Non-additive image steganographic framework based on variational inference in Markov Random Fields

Maximum a posteriori (MAP) inference in Markov random field (MRF) lays the foundation for many computer vision tasks, which can be formulated by a binary quadratic programming (BQP) problem. Compar...

We consider general discrete Markov Random Fields(MRFs) with additional bottleneck potentials which penalize the maximum (instead of the sum) over local potential value taken by the MRF-assignment. Bottleneck potentials or analogous constructions have been considered in (i) combinatorial optimization (e.g. bottleneck shortest path problem, the minimum bottleneck spanning tree problem, bottleneck function minimization in greedoids), (ii) inverse problems with $L_{\infty}$-norm regularization and (iii) valued constraint satisfaction on the $(\min,\max)$-pre-semirings. Bottleneck potentials for general discrete MRFs are a natural generalization of the above direction of modeling work to Maximum-A-Posteriori (MAP) inference in MRFs. To this end we propose MRFs whose objective consists of two parts: terms that factorize according to (i) $(\min,+)$, i.e. potentials as in plain MRFs, and (ii) $(\min,\max)$, i.e. bottleneck potentials. To solve the ensuing inference problem, we propose high-quality relaxations and efficient algorithms for solving them. We empirically show efficacy of our approach on large scale seismic horizon tracking problems.

This paper presents a new color image analysis approach which fuses several processing maps by Graph-Cuts algorithm for Markov Random Field (MRF) in different color spaces. Recently, graph-based image analysis methods, such as Graph-Cuts, have been achieved exciting results for approximate inference in Markov Random Field. One color image can be represented in many color spaces, such as RGB, LAB and HSV, but existing Graph-Cuts approaches often compute global energy function only in one color spaces and ignore that each color space has an interesting property for certain applications respectively. This paper processes images in MRF and represents them in one MRF model firstly. Then Graph-Cuts algorithms are used to process images in each color space and generate one map. Several processing maps can be acquired from some color spaces. These maps are fused to get more reliable and accurate results. We select stereo matching which can get depth maps from multi-view images to evaluate our image analysis approach. The experiments herein reported in this paper illustrate the potential of this approach compared to existing Graph-Cuts methods from processing results.

Markov Random Fields (MRFs) are a popular model for several pattern recognition and reconstruction problems in robotics and computer vision. Inference in MRFs is intractable in general and related work resorts to approximation algorithms. Among those techniques, semidefinite programming (SDP) relaxations have been shown to provide accurate estimates while scaling poorly with the problem size and being typically slow for practical applications. Our first contribution is to design a dual ascent method to solve standard SDP relaxations that takes advantage of the geometric structure of the problem to speed up computation. This technique, named Dual Ascent Riemannian Staircase (DARS), is able to solve large problem instances in seconds. Our second contribution is to develop a second and faster approach. The backbone of this second approach is a novel SDP relaxation combined with a fast and scalable solver based on smooth Riemannian optimization. We show that this approach, named Fast Unconstrained SEmidefinite Solver (FUSES), can solve large problems in milliseconds. Contrarily to local MRF solvers, e.g., loopy belief propagation, our approaches do not require an initial guess. Moreover, we leverage recent results from optimization theory to provide per-instance sub-optimality guarantees. We demonstrate the proposed approaches in multi-class image segmentation problems. Extensive experimental evidence shows that (i) FUSES and DARS produce near-optimal solutions, attaining an objective within 0.1% of the optimum, (ii) FUSES and DARS are remarkably faster than general-purpose SDP solvers, and FUSES is more than two orders of magnitude faster than DARS while attaining similar solution quality, (iii) FUSES is faster than local search methods while being a global solver.

Herding is an algorithm of recent interest in the machine learning community, motivated by inference in Markov random fields. It solves the following sampling problem: given a setX R d with mean , construct an infinite sequence of points fromX such that, for every t 1, the mean of the first t points in that sequence lies within Euclidean distance O(1=t) of . The classic Perceptron boundedness theorem implies that such a result actually holds for a wide class of algorithms, although the factors suppressed by the O(1=t) notation are exponential in d. Thus, to establish a non-trivial result for the sampling problem, one must carefully analyze the factors suppressed by theO(1=t) error bound. This paper studies the best error that can be achieved for the sampling problem. Known analysis of the Herding algorithm give an error bound that depends on geometric properties ofX but, even under favorable conditions, this bound depends linearly on d. We present a new polynomialtime algorithm that solves the sampling problem with error O p d log 2:5 jXj=t assuming thatX is finite. Our algorithm is based on recent algorithmic results in discrepancy theory. We also show that any algorithm for the sampling problem must have error ( p d=t). This implies that our

This paper introduces a multimodal approach for reranking of image retrieval results based on relevance feedback. We consider the problem of reordering the ranked list of images returned by an image retrieval system, in such a way that relevant images to a query are moved to the first positions of the list. We propose a Markov random field (MRF) model that aims at classifying the images in the initial retrieval-result list as relevant or irrelevant; the output of the MRF is used to generate a new list of ranked images. The MRF takes into account (1) the rank information provided by the initial retrieval system, (2) similarities among images in the list, and (3) relevance feedback information. Hence, the problem of image reranking is reduced to that of minimizing an energy function that represents a trade-off between image relevance and interimage similarity. The proposed MRF is a multimodal as it can take advantage of both visual and textual information by which images are described with. We report experimental results in the IAPR TC12 collection using visual and textual features to represent images. Experimental results show that our method is able to improve the ranking provided by the base retrieval system. Also, the multimodal MRF outperforms unimodal (i.e., either text-based or image-based) MRFs that we have developed in previous work. Furthermore, the proposed MRF outperforms baseline multimodal methods that combine information from unimodal MRFs.

Broadcast Encryption (BE) schemes allow a sender to efficiently encrypt messages for a large set of receivers. The currently most efficient BE schemes in the stateless receiver scenario are based on symmetric cryptography. However, a variety of business models with mutually mistrusting senders necessitates the use of asymmetric cryptography. We propose a generic framework that allows to transform a large class of symmetric BE schemes into asymmetric schemes, where the transformation employs an arbitrary hierarchical identity based encryption scheme. Applying our framework, we transform a recent symmetric scheme, called layered punctured interval scheme, for which no asymmetric version has yet been published. In addition, we give a formal proof of the chosen ciphertext security of our framework, which allows to generically transform any future symmetric BE scheme within the large class into a chosen-ciphertext-secure asymmetric scheme with the same efficiency measures.

In this paper we propose an identification and restoration algorithm for image degraded by noise as well as blurring. In our proposed method, the original images are modeled as Markov Random Fields(MRF) and the blurred image is presented by the gaussian blurred model. To estimate the parameters involved in the image model and to restore the degraded images, we use Generalized Maximum Likelihood(GML) estimation. The GML consists of the two procedures which is a Maximum Likelihood(ML) estimation and a Maximum A Posteriori(MAP) estimation. These procedures are implemented by using the Expectation-Maximization(EM) algorithm and mean field annealing(MFA) based on the mean field theory.

A novel method for obtaining dense displacement fields from a sequence of frames is presented. The algorithm is based on modeling the displacement field as a Markov random field, hence making it possible to use the equivalence of a Markov random field and a Gibbs distribution. The Gibbs distribution is used to define a mean field probability density function, and the displacement field is found using a mean field annealing algorithm. Mean field annealing is a technique which finds the global or near global minima in nonconvex optimization problems. Analysis of the algorithm and experimental results are presented. >

For short reach and metro applications, single sideband (SSB) is a promising scheme due to its high spectral efficiency and tolerance to chromatic dispersion. In this study, we propose a novel asymmetric twin-SSB scheme based on Nyquist pulse shaping. Without joint equalization, the two sidebands can be separately detected with a small guard band. We experimentally demonstrate 224-Gb/s 16-ary quadrature amplitude modulation (16-QAM) asymmetric twin-SSB transmission with direct detection. After 240-km standard single mode fiber (SSMF) transmission, the bit error rates (BERs) of the right-sideband (RSB) and the left-sideband (LSB) are 3.2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> and 2.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , respectively, which are below the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . The net bitrate is 203.7 Gb/s with consideration of both frame redundancy and HD-FEC overhead. To our best knowledge, we report the longest transmission distance for 200G single wavelength and single polarization direct detection systems. The advantages of the asymmetric twin-SSB scheme over the symmetric scheme are discussed through simulating the crosstalk resistance of both two schemes. We also demonstrate 300-Gb/s 32-QAM transmission over 80-km SSMF. The BERs of RSB and LSB are 1.50 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> and 1.61 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> , respectively, which are below the 15% soft-decision forward error correction (SD-FEC) threshold of 1.8 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> . The net bitrate is 254.3 Gb/s with consideration of both frame redundancy and SD-FEC overhead. To our best knowledge, it is the maximum bitrate ever reported for C-band 80-km single wavelength and single polarization direct detection transmission. The proposed scheme provides a useful and low-cost solution for high speed datacenter interconnection and metro-scale transmission.

The security of the linear optics cloning machine-enhanced passive continuous-variable measurement-device-independent quantum key distribution is investigated. Passive state preparation is employed at both legitimate parties to reduce the system complexity and eliminate the strict requirements on electro-optical modulators. At the receiver, linear optics cloning machine is utilized to compensate for the degradation induced by the preparation noise. In the presence of detection noise, the expression of the composable secret key rate of the proposed scheme under collective attacks is derived, and simulation results show that the proposed scheme can flexibly optimize the system performance under both symmetric scheme and asymmetric scheme.

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully applied to various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions.

Markov random field (MRF) based methods have been widely used in high spatial resolution (HSR) image classification. However, many existing MRF-based methods put more emphasis on pixel level contexts while less on superpixel level contextual information. To cope with this issue, this article presents a novel bilevel contextual MRF framework, named BLC-MRF, for HSR imagery classification. Specifically, pixel and superpixel level dependence are incorporated into the proposed MRF model to fully exploit spectral–spatial contextual information and preserve object boundaries in HSR images. In BLC-MRF, a pixel level MRF model is first performed and then cascaded as an input of a superpixel level MRF. In superpixel level, unary and pairwise potential terms are constructed by using the superpixel probability estimation method and spectral histogram distance, respectively. At last, a contextual MRF model is conducted and the final classification map can be computed by using $\alpha$ -expansion algorithm. The benefits of BLC-MRF are twofold: first, the pixel and superpixel level contextual information can be exploited under MRF framework to preserve object boundaries for improving the classification performance, and, second, the algorithm can provide promising results with a small number of training samples. Experimental results on three HSR datasets demonstrate that the proposed approach outperforms several state-of-the-art methods in terms of the classification performance.

In this paper, we propose a sequence labeling method by using SVM posterior probabilities with a Markov Random Field (MRF) model for colorectal Narrow Band Imaging (NBI) zoom-videoendoscope. Classifying each frame of a video sequence by SVM classifiers independently leads to an output sequence which is unstable and hard to understand by endoscopists. To make it more stable and readable, we use an MRF model to label the sequence of posterior probabilities. In addition, we introduce class asymmetry for the NBI images in order to keep and enhance frames where there is a possibility that cancers might have been detected. Experimental results with NBI video sequences demonstrate that the proposed MRF model with class asymmetry performs much better than a model without asymmetry.

Segmentation is a low-level processing aimed at the partition of an image in disjoint regions, each one homogeneous with respect to some properties like intensity, texture, shape, etc. Such a task is needed in many high-level processing and applications in such diverse fields as remote-sensing, medical imaging, video coding, and industrial automation, just to name a few. In this work of thesis, we first deal with the problem of color based image segmentation, that is based on some form of homogeneity in the color/spectral properties of the image, and then move to the more complex task of texture based segmentation, where the aim is to recognize complex structures in the image which are typically non homogeneous in terms of spectral properties. Concerning color based segmentation, we focus on a specific class of Markov Random Field (MRF) probability models, namely the Tree-Structured Markov Random Fields (TS-MRF), recently proposed to provide a hierarchical multiscale description of images. Based on such a model, the unsupervised image segmentation is carried out by means of a sequence of nested class splits, where each class is modeled as a local binary MRF. As a first contribution, we first extend the model to generic tree structures removing the unnecessary binary constraint, and then devise a new TS-MRF unsupervised segmentation technique which improves upon the original algorithm by selecting a better tree structure and eliminating spurious classes. Such results are obtained by using the Mean-Shift procedure to estimate the number of pdf modes at each node, and to obtain a more reliable initial clustering for subsequent MRF optimization. To this end, we devise a new reliable and fast clustering algorithm based on the Mean-Shift technique, which makes use of a variable-bandwidth strategy based on the k-Nearest Neighbors (k-NN) technique, and is implemented with a speed-up strategy that cuts significantly the computational complexity. Experimental results on synthetic data and real life images from the remote sensing domain prove the potential of the proposed method. Turning to texture based segmentation, we present a novel multiscale texture model, and a related algorithm for the unsupervised segmentation of color images. Elementary textures are characterized by their spatial interactions with neighboring regions along selected directions. Such interactions are modeled in turn by means of a set of Markov chains, one for each direction, whose parameters are collected in a feature vector that synthetically describes the texture. Based on the feature vectors, the texture are then recursively merged, giving rise to larger and more complex textures, which appear at different scales of observation: accordingly, the model is named Hierarchical Multiple Markov Chain (H-MMC). The Texture Fragmentation and Reconstruction (TFR) algorithm, addresses the unsupervised segmentation problem based on the H-MMC model. The ``fragmentation'' step allows one to find the elementary textures of the model, while the ``reconstruction'' step defines the hierarchical image segmentation based on a probabilistic measure (texture score) which takes into account both region scale and inter-region interactions. The performance of the proposed method was assessed through the Prague segmentation benchmark, based on mosaics of real natural textures, and also tested on real-world natural images from the Berkeley dataset. Finally, an application of the TFR algorithm for the unsupervised segmentation of multiresolution remotely sensed images is proposed, based on the significant presence of textural content in last generation high-resolution satellite images. The obtained results further assess the potential of the proposed method for such real life applications.