Block Representation Research Articles

Non-regular homogenous block representation for low bit rate depth coding in 3D video

In multi-view video plus depth (MVD) format based 3D video (3DV) systems, the quality of the rendered virtual views depends highly on the quality of the compressed depth maps. Therefore, depth coding technology is vital for 3DV applications. This paper proposed a superpixel based non-regular homogenous block (NRHB) representation for low bit rate depth map coding. At the encoder side, with the aid of the superpixel segmentation of the associated texture images and the synthesis distortion estimation of the virtual views, the original depth maps are partitioned into several NRHBs and represented with only a small amount of pixels. Then, the NRHB represented depth maps are compressed by using the standard video coding approach afterward. At the decoder side, the depth maps are reconstructed through position mapping of the superpixel segmentation of the decoded texture images, and enhanced by a false edge filter. The experimental results show that the proposed method could impressively increase both the coding efficiency of the depth maps and the rendering quality of the virtual views. It also can be seen that the proposed method significantly reduced the encoding computational complexity for depth maps, which makes it particularly useful for the low bandwidth mobile consumer devices with limited computational resources.

Assessment of Soil Variability of South Moravian Region Based on the Satellite Imagery

The aim of this study was to analyse the sets of atmospherically corrected Remote Sensing (RS) data in order to assess the variability of bare arable land between different soil blocks in the selected area and evaluate the suitability of this approach for locally targeted management. The study was carried out on the territory of parts of South Moravian, Vysocina and Zlín regions. The RS data was analyzed by two models developed in the Arc GIS 10.22 environment using the Normalized Differential Vegetation Index (NDVI) and the Principal component analysis (PCA) analyzing bare soil (BS) with more than 50 % and more than 95 % of the block representation. A layer of agricultural land from the LPIS system was used to delimit arable land areas. For correct determinig of BS value for NDVI were carried out the terrestrial measurements in the monitored area by using the GreenSeeker handheld crop sensor and The FieldSpec® HandHeld 2 spectrometer. Based on these measurements and image dates, 0.2 NDVI was selected as the limit value. As a more suitable source for identifying BS, RapidEye appears to be able to identify an average of 26 % of the observed area as bare ground compared to Sentinel 2 data (22.5 % of the observed area) in models with more than 50 % By representing the BS in a block (NDVI 50, PCA 50). In these versions of the model was more variable soil (VS) indicated by RapidEye. With more than 95 % of the BS in the block (NDVI 95, PCA 95) was found more variable soils by Sentinel 2. This method of indirectly identifying soil variability can assist in the application of fertilizer or soil treatment in the area of site‑specific management.

Block Representation and Spectral Properties of Constant Sum Matrices

An equivalent representation of constant sum matrices in terms of block-structured matrices is given in this paper. This provides an easy way of constructing all constant sum matrices, including those with further symmetry properties. The block representation gives a convenient description of the dihedral equivalence of such matrices. It is also shown how it can be used to study their spectral properties, giving explicit formulae for eigenvalues and eigenvectors in special situations, as well as for quasi-inverses when these exist.

Fast and Stable Computation of the Charlier Moments and Their Inverses Using Digital Filters and Image Block Representation

In this paper, we suggest a new method of fast and stable calculation of the discrete orthogonal moments of Charlier and their inverses. This method is meant to accelerate the computation time and improve the quality of images reconstruction. In this method, we have combined two main concepts. The first concept is the digital filters based on the Z-transform to accelerate the calculation process of the discrete orthogonal moments of Charlier. The second concept is the partitioning of the image into a set of blocks of fixed sizes where each block is processed independently. The significant reduction in the image space during partitioning makes it possible to represent the minute details of the image with only low orders of Charlier’s discrete orthogonal moments, which ensures the digital stability during the processing of the image. In order to demonstrate the efficiency, stability, and precision of our method compared to other existing methods, some simulations have been performed on different types of binary images and gray images with and without noise.

Spectrum of J-frame operators

A $J$-frame is a frame $\mathcal{F}$ for a Krein space $(\mathcal{H}, [\, , \,])$ which is compatible with the indefinite inner product $[\, , \, ]$ in the sense that it induces an indefinite reconstruction formula that resembles those produced by orthonormal bases in $\mathcal{H}$. With every $J$-frame the so-called $J$-frame operator is associated, which is a self-adjoint operator in the Krein space $\mathcal{H}$. The $J$-frame operator plays an essential role in the indefinite reconstruction formula. In this paper we characterize the class of $J$-frame operators in a Krein space by a $2\times 2$ block operator representation. The $J$-frame bounds of $\mathcal{F}$ are then recovered as the suprema and infima of the numerical ranges of some uniformly positive operators which are build from the entries of the $2\times 2$ block representation. Moreover, this $2\times 2$ block representation is utilized to obtain enclosures for the spectrum of $J$-frame operators, which finally leads to the construction of a square root. This square root allows a complete description of all $J$-frames associated with a given $J$-frame operator.

Numerical modelling of cantilever failure and effect of slump blocks on meander migration

This study proposes a new numerical model to study cantilever failures and the effect of slump blocks on meander migration in cohesive river banks. Previous models have incorporated the effect of slump blocks using different methodologies but most of them used an “indirect approach” (such as increasing the critical shear stresses or introducing armouring factors) which does not allow to evaluate the effect of slump blocks directly. The new numerical model introduces an explicit representation of slump blocks and it was obtained by coupling two models available on the literature. The model was able to represent the mechanisms of cantilever failure with slump blocks and their effect in meander migration in a hypothetical small scale channel.

Operator product expansion for conformal defects

We study the operator product expansion (OPE) for scalar conformal defects of any codimension in CFT. The OPE for defects is decomposed into “defect OPE blocks”, the irreducible representations of the conformal group, each of which packages the contribution from a primary operator and its descendants. We use the shadow formalism to deduce an integral representation of the defect OPE blocks. They are shown to obey a set of constraint equations that can be regarded as equations of motion for a scalar field propagating on the moduli space of the defects. By employing the Radon transform between the AdS space and the moduli space, we obtain a formula of constructing an AdS scalar field from the defect OPE block for a conformal defect of any codimension in a scalar representation of the conformal group, which turns out to be the Euclidean version of the HKLL formula. We also introduce a duality between conformal defects of different codimensions and prove the equivalence between the defect OPE block for codimension-two defects and the OPE block for a pair of local operators.

Quantum Hitchin Systems via $${\beta}$$ β -Deformed Matrix Models

We study the quantization of Hitchin systems in terms of $${\beta}$$ -deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov–Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the $${\epsilon_1}$$ -deformation of the chiral observables of the corresponding $${{\mathcal{N}=2}}$$ four dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions.

Solving fuzzy linear systems using a block representation of generalized inverses: The Moore–Penrose inverse

In this paper we present a new method for solving an m×n fuzzy linear system (FLS), AX˜=Y˜, where the coefficient matrix A is real, using the block representation of generalized inverses. A necessary and sufficient condition for a block matrix to be the Moore–Penrose inverse of the full rank matrix associated to a FLS is given. We obtain a necessary and sufficient condition for the existence of solutions of a FLS, with arbitrary real coefficient matrix. The exact algebraic form, with respect to the Moore–Penrose inverse, of any solution of FLS of this type is established. A general, efficient and universal method for obtaining the exact solutions is introduced. Some numerical examples are presented to illustrate the proposed method.

Spinning geodesic Witten diagrams

We present an expression for the four-point conformal blocks of symmetric traceless operators of arbitrary spin as an integral over a pair of geodesics in Anti-de Sitter space, generalizing the geodesic Witten diagram formalism of Hijano et al. [1] to arbitrary spin. As an intermediate step in the derivation, we identify a convenient basis of bulk threepoint interaction vertices which give rise to all possible boundary three point structures. We highlight a direct connection between the representation of the conformal block as geodesic Witten diagram and the shadow operator formalism.

Deep linear autoencoder and patch clustering-based unified one-dimensional coding of image and video

This paper proposes a unified one-dimensional (1-D) coding framework of image and video, which depends on deep learning neural network and image patch clustering. First, an improved K-means clustering algorithm for image patches is employed to obtain the compact inputs of deep artificial neural network. Second, for the purpose of best reconstructing original image patches, deep linear autoencoder (DLA), a linear version of the classical deep nonlinear autoencoder, is introduced to achieve the 1-D representation of image blocks. Under the circumstances of 1-D representation, DLA is capable of attaining zero reconstruction error, which is impossible for the classical nonlinear dimensionality reduction methods. Third, a unified 1-D coding infrastructure for image, intraframe, interframe, multiview video, three-dimensional (3-D) video, and multiview 3-D video is built by incorporating different categories of videos into the inputs of patch clustering algorithm. Finally, it is shown in the results of simulation experiments that the proposed methods can simultaneously gain higher compression ratio and peak signal-to-noise ratio than those of the state-of-the-art methods in the situation of low bitrate transmission.

Synthesis of generalized neural elements by means of the tolerance matrices

Application of neuromorphic structures in various spheres of human activity on the basis of generalized neural elements will become possible if effective methods for verifying realizability of the logic algebra functions by one neuron element with a generalized threshold activation function and synthesis of such elements with a large number of edntries are developed. A notion of nucleus of Boolean functions in relation to a given system of characters was introduced and algebraic structure of nuclei and reduced nuclei of Boolean functions was investigated. Relation between the nuclei of the logic algebra functions which are realized by one generalized neural element and matrices of tolerance was established. It was shown that the Boolean function is realized by one generalized neuron element if and only if the nucleus of this function admits representation by the matrices of tolerance. If there is no nucleus relative to a specified system of characters for a Boolean function, then such a function is not realized by one generalized neural element in relation to a specified system of characters. On the basis of the properties of the matrices of tolerance, a number of necessary and sufficient conditions for realization of the logic algebra functions by one generalized neural element were obtained. Based on the sufficient conditions, an algorithm for synthesis of integer-valued generalized neural elements with a large number of entries was constructed. In the synthesis of integer-valued generic neural elements for realization of the logic algebra functions, a block representation of the Boolean function nucleus was used and based on the properties of the matrices of tolerance, coordinates of the integer vector of the structure of the generalized neural element were sequentially found

A Novel Machine Vision Based Image Analysis Method for the Analysis of Mixing Elements in Rotary Drums

Mixing performance in continuous rotary drums has been studied. The video analysis method was developed to evaluate different configurations of straight lifters in the rotary drum. The method converts a captured video into a single image, called stack image. The color marker tracking was estimated based on the color saturation of the stack image. Coefficients of variation and mixing indices were calculated from the color saturation profiles for different straight blade lifter configurations. The video analysis method was confronted to the impulse response of acid concentrations in water solutions. The developed analysis method has been superior with viscous fluids compared to traditional tracer impulse method in mixing evaluations. Water and 1% CMC-water solution were used in this mixing study for covering broadly different viscous materials. The drum lengthwise results for one lifter configuration were obtained from a single experiment due to the block representation of the image analysis method. It enables mixing analysis of axial segments and interaction analysis of mixer configurations. Thus, the axial mixing can be studied in more detail with rotary drums. The increase of lifters, residence time, and tip speed improved axial mixing in the studied experimental setup.

Various semiclassical limits of torus conformal blocks

We study four types of one-point torus blocks arising in the large central charge regime. There are the global block, the light block, the heavy-light block, and the linearized classical block, according to different regimes of conformal dimensions. It is shown that the blocks are not independent being connected to each other by various links. We find that the global, light, and heavy-light blocks correspond to three different contractions of the Virasoro algebra. Also, we formulate the c-recursive representation of the one-point torus blocks which is relevant in the semiclassical approximation.

Multiple representation based sample diversity for face recognition

Proper representation plays a significant role in pattern recognition fields, effective representation of an image makes it easier to be distinguished from images of other classes and can improve the accuracy of classification. In this paper, to obtain appropriate representation of a face, we propose a novel method to represent an original sample. We crop the original image into a number of non-overlapping blocks, and certain operations are applied to each block, then merge all the modified blocks and obtain a new representation of the original sample. Furthermore, we integrate original samples and its corresponding block representations, which provide more local information of images and allow higher accuracy to be achieved. The extensive experiments demonstrate that our proposed method is robust and obtain better accuracy for face recognition in comparison with previous methods.

Fast iterative solution of the Bethe–Salpeter eigenvalue problem using low-rank and QTT tensor approximation

In this paper, we propose and study two approaches to approximate the solution of the Bethe–Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both approaches are based on the reduced basis method and low-rank factorizations of the generating matrices. We also propose to represent the static screen interaction part in the BSE matrix by a small active sub-block, with a size balancing the storage for rank-structured representations of other matrix blocks. We demonstrate by various numerical tests that the combination of the diagonal plus low-rank plus reduced-block approximation exhibits higher precision with low numerical cost, providing as well a distinct two-sided error estimate for the smallest eigenvalues of the Bethe–Salpeter operator. The complexity is reduced to O(Nb2) in the size of the atomic orbitals basis set, Nb, instead of the practically intractable O(Nb6) scaling for the direct diagonalization. In the second approach, we apply the quantized-TT (QTT) tensor representation to both, the long eigenvectors and the column vectors in the rank-structured BSE matrix blocks, and combine this with the ALS-type iteration in block QTT format. The QTT-rank of the matrix entities possesses almost the same magnitude as the number of occupied orbitals in the molecular systems, No<Nb, hence the overall asymptotic complexity for solving the BSE problem by the QTT approximation is estimated by O(log⁡(No)No2). We confirm numerically a considerable decrease in computational time for the presented iterative approaches applied to various compact and chain-type molecules, while supporting sufficient accuracy.

The Resolution Sensitivity of Northern Hemisphere Blocking in Four 25-km Atmospheric Global Circulation Models

The aim of this study is to investigate if the representation of Northern Hemisphere blocking is sensitive to resolution in current-generation atmospheric global circulation models (AGCMs). An evaluation is conducted of how well atmospheric blocking is represented in four AGCMs whose horizontal resolution is increased from a grid spacing of more than 100 km to about 25 km. It is shown that Euro-Atlantic blocking is simulated overall more credibly at higher resolution (i.e., in better agreement with a 50-yr reference blocking climatology created from the reanalyses ERA-40 and ERA-Interim). The improvement seen with resolution depends on the season and to some extent on the model considered. Euro-Atlantic blocking is simulated more realistically at higher resolution in winter, spring, and autumn, and robustly so across the model ensemble. The improvement in spring is larger than that in winter and autumn. Summer blocking is found to be better simulated at higher resolution by one model only, with little change seen in the other three models. The representation of Pacific blocking is not found to systematically depend on resolution. Despite the improvements seen with resolution, the 25-km models still exhibit large biases in Euro-Atlantic blocking. For example, three of the four 25-km models underestimate winter northern European blocking frequency by about one-third. The resolution sensitivity and biases in the simulated blocking are shown to be in part associated with the mean-state biases in the models’ midlatitude circulation.

System performance indicators of regional economic security

The article presents the scientific analysis of the elements of the developed methods for constructing effective system of the regional economic security, which is important for the national security in the whole. The purposes of economic security management, which determines the ways of applying the proposed methods, are outlined. The notion of “regional system of providing economic security” is introduced and the objects of providing security are identified. The relevance of creating the direct and reversed data streams is clarified with federal executive bodies, especially with fiscal and law enforcement, and the development of the forms of interaction with social groups and economic agents is presented. The socio-economic indicators, which serve as criteria for effectiveness of the economic security system, are stressed. All the elements of the given system integrated into the system of management of socio-economic region development have block representation. The article emphasizes the necessity of identifying specific weight value of each constituent element of security during the complex estimation. Keywords – economic security, effective system, interconnected components of the system, the regional program, the public demands, minimizing internal and external threats.

Resolution, physics and atmosphere–ocean interaction – How do they influence climate model representation of Euro-Atlantic atmospheric blocking?

Atmospheric blocking events are known to locally explain a large part of climate variability. However, despite their relevance, many current climate models still struggle to represent the observed blocking statistics. In this study, simulations of the global climate model EC-Earth are analysed with respect to atmospheric blocking. Seventeen simulations map the uncertainty space defined by the three-model characteristics: atmospheric resolution, physical parameterization and complexity of atmosphere–ocean interaction, namely an atmosphere coupled to an ocean model or forced by surface data. Representation of the real-world statistics is obtained from reanalyses ERA-20C, JRA-55 and ERA-Interim which agree on Northern Hemisphere blocking characteristics. Blocking events are detected on a central blocking latitude which is individually determined for each simulation. The frequency of blocking events tends to be underestimated relative to ERA-Interim over the Atlantic and western Eurasia in winter and overestimated during spring months. However, only few model setups show statistically significant differences compared to ERA-Interim which can be explained by the large inter-annual variability of blocking. Results indicate slightly larger biases relative to ERA-Interim in coupled than in atmosphere-only models but differences between the two are not statistically significant. Although some resolution dependence is present in spring, the signal is weak and only statistically significant if the physical parameterizations of the model are improved simultaneously. Winter blocking is relatively more sensitive to physical parameterizations, and this signal is robust in both atmosphere-only and coupled simulations, although stronger in the latter. Overall, the model can capture blocking frequency well despite biases in representing the mean state of geopotential height over this area. Blocking signatures of geopotential height are represented more similar to ERA-Interim and only weak sensitivities to model characteristics remain.

Benefits of Increasing the Model Resolution for the Seasonal Forecast Quality in EC-Earth

Abstract Resolution in climate models is thought to be an important factor for advancing seasonal prediction capability. To test this hypothesis, seasonal ensemble reforecasts are conducted over 1993–2009 with the European community model EC-Earth in three configurations: standard resolution (~1° and ~60 km in the ocean and atmosphere models, respectively), intermediate resolution (~0.25° and ~60 km), and high resolution (~0.25° and ~39 km), the two latter configurations being used without any specific tuning. The model systematic biases of 2-m temperature, sea surface temperature (SST), and wind speed are generally reduced. Notably, the tropical Pacific cold tongue bias is significantly reduced, the Somali upwelling is better represented, and excessive precipitation over the Indian Ocean and over the Maritime Continent is decreased. In terms of skill, tropical SSTs and precipitation are better reforecasted in the Pacific and the Indian Oceans at higher resolutions. In particular, the Indian monsoon is better predicted. Improvements are more difficult to detect at middle and high latitudes. Still, a slight improvement is found in the prediction of the winter North Atlantic Oscillation (NAO) along with a more realistic representation of atmospheric blocking. The sea ice extent bias is unchanged, but the skill of the reforecasts increases in some cases, such as in summer for the pan-Arctic sea ice. All these results emphasize the idea that the resolution increase is an essential feature for forecast system development. At the same time, resolution alone cannot tackle all the forecast system deficiencies and will have to be implemented alongside new physical improvements to significantly push the boundaries of seasonal prediction.