms a discrete algebraic polymatroid. In algebraic terms, we characterize the positivity of the mixed multiplicities of a standard multigraded algebra over an Artinian local ring, and we apply this to the positivity of mixed multiplicities of ideals. Furthermore, we use our results to recover several results in the literature in the context of combinatorial algebraic geometry., Comment: This is a generalized and expanded version of arXiv:1612.00154. Final version, to appear in Advances in Mathematics

Recently many works attempt to develop image compression models based on deep learning architectures, where the uniform scalar quantizer (SQ) is commonly applied to the feature maps between the encoder and decoder. In this paper, we propose to incorporate trellis coded quantizer (TCQ) into a deep learning based image compression framework. A soft-to-hard strategy is applied to allow for back propagation during training. We develop a simple image compression model that consists of three subnetworks (encoder, decoder and entropy estimation), and optimize all of the components in an end-to-end manner. We experiment on two high resolution image datasets and both show that our model can achieve superior performance at low bit rates. We also show the comparisons between TCQ and SQ based on our proposed baseline model and demonstrate the advantage of TCQ., Comment: Accepted in Data Compression Conference (DCC) 2020

In this paper, we aim to provide a systematic study of the relationship between Chernoff information and topological, as well as algebraic properties of the corresponding Gaussian tree graphs for the underlying graphical testing problems. We first show the relationship between Chernoff information and generalized eigenvalues of the associated covariance matrices. It is then proved that Chernoff information between two Gaussian trees sharing certain local subtree structures can be transformed into that of two smaller trees. Under our proposed grafting operations, bottleneck Gaussian trees, namely, Gaussian trees connected by one such operation, can thus be simplified into two 3-node Gaussian trees, whose topologies and edge weights are subject to the specifics of the operation. Thereafter, we provide a thorough study about how Chernoff information changes when small differences are accumulated into bigger ones via concatenated grafting operations. It is shown that the two Gaussian trees connected by more than one grafting operation may not have bigger Chernoff information than that of one grafting operation unless these grafting operations are separate and independent. At the end, we propose an optimal linear dimensional reduction method related to generalized eigenvalues., Comment: Submitted to Information Sciences, and this version contains proofs of the propositions in the paper. arXiv admin note: substantial text overlap with arXiv:1712.09741

In this paper, we want to find out the determining factors of Chernoff information in distinguishing a set of Gaussian graphs. We find that Chernoff information of two Gaussian graphs can be determined by the generalized eigenvalues of their covariance matrices. We find that the unit generalized eigenvalue doesn't affect Chernoff information and its corresponding dimension doesn't provide information for classification purpose. In addition, we can provide a partial ordering using Chernoff information between a series of Gaussian trees connected by independent grafting operations. With the relationship between generalized eigenvalues and Chernoff information, we can do optimal linear dimension reduction with least loss of information for classification., Comment: Submitted to Allerton2018, and this version contains proofs of the propositions in the paper

Mustafin varieties are flat degenerations of projective spaces, induced by a choice of an $n-$tuple of lattices in a vector space over a non-archimedean field. They were introduced by Mustafin in the 70s in order to generalise Mumford's groundbreaking work on the unformisation of curves to higher dimension. These varieties have a rich combinatorial structure as can be seen in pioneering work of Cartwright, H\"abich, Sturmfels and Werner. In this paper, we introduce a new approach to Mustafin varieties in terms of images of rational maps, which were studied by Li. Applying tropical intersection theory and tropical convex hull computations, we use this method to give a new combinatorial description of the irreducible components of the special fibers of Mustafin varieties. This enables connections to various topics. In particular, we see that any multiview variety appears as an irreducible component of the special fiber of some Mustafin variety. Furthermore, we use an interpretation of Mustafin varieties as a moduli functor introduced by Faltings to relate them to certain moduli functors, called linked Grassmannians. These objects are featured in limit linear series theory. The focal point of study regarding linked Grassmannians are so-called \textit{simple points}. As a direct consequence of the new combinatorial description of Mustafin varieties, we prove that the simple points of linked Grassmannians are dense in every fiber. Finally, we use the connection to linked Grassmannians, to relate the special fibers of Mustafin varieties to certain local models of unitary Shimura varieties.

Inside a product of projective spaces, we try to understand which Chow classes come from irreducible subvarieties. The answer is closely related to the theory of integer polymatroids. The support of a representable class can be (partially) characterized as some integer point inside a particular polymatroid. If the class is multiplicity-free, we obtain a complete characterization in terms of representable polymatroids. We also generalize some of the results to the case of products of Grassmannians., Comment: This has been generalized and expanded in another paper that also includes additional coauthors, available at arXiv:2005.07808

In this paper, our objective is to find out the determining factors of Chernoff information in distinguishing a set of Gaussian trees. In this set, each tree can be attained via an edge removal and grafting operation from another tree. This is equivalent to asking for the Chernoff information between the most-likely confused, i.e. "bottleneck", Gaussian trees, as shown to be the case in ML estimated Gaussian tree graphs lately. We prove that the Chernoff information between two Gaussian trees related through an edge removal and a grafting operation is the same as that between two three-node Gaussian trees, whose topologies and edge weights are subject to the underlying graph operation. In addition, such Chernoff information is shown to be determined only by the maximum generalized eigenvalue of the two Gaussian covariance matrices. The Chernoff information of scalar Gaussian variables as a result of linear transformation (LT) of the original Gaussian vectors is also uniquely determined by the same maximum generalized eigenvalue. What is even more interesting is that after incorporating the cost of measurements into a normalized Chernoff information, Gaussian variables from LT have larger normalized Chernoff information than the one based on the original Gaussian vectors, as shown in our proved bounds, Comment: Submitted to ISIT2016, and this version contains proofs of the propositions in the paper