Variable Block Size Research Articles

Quadtree-structured recursive plane decomposition coding of images

The approximation of two-dimensional highly correlated grey value functions can be performed using a linear model of the type f(x, y)=a+bx+cy. The set of plane parameters (PPs) (a, b, c) can be determined in the least squares sense for a block of size N*N pixels, for example. Starting with a block size of 2*2 pixels, it is shown that the PPs obey a recursive law such that the PPs of a 2N*2N block can be computed recursively when only the PPs of the four adjacent subblocks of size N*N in the lower decomposition level are known. This concept of recursive plane decomposition (RPD) is embedded in a quadtree data structure to obtain a new variable block size image coding algorithm that offers a high performance at a low computational cost. Extensive comparisons to other state-of-the-art image coding algorithms are reported.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Image sequence coding by adaptive vector quantization with variable block size

One problem with vector quantization for image sequence coding is poor reproduction of edges. This problem is particularly serious in applications to angiographic image sequences, where the edge information is often the crucial diagnostic information. A novel method proposed in this paper is adaptive vector quantization with variable block size. A large block size is desirable as it requires a lower bit rate; however, it can result in poor edge reproduction. On other hand, a smaller block size requires a higher bit rate but edges are better reproduced. An activity index is used to separate the blocks into two classes: active and nonactive. The nonactive blocks are coded by a primary codebook with a vector dimensionality of 16. The active blocks are further divided into smaller blocks of size 2 × 2 and coded by a secondary codebook. We show that it is possible to derive one codebook that applies to both vector dimensions. The temporal redundancies of the image sequence are exploited by using a modified replenishment technique: only the vector labels which change from frame to frame are transmitted. Pictorial results show that the edge features are well preserved upon reconstruction at bit rates about 0.7 bit/pixel.

Dynamic response of elastic blocks by time domain BEM and FEM

The dynamic behavior of massive elastic blocks bonded to an infinite soil medium (halfspace), and subjected to horizontal and vertical transient loads, is explored. The blocks, and, in some cases, a small portion of the underlying soil, are modeled by plane strain finite elements, whereas the remaining part of the halfspace is treated by a time domain boundary element method (BEM). Comprehensive investigations are performed to provide a quantitative assessment of the effects of various system parameters on the dynamic response of blocks. Thus, different soil stiffnesses, blocks of variable sizes and the effect of an embedment of the block into the soil, are considered. In addition, investigations taking into account an elastic inclusion in the interior of the halfspace or a second block (structure-soil-structure interaction effects) are discussed. Besides these studies, the finite element method (FEM)-BEM coupling approach presented permits an extension to consider nonlinear effects, as the entire formulation is given directly in the time domain.

Hierarchical address vector quantization for image coding

This paper presents a novel approach for utilizing the concept of interblock correlation to form variable size blocks. These blocks are then coded using a hierarchical coding model. Compared to the traditional mean-removed variable-block-size coding techniques, where a large block is successively partitioned into four smaller blocks as long as certain segmentation criteria are satisfied, the algorithm proposed in this paper is based on allowing a small mean-removed basic block to grow (by a factor of 2) recursively to a preset maximum (large) super block size as long as certain block correlation conditions are met. The block correlation condition is defined by whether or not an address codebook is addressable to code the larger-size block, where the address codebooks are designed ahead of time over a database of training images. For encoding the variable size blocks, the proposed algorithm utilizes only one pixel codebook for the basic block size and several address codebooks to encode larger block sizes. Through experiments, it is found that peak S N ratios in excess of 30 dB at bit rates lower than 0.2 bpp are easily obtained.

A Block Ordering Method for Sparse Matrices

Block iterative methods used for the solution of linear systems of algebraic equations can perform better when the diagonal blocks of the corresponding matrix are carefully chosen. A method is presented based on combinatorial considerations which permutes the rows and columns of a general matrix in such a way that relatively dense blocks of various sizes appear along the diagonal. The method is particularly useful when no natural partitioning of the matrix is available. Two parameters govern the method which is $O(n + \nu )$ in time and space, where n is the order of the matrix and $\nu $ is the number of nonzeros in the matrix. Numerical test results are presented which illustrate the performance of both the ordering algorithm and the block iterative methods with the resulting orderings.

Vector quantisation of image sequences using variable size and variable shape blocks

An algorithm for coding image sequences based on the segmentation of the differential image into variable size and variable shape blocks is described. The differential image is split into 4 × 4 blocks, that are grouped to form square and rectangular macro blocks of several areas. Each macro block is then vector quantised. Simulation results presented show that compression rates and subjective quality compare favourably with methods previously described.

Variable size block matching motion compensation with applications to video coding

Indexing term: Codes and decoding: Algorithms Abstract: In block matching type motion com- pensation schemes, the image is divided into blocks of the same size. For each block a search is conducted in the previous frame to locate the best correspondence. For the scheme to succeed an implicit assumption has to be made that the motion within each block is uniform, an assump- tion which may not necessarily be correct, and as a result the quality of the prediction suffers. In the paper, a new motion compensation scheme based on block matching is presented, where the size for each block is variable. The proposed algorithm adaptively divides the image into blocks of vari- able size to meet the assumption on uniform motion for all blocks. The scheme has been suc- cessfully applied to simple interframe video coding. It is shown that the proposed algorithm can be extended to form the basis of a complete and efficient codec with low complexity. The possibility of the combination of the scheme with novel hybrid coding techniques to form sophisti- cated systems with low bit-rate performance, that compare favourably with other existing schemes, is also demonstrated.

SOLVING SPARSE TRIANGULAR LINEAR SYSTEMS ON PARALLEL COMPUTERS

This paper describes and compares three parallel algorithms for solving sparse triangular systems of equations. These methods involve some preprocessing overhead and are primarily of interest in solving many systems with the same coefficient matrix. The first approach is to use a fixed blocksize and form the inverse of the diagonal blocks. The second approach is to use a variable blocksize and reorder the unknowns so that the diagonal blocks are diagonal matrices. The latter technique is called level scheduling because of how it is represented in the adjacency graph, and both row-wise and jagged diagonal storage for the off-diagonal blocks are considered. These techniques are analyzed for general parallel computers and experiments are presented for the eight-processor Alliant FX/8.

Compression of digital images based on vector quantization with variable block size

AbstractThe vector quantization recently has been considered interesting as a highly efficient coding for compressing digital images. For this purpose, the predictive coding and the transform coding have been known, but the vector quantization can realize the coding with fewer bits per pixel, which is a drastic compression compared with past methods. the image contains parts with different local properties such as parts with rapid intensity changes such as edge, and parts with slow intensity changes such as flat part. If this situation is taken into consideration, a more efficient coding can be realized. In the usual vector quantization, the overall image is divided into blocks of a constant size. In the coding based on the local property of the image, however, it is desirable to use blocks with variable sizes rather than a constant size. From such a viewpoint, this paper proposes a new vector quantization in which the block size resulting from the division is adjusted adaptively according to the local property of the image. First, the vector quantization with variable block size is described in detail. Then the proposed method is applied in several simulation problems, and the actual usefulness of the method using variable block sizes is demonstrated.

Sandstone dykes as evidence of localized transtension in a Transpressive Regime, Bir Zreir Area, eastern Sinai

The Bir Zreir area, NE Sinai, is part of the 40‐km‐wide eastern Sinai shear zone stretching along the western margin of the Gulf of Elat. Sinistral movement along faults comprising this shear zone is consistent with the regional NNW‐SSE compression in which the Dead Sea transform fault was formed. In the Bir Zreir area, sandstone dykes within NE striking fault breccias were developed within the Precambrian crystalline basement. These breccias, up to 200 m in width, resulted from transpression along the NE striking faults in response to sinistral movement along the NNE striking major faults. Paradoxically, the sandstone dykes developed by infilling of transtensional open fissures which share the NE trend of the breccia zones. The source rock for the dykes is Nubian Sandstone unconformably overlying the basement. The depth beneath the unconformity to which the sandstone collapsed is 500–600 m. Local NW‐SE transtension along parts of the NE striking faults enabled the formation of fissures and their infilling by sand and sandstone blocks of various sizes as dykes. The infilling occurred despite the regional NNW‐SSE compression which prevailed in the study area. A kinematic model is developed which combines sinistral movement and clockwise rotation of rigid blocks between the faults with resultant local NW‐SE transtension along the northern segment of the NE trending strike‐slip faults.

Fourth time-slice: mid-Devonian to Permian synthesis

Summary By some time in the middle Devonian, the Iapetus Ocean between Laurentia and Baltica was entirely closed (Acadian orogeny in the Maritimes and New England) and the Rheic Ocean between Baltica and proto-Gondwana was mostly closed (Devonian orogeny in France), although some relict oceanic basins ( cf. Black Sea) may have remained. The Theic Ocean between Laurentia and proto-Gondwana (Africa) may well have remained partly open for much longer, but probably contained already consolidated continental blocks of various sizes. Where closing was fairly complete, late Palaeozoic deformation took the form of relatively narrow zones, often rift zones containing pull-apart basins whose sediments were later strongly deformed (sometimes with plutonism and metamorphism), lacing between larger blocks that remained barely affected but moved en bloc by strike-slip (Maritimes, Armorica) or large-scale thrust movement (southern Appalachians, Mauritanides). Certain zones however, are former continental passive margins, e.g. the Appalachian Valley and Ridge and the folded belt from southern Ireland to the Rheinische Schiefergebirge. Remaining oceanic areas presumably closed diachronously during the Carboniferous or early Permian, but few are available for inspection (Lizard?). The Theic suture is apparently traceable by geophysics beneath the coastal plains and shelves from southern Portugal to Florida. Deformation in any one area was episodic (Stillean phases), but no consistent episodes can be followed over the whole orogen.

ERRORCALC ADAPTED: A BASIC microcomputer program to calculate error measures for variable block sizes

The software described in this paper is a modification of the original ERRORCALC program by Pizzimenti, Weeks, and Lee (1984). The program has been modified for use with the IBM PC and PC-XT (and compatible) microcomputers.

One dimensional 1/|j ? i| S percolation models: The existence of a transition forS?2

Consider a one-dimensional independent bond percolation model withpj denoting the probability of an occupied bond between integer sitesi andi±j,j≧1. Ifpj is fixed forj≧2 and\(\mathop {\lim }\limits_{j \to \infty }\)j2pj>1, then (unoriented) percolation occurs forp1 sufficiently close to 1. This result, analogous to the existence of spontaneous magnetization in long range one-dimensional Ising models, is proved by an inductive series of bounds based on a renormalization group approach using blocks of variable size. Oriented percolation is shown to occur forp1 close to 1 if\(\mathop {\lim }\limits_{j \to \infty }\)jspj>0 for somes<2. Analogous results are valid for one-dimensional site-bond percolation models.

PROPERTIES OF PARTIALLY EFFICIENCY-BALANCED DESIGNS

We consider a class of partially efficiency-balanced (PEB) designs which can be constructed in varying replicates and/or varying block sizes. These designs may be particularly useful for bioassays, com parative varietal trials and factorial experiments. This paper gives some bounds on design parameters, some parametric relations, dual designs, complementary designs and some simple construction-methods for PEB designs.

Radionuclide Transport Modelling in Fissured Zones and Channels

AbstractRadionuclides escaping from a repository for high level nuclear waste in crystalline rock may eventually be carried by the flowing water in fissure zones. In such zones the rock is broken in blocks of varying sizes and shapes. Also, the water velocity may vary very much along the flow path. The integrated finite difference method (IFDM) is proposed for numerical calculations of radionuclide transport in such zones. A method for lumping blocks of various sizes and shapes into a single PSEUDOBODY is tested by comparing it with an exact analytical solution which can account for the diffusion into blocks of any size distribution. The errors obtained in using the PSEUDOBODY-approach are found to be small. Furthermore, a method for determining an “average” Peclet number in a strongly varying velocity field is tested and found to give comparatively small errors.

An approach to modelling radionuclide migration in a medium with strongly varying velocity and block sizes along the flow path

Radionuclides escaping from a repository in crystalline rock for spent nuclear fuel will migrate with the seeping water in the fissures. Most radionuclides will be retarded by sorption on the rock surfaces and by diffusion into the rock matrix. Available surface for sorption and residence time are two prime variables which influence the radionuclide movement. The water velocity may vary very much along a flow path, especially if the flow path enters a strongly fissured zone (lineament). In this paper the radionuclides in a stream tube with an arbitrary velocity along the flow path have been investigated, and a numerical scheme based on the integrated finite difference method (IFDM) is proposed for practical calculations. The transport mechanisms considered are advection and longitudinal dispersion and the retardation mechanisms used are instantaneous sorption in a portion of the rock (surface sorption) and diffusion into the rock matrix and sorption on the micropore surfaces. An attempt is also made to account for blocks of various sizes and shapes in introduction of a “pseudobody.” This method accounts for the large sorption surface but small volume of small blocks and small surface area but large volume of large blocks. Any block size didtrubution can be handled.

Partitions of multisets II

A multiset is a set with repeated elements. We consider the number of partitions of a multiset of given cardinality into blocks which may be sets or multisets and may be repeated or not, giving four partition numbers in all. We first show that the number of blocks in a random partition (each partition equally likely) is asymptotically normal by deriving a local limit theorem. We then indicate how results of Haigh on the number of blocks of various sizes and largest block size can be extended from sets to multisets.

ERRORCALC: A BASIC microcomputer program to calculate psychophysical error measures for variable block sizes

Researchers who employ the method of constant stimuli often run a large number of trials to assess a treatment effect. The result, generally, is two esti­ mates of error: (1) the within-trial error for a particular treatment (i.e., the difference magnitude between the criterion or goal and the subject's estimate of that goal), and (2) the between-trial deviations for a particular number of these difference magnitudes. Behaviorally, these estimates of performance error indicate measures of accuracy and consistency, respectively. In a typical motor learning study, for example, if a subject completes 30 trials in attempting to achieve some criterion-referenced goal, each performance error score (i.e., the performance score-the criterion goal) may be grouped into blocks of, perhaps, 5 trials each. For each of the six blocks, then, estimates of perfor­ mance accuracy and consistency may be assessed and subjected to statistical analyses. The traditional measure of performance accuracy over a block of trials has been

Variable error: variance-covariance heterogeneity, block size and type L error rates.

The degree to which blocked (VE) data satisfies the assumptions of compound symmetry required for a repeated measures ANOVA was studied. Monte Carlo procedures were used to study the effect of violation of this assumption, under varying block sizes, on the Type l error rate. Populations of 10,000 subjects for each of two groups, the underlying variance-covariance matrices reflecting a specific condition of violation of the homogeneity of covariance assumptions, was generated based on each of three actual experimental data sets. The data were blocked in various ways, VE calculated, and subsequently analyzed by a repeated measures ANOVA. The complete process was replicated for four covariance homogeneity conditions for each of the three data sets, resulting in a total of 22,000 simulated experiments. Results indicated that the Type l error rate increases as the degree of heterogeneity within the variance-covariance matrices increases when raw (unblocked) data are analyzed. With VE, the effects of within-matrix heterogeneity on the Type l error rate are inconclusive. However, block size does seem to affect the probability of obtaining a significant interaction, but the nature of this relationship is not clear as there does not appear to be any consistent relationship between the size of the block and the probability of obtaining significance. For both raw and VE data there was no inflation in the number of Type l errors when the covariances within a given matrix were homogeneous, regardless of the differences between the group variance-covariance matrices.

Co-operative blocks in tropomyosin

The intramolecular melting of the α-tropomyosin coiled-coil and four of its fragments were studied by scanning microcalorimetry. It has been shown that: 1. (1) Melting of the native structure of α-tropomyosin is a complex process consisting of several discrete stages. The last stage in this process is a bimolecular reaction in the absence of the interchain S-S crosslink. 2. (2) The observed stages correspond to disruption of distinct co-operative blocks in this molecule. There are seven co-operative blocks of various sizes that can be localized unambiguously along the molecule. 3. (3) The co-operative blocks have different stabilities, which depend largely on the state of the neighbouring regions. Neighbouring blocks destabilize each other. 4. (4) The blocks from the middle part of the molecule are unstable in the absence of the interchain S-S crosslink. The conformation of this part of the tropomyosin molecule is determined by the state of the Cys190 residue. 5. (5) The co-operative regular structure does not include the terminal parts of the molecule The physical basis and biological significance of the subdivision of the tropomyosin coiled-coil into discrete co-operative blocks are discussed.