WO2011131248A1 - Procédé et appareil de compression/décompression de données sans perte - Google Patents

Procédé et appareil de compression/décompression de données sans perte Download PDF

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Publication number
WO2011131248A1
WO2011131248A1 PCT/EP2010/055465 EP2010055465W WO2011131248A1 WO 2011131248 A1 WO2011131248 A1 WO 2011131248A1 EP 2010055465 W EP2010055465 W EP 2010055465W WO 2011131248 A1 WO2011131248 A1 WO 2011131248A1
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WIPO (PCT)
Prior art keywords
node
datum
data
grid
spanning tree
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PCT/EP2010/055465
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English (en)
Inventor
Rudolph A. Lorentz
Matthias Rettenmeier
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Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V.
The Texas A & M University System
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Priority to PCT/EP2010/055465 priority Critical patent/WO2011131248A1/fr
Publication of WO2011131248A1 publication Critical patent/WO2011131248A1/fr

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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]

Definitions

  • the present invention concerns the field of compressing/decompressing data, more specifically, the field for losslessly compressing data stored on an unstructured grid, for example, data as it is provided by numerical simulations, for example, car-crash simulations, oil res- ervoir simulations or computational fluid dynamic simulations. More specifically, the present application is concerned with a method and an apparatus for losslessly compressing data stored on an unstructured grid, wherein a plurality of elements of the grid are associated with a datum. Further, the present invention is concerned with a method and an apparatus for decompressing data that was compressed in accordance with the inventive me- thod. In addition, the present invention concerns a computer-readable medium comprising a program code for executing the inventive method.
  • a further approach is known in the field of 3-D graphics that uses a finite element grid to model the surface of a solid object.
  • the cells are all planar and the goal of the compres- sion approach in this field, for example, the "topological surgery" is to compress the finite element grid.
  • data on the grid may be compressed using differences of data belonging to neighboring points.
  • all methods in this field are restricted to planar grids. But in structural mechanics (crash, NVH) planar and volumetric grids are used. In CFD 3D-volumetric grids are used.
  • the present invention provides a computer-readable medium carrying a program code for executing the inventive method when the program code is run on a computer.
  • the present invention provides a method for losslessly compressing data stored on an unstructured grid, wherein a plurality of elements of the grid are associated with a datum, the method comprising: determining a spanning tree comprising a plurality of nodes, each node corresponding to an element of the grid having associated therewith a datum, the spanning tree defining a sequence of nodes that go from one element of the grid having associated therewith a datum to a related element of the grid having associated therewith a datum such that the spanning tree visits each element of the grid and therewith its associated datum once; and running through the stored data in accordance with the sequence defined by the spanning tree, wherein for each node of the tree: a prediction value is calculated (108); and the difference between the datum associated with the node and its prediction value is stored (112), thereby compressing the datum associated with the node.
  • the present invention provides a method for decompressing data that was compressed in accordance with the inventive method, the method comprising: determining the spanning tree used for compression, the spanning tree comprising a plurality of nodes, each node having associated therewith a compressed datum, the spanning tree defining a sequence of the nodes; and running through the compressed data in accordance with the sequence defined by the spanning tree, wherein for each node of the trees: a prediction value is calculated; and the compressed datum associated with the node and its prediction value are added, thereby decompressing the datum associated with the node.
  • the present invention provides an apparatus for losslessly compressing data, comprising: a memory configured to store data on an unstructured grid, wherein a plurality of elements of the grid are associated with a datum; and a processor configured to determine a spanning tree comprising a plurality of nodes, each node corresponding to an element of the grid having associated therewith a datum, the spanning tree defining a sequence of nodes that goes from one element of the grid having associated therewith a datum to a related element of the grid having associated therewith a datum such that the spanning tree visits each element of the grid having associated the- rewith a database once; and run through the stored data in accordance with the sequence defined by the spanning tree, wherein for each node of the tree: a prediction value is calculated; and the difference between the datum associated with the node and its prediction value is stored, thereby compressing the datum associated with the node.
  • the present invention provides an apparatus for decompressing data, comprising: a memory configured to store the compressed data; and a processor configured to determine a spanning tree comprising the plurality of nodes, each node having associated therewith a compressed datum, the spanning tree defining a sequence of the nodes, run through the compressed datum in accordance with the sequence defined by the spanning tree, wherein for each node of the tree: a prediction value is calculated; and a compressed datum associated with the node and its prediction value are added, thereby decompressing the data associated with the node.
  • Embodiments of the invention provide a new way to losslessly compress integer data coming from numerical simulations.
  • Examples of such data are those coming from a car-crash, an oil reservoir or computational fluid dynamics simulations after quantization.
  • One of the main aspects of the inventive approach is the construction of a tree, which allows to visit each datum exactly once. As a consequence, the inventive approach yields better compres- sion factors than for any known compression program for this type of extrapolation based predictors.
  • the data is associated with a finite element or finite volume grid, which means that the data can belong to a vertex, to an edge, to a cell or to a face of the grid.
  • Embodiments of the invention assume that the data, which usually consists of floating point numbers has been quantized, that is, converted to integers.
  • a spanning tree can only be created for a connected graph.
  • Fig. 1 is a flow diagram representing the inventive method for compressing data in accordance with an embodiment
  • Fig. 2 is a flow diagram of the inventive method for compressing data in accordance with a further embodiment.
  • FIG. 3 shows a computational environment for implementing an apparatus for compressing data in accordance with yet another embodiment of the invention.
  • the method starts at step 100 and at step 102, an unstructured grid having a plurality of elements associated with a datum is provided.
  • the data populating the unstructured grid may be numerical data as it results from car-crash simulations, oil reservoir simulations, or computational fluid dynamics simulations.
  • the data associated with the grid are integer data, which is, for example, obtained by quantizing the floating point numbers obtained, in general, from the above-mentioned simulations. It is noted that the present invention is not limited to data resulting from the above-mentioned specific simulations. Rather, the inventive approach is applicable to any kind of data stored in an unstructured or even structured grids.
  • a spanning tree comprising the plurality of nodes is constructed.
  • a graph has to be formed.
  • the graph represents the relations within the grid (such as neighboring information).
  • a spanning tree for that graph is then created.
  • the me- thod proceeds or runs through the data in accordance with the ordering or sequence defined by the spanning tree. This is achieved by selecting, in step 106, a first node. This is the only node without prediction. Starting from this first node, an unvisited child node is selected, so that in step 108, a prediction value or a prediction for the datum to be com- pressed (the datum of the child node) is calculated.
  • step 110 a difference between the datum and the prediction is calculated.
  • the difference is stored in step 112 thereby compressing the datum.
  • the differences are encoded before they are stored to a medium. If the differences are small, an efficient encoding is possible, allowing a high compression ratio.
  • step 114 it is determined as to whether further child nodes of the currently visited node in the spanning tree exist. In case this is true, the method returns to step 108. If not, the method returns to the previous node to perform 114. If the method is at the first node again and there is no unvisited child the method has completed.
  • the decompression is quite similar and, actually, runs exactly the same way except that after the prediction has been calculated, it is added to the difference to obtain the original value. More specifically, again, the spanning tree that comprises a plurality of nodes is determined. This must be the same tree as during compression. However, each node is now associated with a compressed datum. In a similar manner as described above, again, a prediction value is calculated, which is added to the compressed data and since this com- pressed data is the difference between the original data and the prediction value, adding the prediction value again will retrieve the original value, thereby decompressing the data. In case the data was encoded during compression, also a corresponding decompression is done.
  • Fig. The embodiment described with regard to Fig.
  • the inventive approach is based on two components, namely running through the data in the sequential order as defined by the spanning tree, and a mathematical method (the predictor) to estimate the value of the datum to be compressed using the value of those data in the se- quence, which have already been compressed.
  • step 112 the difference between the correct value and the predictor is stored and provided the predictor is good, the absolute values of the differences are smaller than the absolute values of the original values and small absolute values can be better compressed than larger ones.
  • a status vector for each datum or for each component of the grid contains information on whether the datum/component has been visited
  • a finite grid in, for example, three-dimensional space consists of vertices, edges, faces and cells. Based on the vertices, edges, faces and cells and based on the topology of the grid, several graphs may be constructed to describe rela- tionships within the grid.
  • the graph G(V,E), for example, is the graph of vertices and edges. Two nodes within the graph G(V,E) are connected if they are within the finite element grid.
  • the graph G(V,E) is its dual. This is obtained by switching the role of vertices and edges.
  • the graph G(C,F) is the graph, which has cells as "nodes" and its faces as its "edges”.
  • two nodes of a graph will be connected if the cells they represent share a common face, for example, the cells in the finite element grid are neighbors.
  • many other types of graphs can be constructed for the same purpose. For the method of the inventive approach, these graphs are used and the grids should be completely connected. If this is not the case, the method can be applied to every component of the grid or sub-grid.
  • Each tree can be used to define hierarchical orderings of the nodes of the graph.
  • the hierarchy of the tree provides the necessary "direction" to be able to undo the prediction during decompression.
  • the data of a finite element grid may consist of vertex data, edge data, cell data and face data.
  • step 104 the inventive method constructs a spanning tree for any of the following data types: Vertex data, edge data, cell data and face data.
  • an appropriate graph has to be chosen/constructed, which is then used to construct a spanning tree. Since every node of a graph corresponds to a node/edge/cell/face of the grid, the spanning tree visits each node/edge/cell/face exactly once and is used together with the status vector to construct a sequence, which runs through all of the data exactly once.
  • the relationship between neighboring nodes of the tree is induced by the graph and, therefore, the tree always goes from one vertex/edge /cell/face to a neighboring or related vertex/edge /cell/face on the grid.
  • the sequence constructed goes from any datum to a nearby (related) datum.
  • the tree visiting, for example, each cell once is used to compress, for example, vertex data, as shall be described in further detail below with regard to further embodiments of the invention.
  • the predictor calculates a prediction for the datum being compressed.
  • the predictor uses one or more values of data, which have already been compressed. One ex- ample is just to use the previous datum in the sequence. Due to the hierarchical ordering given by the tree, starting at the root node means that a value at the parent node can always be used to predict a value at a child node. Due to the way the tree/sequence has been constructed, there will be a datum associated with a nearby/related point. As mentioned above, the difference between the predictor and the true value is stored in step 112.
  • a status vector for each datum or for each component in the grid is also provided.
  • the typical information stored in such a status vector for a datum is whether that value has been compressed.
  • the typical information stored in the status vector is whether that element has been visited. This information is used for the creation of the tree.
  • Embodiments of the present invention may allow optimizing the tree. This means that at each point in the construction of the tree, it is decided how to choose the next tree node so that a better compression factor is achieved.
  • An example, for compressing nodal data is to put weights on the edges of the graph C (V,E) containing vertices and edges of the finite element grid. If the variable is f and the value of f at the vertex numbered i is denoted by fi, the weight wij is set to be
  • the method starts at step 200 and is used to compress data that is stored on some sort of grid using a standard prediction method.
  • data usually means data obtained from numerical simulations, which is stored on some sort of a finite element grid or a finite volume grid. On such grids, the data is usually stored as vertex, edge, face or cell values.
  • a simply connected grid is assumed.
  • the problem with the use of prediction methods for data compression is that it must be reversible for decompression to work. For rectangular grids, this is an easy task, as an order is given by the regularity of the grids.
  • unstructured grids especially in three-dimensional unstructured volume grids, there is no such order given and it is, therefore, not clear which prediction path should be followed.
  • the inventive approach uses relations between the values to create a (weighted) graph.
  • the nodes of the graph then correspond to the values that shall be compressed and the edges of the graph indicate a relation between the values corresponding to the nodes connected by a respective edge.
  • This information may be given by the grid itself, for example, by neighboring information that can be derived from the grid, but might as well be any other information that describes relations between the values.
  • weights are in- troduced to the graph, an optimization can also be carried out. From the generated graph, a spanning tree, as discussed above, is then created that implicates an order from its root node to its leaves that allows a reversible compression.
  • Fig. 2 shows an example of an embodiment of this process and assuming that an unstructured grid is given, the processing will be as follows.
  • step 202 it is determined what a neighbor is.
  • neighboring nodes may be determined by respective elements of the grid that are connected, for example, data associated with cells that share a common face in the grid are considered neighbors.
  • faces representing data are considered neighbors in case they share a common cell.
  • Vertices for example, can be considered neighbors if they are endpoints of the same edge or if they belong to the same face or cell.
  • step 204 for every value or datum on the grid a node is added thereby creating all nodes of the draft to be created.
  • step 206 for every pair of nodes an edge is added in case the two nodes are neighbors. To be more specific, it is determined for each pair of nodes whether the two nodes of the pair are neighbored and in case they are, the edge is provided there between. Providing the respective edges between neighboring nodes results in a final form of the graph and the method proceeds to step 208 where creating of the spanning tree on the basis of the graph starts.
  • step 208 a random node in the graph is selected or chosen as a starting point and this node is called the "current node" which, in step 210, is marked as visited.
  • nodes being neighbors to the current node are determined and it is checked as to whether these nodes are unvisited nodes.
  • Step 212 for choosing an unvisited neighboring node may be implemented in accordance with an embodiment in a way that the order in which the nodes are selected is recoverable. In that case the tree does not need to be stored for decompression. The children are determined in a deterministic manner and can therefore be listed in recoverable order. The criteria for the selection could then be to choose the first unvisited child from the list.
  • step 212 the method tries to choose an unvisited neighboring node and in step 214 it is determined whether such a node, an unvisited node, actually exists. In case an unvisited node exists, the method proceeds to step 216 where an edge between the current node and the node selected in step 212 is added to the tree. The selected node is then made the current node in step 218 and the method returns to step 210 where the selected node now being the current node is again marked as visited and the steps 212 and 214 are repeated.
  • step 214 determines whether the current node is the root node of the tree. In case this is not true, the method proceeds to step 222 and goes back to the previous node, i.e. the node preceding the current node. The previous node is then made the current node in step 224 and the method returns to step 212.
  • step 220 determines that the current node is the root node it is determined in step 226 that the tree is now completed, and the approach for generating or determining the spanning tree ends at step 228. Following the completion of the tree, in a manner as discussed with regard to Fig.
  • a value is predicted using the value corresponding to the parent node of the node currently under investigation, i.e. the previous node.
  • the compressed data can be saved, where the compressed data is defined by the differences between the values and their predictions.
  • a global optimized tree can be obtained in a similar manner as described with regard to Fig. 2, however, in this case, after defining what a neighbor is in step 202 and after selecting or determining all nodes for the graph, i.e. a node for every value on the grid, every pair of nodes is provided with a "weighted" edge if the nodes are neighbors thereby creating a weighted graph on the basis of which a "minimal spanning tree" can be created.
  • a minimal spanning tree is a spanning tree with a total weight less or equal to the total weight of every other spanning tree of the same graph.
  • Fig. 3 shows a schematically representation of a computational system for implementing an embodiment of the inventive apparatus for compressing/decompressing data.
  • the exemplary compression/decompression system 300 may comprise a processing device 302 (e.g. a personal computer or a workstation) including a central processing unit (CPU), memories and an interconnect bus.
  • the CPU may contain a single microprocessor, or may contain a plurality of microprocessors.
  • the memories may include a main memory, a read-only-memory, and mass storage devices such as various disk drives, tape drives, etc.
  • the main memory typically includes dynamic random access memory (DRAM) and high-speed cache memory.
  • DRAM dynamic random access memory
  • the main memory stores at least portions of instructions for execution by the processing device 302 and data for processing in accordance with the executed instructions.
  • a storage device 304 may be provided comprising a first storage area 306 providing for a storage space for receiving the uncompressed data from the numerical simulations which is then set via the communication line 308 to the processing device 302 for compressing.
  • the storage device 304 may comprise a further storage area 310 for receiving the compressed data after processing the original data by means of the processing device 302.
  • the storage areas 306, 310 may include one or more magnetic disk or tape drives or optical disk drives for storing data instructions for use by the processing device 302 of the processing system 300.
  • the system 300 may further include appropriate input/output ports for interconnection with the display and a keyboard serving as a respective user interface.
  • the system 300 may include a graphic subsystem to drive the output display.
  • the output display may include a cathode ray tube (CRT) display or a liquid crystal display (LCD).
  • the system may further comprise input control devices such as a mouse, a trackball, a touchpad, stylus or cursor direction keys.
  • the system 300 is an example of a platform supporting processing and control functions of the inventive compression/decompression system and a control processing function may result on a single computer system, or on several separate systems wherein functions may be distributed across a number of computers.
  • the system of Fig. 3 operates in accordance with the inventive method for compress- ing/decompressing data.
  • the system 300 receives from the storage area 306 the data as it is stored in an unstructured grid, and in accordance with the inventive approach described above, the processor device 302 generates the spanning tree, which defines the sequence in which the respective data stored in the storage area 306 is passed, wherein for each node of the tree the prediction value is calculated and the difference be- tween the datum associated with the node and its prediction value is stored in the storage area 310 holding the compressed data.
  • the system 300 decompresses data.
  • the compressed data may be provided in storage area 310 and the processing device 302 determines the span- ning tree, which comprises a plurality of nodes, each node having associated therewith a compressed datum.
  • the tree defines a sequence of the nodes and the processing device 302 operates on the respective data stored in storage area 310 in accordance with the sequence defined by the tree.
  • a prediction value is determined that is then added to the compressed value thereby decompressing the datum.
  • the datum is then stored in storage area 306 holding the decompression data.
  • aspects described in the context of an apparatus also represent a description of the corresponding method, where a block or a device corresponds to a method step or a feature of the method step.
  • embodiments of the invention can be implemented in hardware or in software.
  • the implementation can be performed using a digital storage medium, for example a floppy disk, a DVD, a CD, a ROM, a PROM, an EPROM, an EEPROM or a FLASH memory, having electronically readable control signals stored thereon, which cooperate (or are capable of cooperating) with a programmable computer system such that the respective method is performed.
  • Some embodiments according to the invention comprise a data carrier having electronically readable control signals, which are capable of cooperating with a programmable computer system, such that one of the methods described herein is performed.
  • embodiments of the present invention can be implemented as a computer program product with a program code, the program code being operative for performing one of the methods when the computer program product runs on a computer.
  • the program code may for example be stored on a machine readable carrier.
  • inventions comprise the computer program for performing one of the methods described herein, stored on a machine readable carrier.
  • an embodiment of the inventive method is, therefore, a computer program having a program code for performing one of the methods described herein, when the computer program runs on a computer.
  • a further embodiment of the inventive methods is, therefore, a data carrier (or a digital storage medium, or a computer-readable medium) comprising, recorded thereon, the com- puter program for performing one of the methods described herein.
  • a further embodiment of the inventive method is, therefore, a data stream or a sequence of signals representing the computer program for performing one of the methods described herein.
  • the data stream or the sequence of signals may for example be configured to be transferred via a data communication connection, for example via the Internet.
  • a further embodiment comprises a computer having installed thereon the computer program for performing one of the methods described herein.
  • a programmable logic device for example a field programmable gate array
  • a field programmable gate array may cooperate with a microprocessor in order to perform one of the methods described herein.
  • the methods are preferably performed by any hardware apparatus.

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Abstract

L'invention porte sur un procédé et un appareil de compression de données sans perte, les données étant stockées sur une grille non structurée, une pluralité d'éléments de la grille étant associés à une donnée. Un arbre maximal est déterminé, qui comprend une pluralité de nœuds. Chaque nœud correspond à un élément de la grille auquel est associé une donnée. L'arbre couvrant définit une séquence de nœuds qui va d'un élément de la grille à un élément associé de la grille de telle manière que l'arbre couvrant visite chaque élément de la grille une seule fois. Le procédé parcourt ensuite les données stockées conformément à la séquence définie par l'arbre couvrant. Pour chaque nœud, une valeur de prédiction est calculée et la différence entre la donnée associée au nœud et sa valeur de prédiction est stockée, ce qui compresse la donnée associée au nœud.
PCT/EP2010/055465 2010-04-23 2010-04-23 Procédé et appareil de compression/décompression de données sans perte WO2011131248A1 (fr)

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WO2020051895A1 (fr) * 2018-09-14 2020-03-19 西门子股份公司 Procédé de compression de données, procédé de restauration de données et dispositif

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Publication number Priority date Publication date Assignee Title
JP2016103132A (ja) * 2014-11-28 2016-06-02 富士通株式会社 有限要素演算プログラム、有限要素演算装置および有限要素演算方法
WO2020018428A3 (fr) * 2018-07-16 2020-02-27 Mayo Foundation For Medical Education And Research Systèmes, procédés et supports d'encodage à faible puissance de signaux physiologiques continus dans un moniteur physiologique distant
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CN112673576A (zh) * 2018-09-14 2021-04-16 西门子股份公司 数据压缩方法、数据恢复方法及装置
CN112673576B (zh) * 2018-09-14 2024-04-19 西门子股份公司 数据压缩方法、数据恢复方法及装置

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