JP4012557B2 - Time-series data compression method, recording medium recording a time-series data compression program, and time-series data compression apparatus - Google Patents

Description

  The present invention relates to a time-series data compression method, a time-series data compression program recording medium, and a time-series data compression apparatus, which belong to the field of signal processing technology. The present invention can also be applied to time series data describing deformation of a mesh-like surface, deformation of an elastic object, and the like.

There has been a remarkable development in the Internet in recent years. Since the Internet can handle two-dimensional images and audio signals using HTML (Hyper Text Makeup Language), the Internet can be used as a transmission medium for various multimedia information such as image information and audio information. It has become.
However, although this HTML can handle a two-dimensional image, it cannot handle a three-dimensional CG image, and VRML (Virtual Reality Modeling Language) is proposed as a language that enables processing of a three-dimensional image. Has been done.

However, in VRML, it is difficult to represent a three-dimensional CG image showing human movements. To achieve this, humans are regarded as rigid articulated objects, and their positions are described as time series data for each joint. In this case, the amount of data generated is enormous.
In order to avoid this problem of data amount, multi-dimensional time series data such as joint positions may be decomposed into one-dimensional time series data and compressed for each one-dimensional time series data.

  As a compression method for such one-dimensional time-series data, a generally applied method is an orthogonal transform such as discrete Fourier transform or discrete cosine transform, which is used when performing signal processing in acoustic engineering or the like. This is a method for compressing information.

Non-patent document 1 is a reference document related to this orthogonal transform.
Non-patent document 2 is a reference document related to time-series data of joint angles of rigid and articulated objects.
The Acoustical Society of Japan, Kazuo Nakata, “Speech”, Corona, 1977 Unuma, M, et al., "Fourier Principles for Emotion-based Human Figure Animation", SIGGRAPH95 Proceedings, pp91-95, 1995.

  By the way, in the method of compressing information using this orthogonal transform, first, given one-dimensional time-series data is converted into a discrete Fourier series expansion expression or a discrete cosine series expansion expression using data at all times. . Next, the amount of information is compressed by cutting high-frequency components of the converted series expansion expression.

  Information that has been compressed using such orthogonal transform can be expanded by applying inverse Fourier transform or inverse cosine transform. At that time, as the decompressed data, not only the same number of data as the original data can be generated, but also any number of data different from the original data can be generated. Since the basis is a trigonometric function, its properties are reflected in the expanded data.

  The present invention has been made in order to solve the above-described problems of the prior art, and can perform compression according to the properties of one-dimensional time-series data, and the number of decompressed data can be reduced to the original data. Even if the number is different from the number of data, the compression and decompression process hardly affects the decompressed data, and compression is not performed using the statistical properties of the data. Since this is a compression method that compresses data so that it falls within the error range specified by the original data, a new compression method that complements the conventional compression method can be provided. The purpose of the present invention is to obtain a time-series data compression method, a time-series data compression program recording medium, and a time-series data compression apparatus that can expand the range of method selection.

  The time-series data compression method according to claim 1 of the present invention is a compression method of one-dimensional time-series data in the field of CG image processing, and includes a first step of inputting approximation accuracy with the one-dimensional time-series data. A second step of calculating a node candidate of an interpolation function approximating the one-dimensional time series data, and the one-dimensional time series data generated by the interpolation function based on the node candidate and the original one-dimensional time series data A third step of calculating an error, calculating a value of a first objective function calculated by weighted addition of a maximum value of the error, an average value of the error, and a variance of the error; and a value of the first objective function 4th step of repeatedly changing the node candidates so as to minimize the value, and determining a suboptimal node candidate, and a threshold value determined by the minimum value of the objective function calculated in the fourth step based on the approximation accuracy If it is determined that The fifth step of changing the number of point candidates and returning to the second step, and the minimum value of the objective function calculated in the fourth step is determined not to exceed the threshold value determined based on the approximation accuracy In this case, a sixth step of outputting the suboptimal node candidate data and the corresponding time data as compressed information is included.

  A time-series data compression program recording medium according to claim 2 of the present invention is a recording medium on which a one-dimensional time-series data compression program in the CG image processing field is recorded, and inputs the one-dimensional time-series data and approximate accuracy. A first step of performing, a second step of calculating a node candidate of an interpolation function approximating the one-dimensional time series data, and the one-dimensional time series data generated by the interpolation function based on the node candidate and the original one A third step of calculating an error from the dimension time series data and calculating a value of a first objective function calculated by weighted addition of the maximum value of the error, the average value of the error, and the variance of the error; A fourth step of repeatedly changing the node candidate so that the value of the objective function of 1 is minimized, and determining a suboptimal node candidate; and the minimum value of the objective function calculated in the fourth step is the approximation accuracy Based on When it is determined that the threshold value is exceeded, the fifth step of changing the number of node candidates and returning to the second step, and the minimum value of the objective function calculated in the fourth step are based on the approximation accuracy. Each step including a sixth step of outputting the suboptimal node candidate data and corresponding time data as compressed information when it is determined that the predetermined threshold value is not exceeded. A time-series data compression program for execution is recorded.

  The time-series data compression device according to claim 3 of the present invention is a compression device for one-dimensional time-series data in the field of CG image processing, and an input means for inputting the one-dimensional time-series data and approximate accuracy; A node candidate calculation means for calculating a node candidate of an interpolation function approximating the one-dimensional time series data; and an error between the one-dimensional time series data generated by the interpolation function based on the node candidate and the original one-dimensional time series data. A determining means for calculating and calculating a value of the first objective function calculated by weighted addition of the maximum value of error, the average value of error, and the variance of error; and the value of the first objective function is minimized. In this way, the node position optimizing unit that repeatedly changes the node candidates and determines the suboptimal node candidate and the determination unit cause the minimum value of the first objective function to exceed the threshold value determined based on the approximation accuracy. And The number of node candidates is changed, and the node number changing means for inputting the one-dimensional time-series data with the changed number of nodes to the node candidate calculating means; When it is determined that the value does not exceed a threshold value determined based on the approximation accuracy, output means for outputting the suboptimal node candidate data and the corresponding time data as compressed information It is what I did.

  According to the time-series data compression method of the first aspect of the present invention, there is provided a first-dimensional time-series data compression method in the CG image processing field, wherein the first-dimensional time-series data and the input of approximate accuracy are performed. A second step of calculating a node candidate of an interpolation function that approximates the one-dimensional time-series data, one-dimensional time-series data generated by the interpolation function based on the node candidate, and the original one-dimensional time-series data A third step of calculating a first objective function value calculated by weighted addition of the maximum error value, the average error value, and the variance of the error, and the first objective function The node candidate is repeatedly changed so that the value of the node is minimized, the fourth step of determining the suboptimal node candidate, and the minimum value of the objective function calculated in the fourth step is determined based on the approximation accuracy If it is determined that the threshold is exceeded Further, the fifth step of changing the number of node candidates and returning to the second step, and determining that the minimum value of the objective function calculated in the fourth step does not exceed the threshold value determined based on the approximation accuracy In this case, since the sixth step of outputting the suboptimal node candidate data and the corresponding time data as compressed information is included, the given one-dimensional time-series data There is an effect of obtaining a time-series data compression method that can perform compression according to the property and can grasp the error after decompression in advance.

  According to the time-series data compression program recording medium of claim 2 of the present invention, there is provided a recording medium on which a one-dimensional time-series data compression program in the CG image processing field is recorded. A first step of inputting, a second step of calculating a node candidate of an interpolation function approximating the one-dimensional time series data, a one-dimensional time series data generated by the interpolation function based on the node candidate and the original A third step of calculating an error from the one-dimensional time series data of the first objective function, and calculating a value of a first objective function calculated by weighted addition of the maximum value of the error, the average value of the error, and the variance of the error; The fourth step of repeatedly changing the node candidates so as to minimize the value of the first objective function to determine the suboptimal node candidate, and the minimum value of the objective function calculated in the fourth step is Based on approximation accuracy And when the number of node candidates is determined to be exceeded, the fifth step of returning to the second step and the minimum value of the objective function calculated in the fourth step are the approximation accuracy. Each step including a sixth step of outputting, as compressed information, the data of the sub-optimal node candidate and the data of the time corresponding thereto when it is determined that the threshold determined based on The time series data compression program to be executed by the computer is recorded so that the compression can be performed according to the properties of the given one-dimensional time series data and the error after decompression can be grasped in advance. There is an effect that a data compression program recording medium can be obtained.

  According to the time-series data compressing apparatus of the third aspect of the present invention, there is provided a one-dimensional time-series data compressing apparatus in the field of CG image processing, and an input means for inputting approximation accuracy with the one-dimensional time-series data. A node candidate calculation means for calculating a node candidate of an interpolation function approximating the one-dimensional time series data, and the one-dimensional time series data generated by the interpolation function based on the node candidate and the original one-dimensional time series data Determining means for calculating an error, calculating a value of a first objective function calculated by weighted addition of a maximum value of error, an average value of error, and variance of error; and a value of the first objective function is minimum The node position optimizing unit that repeatedly changes the node candidates so that the sub-optimal node candidate is determined, and the threshold value that the minimum value of the first objective function is determined based on the approximation accuracy by the determination unit Beyond The node number changing means for changing the number of node candidates and inputting the one-dimensional time-series data with the changed node number to the node candidate calculating means, and the determining means Output means for outputting the suboptimal nodal candidate data and the corresponding time data as compressed information when it is determined that the minimum value of the sub-optimal value does not exceed the threshold value determined based on the approximation accuracy; Thus, there is an effect that a time-series data compression apparatus can be obtained that can perform compression in accordance with the properties of given one-dimensional time-series data and can grasp errors after expansion in advance.

Embodiment 1 FIG.
Hereinafter, the time-series data compression method according to the first embodiment of the present invention will be described with reference to the drawings.
FIG. 1 shows the flow of processing of the time-series data compression method according to Embodiment 1 of the present invention.

  In the figure, P4a is an input process for inputting one-dimensional time series data and its approximate accuracy value, P1a is a node candidate calculation process for calculating node candidates through which an interpolation function approximating the one-dimensional time series data passes, P1b Is a node position optimization process for optimizing the position of the node candidate calculated by this node candidate calculation process P1a, and P1c is an interpolation function passing through the node obtained by this node position optimization process P1b and the original one-dimensional time series. A determination process for determining whether an error from the data satisfies a value corresponding to the approximate accuracy value input in the input process P4a, and P1d is determined in this determination process P1c that the approximate accuracy is not satisfied In addition, the node number changing process for changing the number of nodes, P4b is input by the input process P4a by the determination process P1c, and the error between the interpolation function passing through the nodes and the original one-dimensional time-series data is input. Similar is the output process of outputting the node and the index as compressed information if they satisfy the values corresponding to the accuracy value.

  The time-series data compression method according to the first embodiment attempts to realize data compression by generating a smaller number of nodes than the number of given one-dimensional time-series data using an interpolation function. Is. That is, the data is compressed by calculating the nodes of the interpolation function necessary for reproducing the data approximate to the original one-dimensional time series data, and transmitting the data except for the nodes. . The decompression approximates the original time-series data by generating the same data as the data that was omitted during compression, using the same interpolation function as that used for compression. This is done by generating time series data.

  More specifically, as shown in FIG. 1, in the input process P4a, the one-dimensional time series data to be compressed and its approximate accuracy value are input, and in the node candidate calculation process P1a, all of the constituents of the one-dimensional time series data are input. A node candidate is calculated from the one-dimensional data, and a node candidate that can generate one-dimensional time-series data that approximates the original one-dimensional time-series data by passing a predetermined interpolation function through the node data is calculated, In the node position optimization process P1b, the node candidate is moved to optimize the node position, and in the determination process P1c, a predetermined interpolation curve passing through the optimized node candidate and the original one-dimensional time-series data. It is determined whether or not the value based on the error is within the range of the approximate accuracy value input in the input process P4a. If the value is within the range of the approximate accuracy, the node position is immediately output by the output process P4b. Node candidates were optimized and outputs its index as the time series data 1 dimensional compressed.

If it is determined in the determination process P1c that it does not fall within the approximate accuracy range, the number of nodes is changed by appropriately increasing or decreasing the number of nodes in the node number changing process P1d.
After changing the node by the node number changing process P1d, the process returns to the node candidate calculating means P1a to calculate the node candidate again, and thereafter the same process is repeated.

  As described above, the data compression method shown in FIG. 1 attempts to realize data compression by generating a smaller number of nodes than the number of given one-dimensional time-series data using an interpolation function. Therefore, if a discrete Fourier series expansion or a discrete cosine series expansion is used as an interpolation function, the positions for obtaining these coefficients can be surely reduced from the original time series data. Further, since not only the positions of nodes but also the number of nodes are optimized, there is little error between the decompressed data and the original data, and compression with a good compression rate is possible. Also, if a large range of errors that occur during decompression is specified during compression, the number of nodes can be reduced accordingly, and data compression with a better compression rate can be realized. .

However, these are determined depending on the reproduction accuracy when the data is expanded. In addition, since the data compression rate depends on how the original time-series data can be approximated within a specified error accuracy range, the data compression rate is generally not constant.
Furthermore, if the data is also cut for high frequency components as in the prior art, the compression rate can be further increased as compared with the prior art. That is, when used together with the conventional technique, it can also be used as a complementing method for further increasing the compression rate in the conventional technique.

Of course, even when data is compressed only by the compression method of the first embodiment without cutting high frequency components, the number of selected nodes is larger than the number of frequency components remaining after cutting high frequency components in the conventional compression method. If it is less, the compression rate of the present invention is higher. However, since it depends on the nature of the given one-dimensional time-series data, it is generally impossible to determine which method has a high compression rate.
However, the scope of selection of the data compression method has been expanded by the present invention.

In addition, when an interpolation function having a polynomial format, such as a spline function, is used, the data when decompressed is data that changes in a polynomial fashion. This works effectively in maintaining the accuracy when decompressing one-dimensional time-series data having no periodicity.
Therefore, even if the number of data to be decompressed is different from the number of the original data, the accuracy can be maintained, so if the amount of data generated at the time of decompression is reduced, the original data can be reproduced at high speed, Even if high-speed playback is performed, the accuracy of the data can be maintained.
Conversely, if the amount of data generated at the time of decompression is increased, the original data can be reproduced in slow speed, and the accuracy of the data can be maintained even if the data is reproduced in slow speed.

  As described above, the first embodiment not only complements the conventional compression method by providing a new compression method for performing compression suitable for the properties of the one-dimensional time-series data, but also allows selection of the compression method. The width can be increased.

  Hereinafter, the processing of Embodiment 1 of the present invention will be described in more detail. Before that, the one-dimensional time series data will be described with reference to FIG. FIG. 12 is a graph of one-dimensional time series data, and the black circles in the figure represent one-dimensional data. In this way, data in which one-dimensional data is paired with time corresponding to the one-dimensional data is referred to as one-dimensional time series data. Then, as shown in FIG. . . , Tn, the value of ti-ti-1 is arbitrary i = 1,. . . , N is called a time equal interval, and the other case is called a time unequal interval.

  FIG. 2 shows the flow of processing of the time-series data compression method according to Embodiment 1 of the present invention. As shown in FIG. 2, the entire process is executed in nine stages from the first stage S1 to the ninth stage S9. The first stage S1 is composed of processes P1 to P3, the second stage S2 is composed of processes P4, the third stage S3 is composed of processes P5 and P6, and the fourth stage S4 is composed of processes P7. The fifth stage S5 is composed of process P8, the sixth stage S6 is composed of process P9 and process P10, the seventh stage S7 is composed of process P11, and the eighth stage S8 is from process P4 to process P13. The ninth stage S9 is composed of process P14.

FIG. 3 shows an example of the configuration of a computer that performs the flow process of FIG. 1 with detailed processing shown in FIG. 2. In FIG. 3A, 1 is an arithmetic process according to a control program corresponding to the process of FIG. 2 is a data memory for storing data to be processed by the CPU 1, 3 is a main memory in which a control program corresponding to the processing in FIG. 2 is stored in advance, and 4 is a data memory between the computer and the outside. An input / output device 5 for performing input / output is a bus for the CPU 1, data memory 2, main memory 3 and input / output device 4 to exchange data and the like. The data memory 2 and the main memory 3 may be configured using the same memory.
The CPU 1 executes a compression process shown as a flow in FIG. 2 according to a control program stored in the main memory 3 in advance.

  FIG. 3B shows a configuration example of a computer that reads a program from a program recording medium or the like and performs a compression operation. In FIG. 3B, 6 is an external storage device connected to the bus 5. A control program corresponding to the process of FIG. 2 is recorded in advance on the recording medium of the external storage device, and the external storage device 6 reads the control program corresponding to the process of FIG. Load to 3. The CPU 1 executes the compression process shown as the flow in FIG. 2 according to the control program loaded in the main memory 3. Alternatively, a control program supplied from the outside via the input / output device 4 may be loaded into the main memory 3.

Next, the first step S1 to the ninth step S9 of FIG. 2 configured as described above will be described.
First, in process P1, one-dimensional time-series data to be compressed and approximate accuracy values of interpolation functions approximating it are input. In process P2, one-dimensional time-series data is indexed in the order of its time. As this time, a sample time, generation time, input time, or the like of the one-dimensional time series data can be used. Note that this index may use data that increases sequentially or data that decreases sequentially instead of time. In process P3, the initial number of nodes is calculated. Since the initial value of the number of nodes used at that time is determined in accordance with the type of the interpolation function, it is only necessary to set the initial value in advance. Therefore, for example, the ratio to the initial number of data is determined in advance. This can be calculated. Here, the initial number of nodes is calculated in the form of 1 / a of the total number of one-dimensional time-series data as the initial value of the number of nodes to be used (where a> 0).

  In the process P4, the data at the beginning and the end of the one-dimensional time-series data to be compressed are always included, and the remaining data is selected at random intervals, and these are summed to calculate the above. Node candidates are determined so that the number is equal to the number of nodes.

This operation will be described with reference to FIG. If the number of nodes is m + 1, the data at time t0 is the first data, and this is selected as the first node candidate. Next, the data at the time tn is the last data, and this is selected as the last node candidate.
Next, the remaining m-1 node candidates are selected without allowing duplication with each other, using random numbers generated with a uniform probability of 1 / (n-1). After a total of m + 1 node candidates are selected in this way, they are sorted in ascending order of time, and the node candidate indexes are stored as I (j), 0 ≦ j ≦ m. In the example of FIG. 13, data indicated by white circles is selected as a node candidate.

  The above is the case of random selection, but the process P4 for obtaining the node candidate may be selected at approximately equal intervals with respect to the index. In this case, the interval [n / m] is first calculated for the index, and a total of m node candidates separated by this interval [n / m] starting from the first data at the time t0 are selected and used as the (m + 1) th node candidate. The process ends by selecting end data at time tn. Here, [x] is a Gaussian symbol. Also in this case, I (j) as described above is stored.

  The operation performed in this process P4 determines the initial value of the position of the nodal candidate, and it is known that it is effective to use a random number for this type of problem, but even in the case of the first embodiment, too. A better value is obtained experimentally when the node positions are selected using random numbers than when they are selected at approximately equal intervals.

  In process P5, data for interpolating between each node candidate is generated by an interpolation function having an index number as an independent variable, and one-dimensional time-series data approximating the original one-dimensional time-series data is obtained. An error from the one-dimensional time series data is calculated. Any interpolation function may be used as long as it passes through nodes. For example, a spline function has a property that can be used as an interpolation function passing through nodes. However, if the decompressed data should reproduce a waveform that is faithful to the waveform of the original data, it is desirable to use an interpolation function that can faithfully approximate the original one-dimensional time-series data. If a rate is required, the interpolation function is not required to be very close. In addition, a series expansion expression using a discrete Fourier transform, a series expansion expression using a discrete cosine transform, or the like can also be used as an interpolation function. However, any one of the above-mentioned interpolation functions is selected in advance and used. Then, the same interpolation function as that used at the time of compression is used in the decompression process described later. In this case, the interpolation function prepares a plurality of candidates in advance, sends the identifier of the interpolation function used at the time of compression to the expansion processing side, and uses the same interpolation function as at the time of compression on the expansion side. Also good.

FIG. 14 is a graph showing an interpolation function for interpolating the curve of FIG. Black circles in the figure are data obtained by interpolating node candidates represented by white circles using an interpolation function, and these are rejected during data compression. Most of the data indicated by the black circles has the same value as the original data, but an error has occurred with respect to the data at time tn-1.
In the process P6, as shown in FIG. 14, the error between the one-dimensional time series data other than the node candidates and the interpolation function is calculated. In the case of FIG. 14, the error is calculated using an absolute value error. However, this error calculation may be performed using a square error or the like.
In process P7, the value of the first objective function is calculated from the error calculated in process P6. This first objective function can be calculated by first obtaining the maximum error value, the error average, and the error variance calculated in process P6, and weighting and adding them.

  In other words, this objective function is an error evaluation function, and the maximum value of errors, the average of errors, and the variance of errors between the one-dimensional time-series data generated from the selected node candidates and the original one-dimensional time-series data are both. Error evaluation is performed by weighting and adding the maximum error value, error average, and error variance so that the error is evaluated from the viewpoint that a small value is the optimal node candidate. It is intended to be used as a function.

  The weighting coefficient includes a method in which the value is fixed from the beginning and a method in which the weighting factor is variably determined in accordance with data. In the case of variably determining, for example, when it is desired to assign the weights equally for the maximum error, the error average, and the error variance, it is only necessary to determine that the products of the respective weights and their values are all equal. When it is determined from the beginning, for example, all the values of the weighting factor are determined in advance to be “1/3”. In general, the actual data is often processed several times to determine a value that seems to be good empirically.

  In the process P8, the node candidate is repeatedly changed so as to minimize the value of the first objective function, and the sub-optimal node candidate is determined. This is illustrated in FIG. 10 and the first method shown in FIG. There are two ways of the second method shown.

The process of determining this sub-optimal node candidate is to obtain the difference between the objective function value when a node candidate is determined and the objective function value when the node candidate is changed. A local optimum solution is obtained by selecting node candidates so that becomes smaller.
In determining the node candidates, an optimal solution may be obtained when the number of nodes is small, but it is unknown whether the optimal solution is truly optimal when the number of nodes is large. In the case of 1, it is sufficient to obtain a local optimum solution, that is, a suboptimal solution.

  First, the first method shown in FIG. 10 will be described. As can be seen from FIG. 10, this processing is composed of processing P41 to processing P59. However, as described above, the node candidate indexes are numbered in ascending order of time, and I (j), 0 ≦ j ≦ m. In the following description of FIG. 10, j is a loop control variable.

In the process P41, loop control is performed. There are the following six methods, and loop control is performed using any one of them.
(1) For odd-numbered j, processing is performed in order from the smallest to the largest, and for even-numbered j, the processing is performed from the largest to the smallest.
(2) For odd-numbered j, processing is performed from the largest to the smallest, and for even-numbered j, the processing is performed from the smallest to the largest.
(3) Processing is sequentially performed from j = 1 to [m / 2] and from j = m−1 to [m / 2] +1.
(4) Processing is sequentially performed from j = [m / 2] to 1, and j = [m / 2] +1 to m-1.
(5) Processing is performed sequentially from j = 1 to m-1.
(6) Processing is sequentially performed from j = m−1 to 1.
In process P42, it is determined whether or not the relationship of I (j-1) <I (j) -1 holds for the loop control variable j that controls the loop of a series of processes. If this relationship is established, the process proceeds to process P43, and if not, the process proceeds to process P45.

  In the process P43, the node candidate I (j) and the node candidate I (j) -1 are temporarily exchanged as shown in FIG. Next, the value of the first objective function after exchange is calculated. After the function value is calculated, the node candidate that was exchanged is restored.

In process P44, a value ΔE (1-) obtained by subtracting the value of the first first objective function calculated in process P7 of FIG. 2 from the value of the first objective function calculated in process P43 is calculated. Note that “1-” in the parentheses of ΔE means that the left is shifted by “1”, that is, the index is decreased by “1”. In process P45, the value of the first objective function is not calculated, and ΔE (1-) is forcibly set to “0”.
In process P46, it is determined whether or not the relationship of I (j) +1 <I (j + 1) is established. If this relationship is established, the process proceeds to process P47, and if not, the process proceeds to process P49.

In the process P47, as shown in FIG. 15, the node candidate I (j) and the node candidate I (j) +1 are temporarily exchanged, and the value of the first objective function at this time is calculated.
In process P48, a value ΔE (1+) obtained by subtracting the value of the first first objective function calculated in process P7 of FIG. 2 from the value of the first objective function calculated in process 47 is calculated. In process P49, ΔE (1+) is forcibly set to “0” without calculating the value of the first objective function.

In process P50, it is determined whether or not ΔE (1 −) <0 and ΔE (1+) ≧ 0. If this relationship is established, the process proceeds to process P51, and if not, the process proceeds to process P52. In the process P51, the node candidate I (j) is exchanged for the node candidate I (j) -1, and after the exchange, the process returns to the process P41.
In process P52, it is determined whether or not ΔE (1−) ≧ 0 and ΔE (1 +) <0 are satisfied. If this relationship is established, the process proceeds to process P53, and if not, the process proceeds to process P54. To do. In the process P53, the node candidate I (j) is exchanged with the node candidate I (j) +1, and after the exchange, the process returns to the process P41.

In the process P54, it is determined whether or not the relationship of ΔE (1-) <0 and ΔE (1 +) <0 is established. If this relationship is established, the process proceeds to the process P55, and if not, the process proceeds to the process P41. Return.
In the process P55, it is determined whether or not the relationship ΔE (1-) ≦ ΔE (1+) is established. If this relationship is established, the process proceeds to the process P56, and if not, the process proceeds to the process P57. In the process P56, the node candidate I (j) is exchanged for the node candidate I (j) -1, and when the exchange is completed, the process returns to the process P41. In the process P57, the node candidate I (j) is exchanged with the node candidate I (j) +1, and after the exchange, the process returns to the process P41.
When the above processing is completed for all the loop control variables j, the processing shifts to processing P58.

  In process P58, end determination is performed. In this end determination, the value of the first objective function when the operations from process P41 to process P57 are completed for all j is greater than the original first objective function value minus the threshold value, or all j is executed by determining whether or not the node candidates have not been exchanged at all, and if either condition is satisfied, the series of processing is terminated, and the solution at the time of termination is a suboptimal node. Be a candidate. Otherwise, in process P59, the value of the original first objective function is replaced with the first objective function when the operation is completed, and a series of processes from process P41 to process P57 is repeated.

  The above operation is repeated until the end determination in the process P58 is established and the value of the first objective function converges. Note that a determination condition based on the number of repetitions of processing may be added to this end determination. However, in this case, the optimum degree may be worse than the case where the determination condition for the number of repetitions is not added, but the process can always be finished within a certain time.

Next, the second method shown in FIG. 11 will be described. As can be seen from FIG. 11, this process is composed of process P61 to process P79.
However, as described above, the node candidate indexes are numbered in ascending order of time, and are expressed as I (j), 0 ≦ j ≦ m. Similarly to the description of FIG. 10, j is a loop control variable.

In the process P61, as in the first method of FIG. 10, loop control is performed to determine whether or not to repeat a series of processes. This method includes the following six methods, one of which is Loop control is performed using one of them.
(1) For odd-numbered j, processing is performed in order from the smallest to the largest, and for even-numbered j, the processing is performed from the largest to the smallest.
(2) For odd-numbered j, processing is performed from the largest to the smallest, and for even-numbered j, the processing is performed from the smallest to the largest.
(3) Processing is sequentially performed from j = 1 to [m / 2] and from j = m−1 to [m / 2] +1.
(4) Processing is sequentially performed from j = [m / 2] to 1, and j = [m / 2] +1 to m-1.
(5) Processing is performed sequentially from j = 1 to m-1.
(6) Processing is sequentially performed from j = m−1 to 1.
Process P62 to process P70 are the same as process P42 to process P50 of the first method in FIG.

In the process P71, first, the node candidate I (j) is exchanged for the node candidate I (j) -1. Further, the original value of the first objective function is updated to the value of the first objective function calculated at the time of this exchange. And after performing this update, it returns to the process P61.
The process P72 is the same as the process P52 of the first method in FIG.
In the process P73, first, the node candidate I (j) is exchanged with the node candidate I (j) +1. Further, the original value of the first objective function is updated to the value of the first objective function calculated at the time of this exchange. And after performing this update, it returns to the process P61.
Process P74 and process P75 are the same as process P54 and process P55 of the first method in FIG.
In the process P76, the node candidate I (j) is exchanged with the node candidate I (j) -1. Next, the original value of the first objective function is updated to the value of the first objective function calculated at the time of this exchange. And after performing this update, it returns to the process P61.

In the process P77, the node candidate I (j) is exchanged with the node candidate I (j) +1. Next, the original value of the first objective function is updated to the value of the first objective function calculated at the time of this exchange. And after performing this update, it returns to the process P61.
When the above processing is completed for all the loop control variables j, it is determined whether or not the processing P78 is finished, which is the same as the processing P58 of the first method in FIG. The process P79 is the same as the process P59 of the first method in FIG.

  In the second method, the first objective function value is changed when the first method finishes executing a series of processing on the node candidates. On the other hand, each time the node candidates are updated, the first method The value is also updated. Which of these first and second methods is superior as a sub-optimal node candidate determination method depends on the nature of the data, so it cannot be said to be obvious. Generally, the convergence of the objective function value is the first. This method seems to be faster.

  If the sub-optimal node candidate is determined by the first method shown in FIG. 10 or the second method shown in FIG. 11, the sub-optimal node candidate is processed by the above-described interpolation function in process P9 of FIG. Interpolation similar to P5 is performed. Next, an error between the one-dimensional time series data obtained by the interpolation and the original one-dimensional time series data is calculated in the same manner as in the process P6.

  In process P11, the value of the second objective function defined by the weighted addition of the maximum value of the error, the error average, and the error variance is calculated from the error calculated in process P10. This second objective function is an error evaluation function for the original node. For example, when only the maximum error value is a problem, the weight value may be “1” for the maximum error and “0” for the error average and error variance. Other than that, when it is desired to assign the weights equally for the maximum error, the error average, and the error variance, just as in the case of the first objective function in the process P7, for example, the products of the respective weights and their values are all equal. Or when determining from the beginning, for example, all the values of the weighting factor may be determined to be “1/3” in advance, and each weight at the time of the first objective function is determined. You may determine on the basis of the ratio with respect to.

  In the process P12, a threshold value determination is performed on the second objective function value obtained in the process P11. For example, when the weight of the maximum error is “1” and the error average and the error variance are “0”, in the process P1, the approximate accuracy error value input first may be used as a threshold value. In this case, it is determined whether all the data are within the approximate accuracy. As a result of the threshold determination, when it is determined that the value is larger than the threshold, the process proceeds to process P13. Otherwise, the process proceeds to process P14.

In process P13, the number of nodes after the change is obtained by adding the increment amount to the original number of nodes. The increment amount at that time is determined in advance.
When the number of nodes is increased by a predetermined amount, the process returns to process P4, a series of processes after determination of the node candidates are performed, and the series of processes until the value of the second objective function is determined to be equal to or less than the threshold in process P12. repeat.

  If it is determined in process P12 that the value of the second objective function is equal to or smaller than the threshold value, the process proceeds to process P14 as described above. In process P14, the initial time, the time interval amount, and the obtained node candidate index number and The data value at that time is output. The format of the output data in this case is as shown in FIG.

Regarding the output of the index, there is a method of switching and outputting depending on whether the number of node candidates is less than half of the number of one-dimensional time-series data input first or more. That is, when it is less than half, the identifier indicating it and the index number of the node candidate are output, and in the above case, the identifier indicating it and the index other than the node candidate are listed.
Further, when the initial time and time interval of the one-dimensional time series data to be handled are always constant and known, the initial time and time interval may be omitted in the output in the process P14.

As described above, according to the first embodiment, an initial node candidate is determined from each data constituting the one-dimensional time-series data, and the original one-dimensional time is determined from the initial node candidate using an interpolation function. Generate one-dimensional time-series data that approximates the series data, calculate and evaluate these errors, and move the node candidates so that the error evaluation falls within the expected range to calculate a sub-optimal node candidate Then, using this interpolation function, one-dimensional time-series data that approximates the original one-dimensional time-series data is generated from the quasi-optimal node candidates, and these errors are calculated and evaluated. If it does not fall within the range, the number of nodes is increased and the above processing is repeated to optimize both the position and number of nodes, and data other than the nodes is not transmitted and the data is compressed. I did In, it can be compressed to suit the nature of the one-dimensional time series data given is performed.
Further, since the compression rate of the data is controlled by the approximation accuracy, the error after decompression can be grasped in advance.

Embodiment 2. FIG.
In the first embodiment, the one-dimensional time-series data compression process is realized by software. However, this data compression process may be realized by dedicated hardware.
FIG. 4 shows a time-series data compression apparatus in which the processing flow of FIG. 1 is implemented as dedicated hardware. In the figure, 40a is an input means for inputting one-dimensional time-series data and its approximate accuracy value, and 10a is this 1 Node candidate calculation means 10b for calculating a node candidate through which an interpolation function approximating dimensional time-series data passes, node position optimization means 10c for optimizing the position of the node candidate calculated by this node candidate calculation means 10a, 10c Indicates whether the error between the interpolation function passing through the node obtained by the node position optimizing means 10b and the original one-dimensional time-series data satisfies a value corresponding to the approximate accuracy value input by the input means 40a. The determining means 10d for determining determines the number of nodes to change the number of nodes when the determining means 10c determines that the approximate accuracy is not satisfied, and 40b is determined by the determining means 10c. Output means for outputting the node and its index as compression information when the error between the interpolation function passing through the node and the original one-dimensional time series data satisfies a value corresponding to the approximate accuracy value input by the input means 40a. It is.

  Next, the operation will be described. As shown in FIG. 4, the input means 40a inputs the one-dimensional time series data to be compressed and its approximate accuracy value, and the node candidate calculation means 10a inputs all the one-dimensional data constituting the one-dimensional time series data. Node candidates are calculated from them, and node candidates that can generate one-dimensional time-series data that approximates the original one-dimensional time-series data by passing through this node data by a predetermined interpolation function are calculated, and node positions are optimized. The means 10b moves the node candidate to optimize the node position, and the determination means 10c determines the error between a predetermined interpolation curve passing through the optimized node candidate and the original one-dimensional time series data. It is determined whether or not the base value is within the range of the approximate accuracy value input in the input unit 40a. If the value is within the range of the approximate accuracy, the node position is immediately optimized by the output unit 40b. Node candidate is output as one-dimensional time series data obtained by compressing the index.

If it is determined that the determination means 10c does not fall within the approximate accuracy range, the node number changing means 10d optimizes the number of nodes by appropriately increasing or decreasing the number of nodes.
After the number of nodes is changed by the node number changing means 10d, the node candidate calculation means 10a is returned to calculate the node candidates again, and the same processing is repeated thereafter.

FIG. 5 shows a more detailed configuration of the time-series data compression apparatus of FIG.
In the figure, 40a is an input means for inputting one-dimensional time-series data to be compressed from the outside and its approximation accuracy, 11 is an index adding means for adding an index to the one-dimensional time-series data, and 12 is this 1 An initial node number calculating means for calculating the initial number of nodes through which the interpolation function approximating the dimensional time series data passes, 13 is a node candidate determining means for determining node candidates through which the interpolation function passes, and 14 is the node candidate. Interpolation execution means for interpolating data between nodal candidates using a passing interpolation function, 15 is an error calculation means for calculating an error between the one-dimensional time series data obtained by this interpolation function and the original one-dimensional time series data , 16 is a first objective function calculation means for calculating a first objective function value that is an evaluation function of this error, and 17 is a node for moving the node candidate as appropriate to obtain a suboptimal node candidate A sub-optimal node candidate determining means 18 for determining, an interpolation executing means 18 for interpolating data between sub-optimal node candidates by an interpolation function passing through the sub-optimal node candidate, and 19 a one-dimensional time-series data obtained by the interpolation function. Error calculating means for calculating an error between the original and one-dimensional time series data, 20 is a second objective function calculating means for calculating a second objective function value that is an evaluation function of the error, and 21 is a second objective function calculating means. Threshold determination means for determining whether or not the function value of the objective function exceeds a threshold corresponding to the approximation accuracy of the original one-dimensional time series, and 22 is an approximation of the original one-dimensional time series data whose function value is the second objective function The node number changing means 40b for changing the number of nodes when the threshold value according to accuracy is exceeded, 40b is used when the function value of the second objective function does not exceed the threshold value according to the approximation accuracy of the original one-dimensional time series data. One-dimensional time series based on suboptimal node candidates As compressed data over data, an output unit that outputs with indexes.

Next, the operation will be described.
First, the input means 40a inputs one-dimensional time-series data to be compressed and an approximate accuracy value of an interpolation function that approximates the data. The index adding means 11 attaches indexes to the one-dimensional time series data in the order of the times. As this time, a sample time, generation time, input time, or the like of the one-dimensional time series data can be used. Note that this index may use data that increases sequentially or data that decreases sequentially instead of time. The initial node number calculating means 12 calculates the initial node number. Since the initial value of the number of nodes used at that time is determined in accordance with the type of the interpolation function, it is only necessary to set the initial value in advance. Therefore, for example, the ratio to the initial number of data is determined in advance. This can be calculated. Here, as in the case of FIG. 2, the initial number of nodes is calculated in the form of 1 / a of the total number of one-dimensional time-series data (where a> 0) as the initial value of the number of nodes to be used. It shall be.

The node candidate determination means 13 always includes data at the beginning and end of the one-dimensional time series data to be compressed, and selects the remaining data at random intervals, and sums them. Node candidates are determined so as to be equal to the calculated number of nodes.
This operation is performed in the same manner as shown in FIG.
The operation performed by the node candidate determination means 13 is to determine the initial value of the position of the node candidate, and it is known that it is effective to use a random number for this type of problem. Even in this case, a better value is obtained experimentally when the node positions are selected using random numbers than when they are selected at approximately equal intervals.

The interpolation execution means 14 generates data for interpolating between node candidates by an interpolation function having an index number as an independent variable, and obtains one-dimensional time-series data that approximates the original one-dimensional time-series data. An error from the original one-dimensional time series data is calculated.
As in the case of FIG. 2, this interpolation function can use a series expansion expression using a spline function or a discrete Fourier transform, a series expansion expression using a discrete cosine transform, or the like.

  The error calculation means 15 calculates an error between the one-dimensional time series data other than the nodal candidate and the interpolation function as shown in FIG. In the case of FIG. 14, the error is calculated using an absolute value error. However, this error calculation may be performed using a square error or the like.

  The first objective function calculation means 16 calculates the value of the first objective function from the error calculated by the error calculation means 15. This first objective function can be calculated by first obtaining the maximum value of error calculated by the error calculation means 15, the error average, and the error variance, and adding these to weight.

  The sub-optimal node candidate determination means 17 repeatedly changes the node candidate so that the value of the first objective function is minimized, and determines the sub-optimal node candidate. This is the same as in the case of FIG. There are two methods, the first method shown in FIG. 10 and the second method shown in FIG.

  If the sub-optimal node candidate is determined by the first method according to FIG. 10 or the second method according to FIG. 11, the sub-optimal node candidate is interpolated by the interpolation function by the interpolation execution means 18 of FIG. Interpolation is performed in the same manner as the execution means 14. Next, the error calculation means 19 calculates the error between the one-dimensional time series data obtained by interpolation and the original one-dimensional time series data in the same manner as the error calculation means 15.

  The second objective function calculation means 20 calculates the value of the second objective function defined by the weighted addition of the maximum value of the error, the error average, and the error variance from the error calculated by the error calculation means 19. This second objective function is an error evaluation function for the original node. For example, when only the maximum error value is a problem, the weight value may be “1” for the maximum error and “0” for the error average and error variance. Other than that, when it is desired to assign the weights equally for the maximum error, the error average, and the error variance in the same manner as the first objective function in the first objective function calculation means 16, for example, the product of the respective weights and their values. Are determined to be equal to each other, or are determined from the beginning, for example, the values of the weighting factors are all determined to be “1/3” in advance, and the first objective function You may determine on the basis of the ratio with respect to each weight, etc. at the time.

  The threshold determination means 21 performs threshold determination for the second objective function value obtained by the second objective function calculation means 20. For example, when the maximum error weight is “1” and the error average and error variance are “0”, the approximation accuracy error input first in the input means 40a may be used as a threshold value. In this case, it is determined whether all the data are within the approximate accuracy. As a result of the threshold determination, when it is determined that the value is larger than the threshold, the process shifts to the node number changing means 22, and when not, the process shifts to the output means 40b.

The node number changing means 22 obtains the change in the number of nodes by adding an increment to the original number of nodes. The increment amount at that time is determined in advance.
Then, when the number of nodes is increased by a predetermined amount, the process returns to the node candidate determination unit 13, performs a series of processes after the node candidate determination, and until the threshold value determination unit 21 determines that the value of the second objective function is equal to or less than the threshold value. These series of processes are repeated.

  When the threshold value determination unit 21 determines that the value of the second objective function is equal to or less than the threshold value, the process proceeds to the output unit 40b as described above. In the output unit 40b, the initial time, the time interval amount, and the obtained node candidate are obtained. The index number and the data value at that time are output. The format of the output data in this case is as shown in FIG.

Regarding the output of the index, there is a method of switching and outputting depending on whether the number of node candidates is less than half of the number of one-dimensional time-series data input first or more. That is, when it is less than half, the identifier indicating it and the index number of the node candidate are output, and in the above case, the identifier indicating it and the index other than the node candidate are listed.
If the initial time and time interval of the one-dimensional time series data to be handled are always constant and known, the initial time and time interval may be omitted in the output by the output means 40b.

As described above, according to the second embodiment, an initial node candidate is determined from each data constituting the one-dimensional time series data, and the original one-dimensional time is determined from the initial node candidate using an interpolation function. Generate one-dimensional time-series data that approximates the series data, calculate and evaluate these errors, and move the node candidates so that the error evaluation falls within the expected range to calculate a sub-optimal node candidate Then, using this interpolation function, one-dimensional time-series data that approximates the original one-dimensional time-series data is generated from the quasi-optimal node candidates, and these errors are calculated and evaluated. If it does not fall within the range, the number of nodes is increased and the above processing is repeated to optimize both the position and number of nodes, and data other than the nodes is not transmitted and the data is compressed. Dedicated processing Since to carry out the Douea, it is possible to perform compression tailored to the nature of the one-dimensional time series data given rapidly.
Further, since the compression rate of the data is controlled by the approximation accuracy, the error after decompression can be grasped in advance.

Embodiment 3 FIG.
Next, a time-series data compression method according to Embodiment 3 of the present invention will be described with reference to the drawings.
In this third embodiment, in the time-series data compression method according to the first embodiment, the so-called 0-sequence, that is, one in which each data of the one-dimensional time-series data falls within a range that can be regarded as almost “0” is continuous. Further, the processing can be omitted.

  FIG. 6 shows the flow of processing of the time-series data compression method in Embodiment 3 of the present invention. As shown in FIG. 6, the entire process is the same as that shown in FIG. 1, but in the third embodiment, a determination process P1f is provided immediately after the input process P4a, and is input in the input process P4a. If the one-dimensional time series data falls within the approximate accuracy, the process immediately proceeds to the output process P4b. Only when the one-dimensional time series data does not fall within the approximate precision, the node candidate calculation process P1a and the like are performed as in FIG. It is a thing.

  FIG. 7 shows the process of FIG. 6 in more detail, and the process of FIG. 7 is executed from the 11th stage S11 to the 20th stage S20 by, for example, the computer of FIG. In this case, the main memory 3 of the computer of FIG. 3 stores a program corresponding to the processing of FIG. 7 in advance or loaded from a program recording medium. The 11th step S11 is from the process P21 to the process P23, the 12th stage S12 is the process P24, the 13th stage S13 is the process P25, the 14th stage S14 is the process S26 and the process S27, and the 15th stage S15 is the process. In P28, the 16th stage S16 is the process P29, the 17th stage S17 is the process P30 and the process P31, the 18th stage S18 is the process P32, the 19th stage S19 is the process P25 to the process P34, the 20th stage. S20 is executed in process P35.

Each process configured as described above will be described in detail.
The processes from the process P21 to the process P23 are the same as the processes from the process P1 to the process P3 according to the first embodiment of the present invention shown in FIG.
For the process P24, it is determined whether or not the absolute values of all the data values of the given one-dimensional time series data are equal to or less than the approximate accuracy input in the process 21. At this time, when it is determined that the approximate accuracy is equal to or less than the input accuracy, it corresponds to a so-called zero column. In this case, information compression is not performed in the information compression method of the third embodiment. Immediately, the process proceeds to process P35. On the other hand, if the absolute value of at least one data value is greater than the approximate accuracy, the process proceeds to process P25.

The processes from the process P25 to the process P34 are the same as the processes from the process P4 to the process P13 in FIG.
As for the process P35, when the 13th step S13 to the 19th step S19 have been performed, the data is output in the format of FIG. 16A in the same manner as the process P14 of the first embodiment of the present invention. On the other hand, when the process P24 has directly shifted to the process P35, the data is output in the format (b) in FIG. That is, an identifier indicating that the initial time, the time interval, and all data values are “0” is output.

  As described above, according to the third embodiment, when the data falls within the range that can be regarded as “0” within the approximate accuracy, the compression process can be omitted, and therefore the data that can be regarded as “0”. The processing can be omitted in the case where the data continues, and particularly when the number is large, there is an effect that the data compression processing can be performed at a higher speed.

Embodiment 4 FIG.
In the third embodiment, the one-dimensional time-series data compression process is realized by software. However, this data compression process may be realized by dedicated hardware.
FIG. 8 shows a time-series data compression apparatus in which the processing flow of FIG. 6 is implemented as dedicated hardware. In the figure, the same reference numerals as those in FIG. 4 denote the same or corresponding parts.
Reference numeral 10f denotes a determination unit, which is provided between the input unit 40a and the node candidate calculation unit 10a. If the one-dimensional time series data input by the input unit 40a falls within the approximate accuracy, the process immediately shifts to the output unit 40b. However, only when it does not fall within the approximate accuracy, the process switching control is performed so that the process proceeds to the node candidate calculation means 10a and a series of data compression processes are performed as in FIG.

  FIG. 9 shows a more detailed configuration of the time-series data compression apparatus of FIG. 8. In the figure, the same reference numerals as those in FIG. 5 denote the same or corresponding parts. 23 is an in-approximation-accuracy determination unit provided between the input unit 40a and the index addition unit 11, and is provided between the input unit 40a and the index addition unit 11 as in the determination unit 10f of FIG. .

Next, the operation of FIG. 9 will be described.
The time-series data compression apparatus of FIG. 9 has an approximate accuracy determining unit 23 between the input unit 40a and the index adding unit 11, and the approximate accuracy determining unit 23 is input by the input unit 40a. It is determined whether or not the one-dimensional time-series data falls within the approximate accuracy. If the one-dimensional time-series data falls within the approximate accuracy, the data compression operation by the time-series data compression apparatus is not performed. As in FIG. 6, the process switching control is performed so that the process proceeds to the index adding means 11 and a series of data compression processes are performed only when the shift does not fall within the approximate accuracy.

  As described above, according to the fourth embodiment, when the data falls within the range that can be regarded as “0” within the approximate accuracy, the compression process can be omitted, and therefore the data that can be regarded as “0”. Can be omitted, especially when the number is large, it is possible to perform higher-speed data compression processing, and since these processing are performed by dedicated hardware, further speedup can be achieved. There is a possible effect.

Embodiment 5 FIG.
Hereinafter, a method for decompressing one-dimensional time-series data that has been data-compressed by the compression method of the first or third embodiment will be described.
In the fifth embodiment, first, a description will be given of a case where it is guaranteed that compressed data is supplied only in the format of FIG.

  FIG. 17 shows a data decompression method when one-dimensional time-series data compressed by the compression method of the first embodiment, that is, data compressed only in the format of FIG. It is. This decompression method is composed of three stages. In the figure, P5a is input processing for inputting compressed data and the like compressed by the one-dimensional time series data compression method according to Embodiment 1, and P101a is compressed data by an interpolation function. Data expansion processing for interpolation and expansion, and P5b is output processing for outputting expanded one-dimensional time-series data.

  Next, the processing method will be described. In the input process P5a, the compressed data compressed by the one-dimensional time-series data compression method according to the first embodiment and the number of data to be generated when this data is expanded are input. Next, in the data decompression process P101a, the compressed data is interpolated and decompressed by the same interpolation function used when compressing the data. In the output process P5b, the one-dimensional time series data expanded by the data expansion process P101a is output.

FIG. 18 shows the expansion method of FIG. 17 in more detail.
In the figure, the first stage S31 includes an input process P101 similar to the input process P5a of FIG. The second stage S32 includes a data interpolation process P102 for interpolating the compressed data, a data calculation process P103 for calculating the expanded data, and a time calculation process P104 for calculating the time corresponding to the expanded data. The third step S33 includes an output process P105 similar to the output process P5b of FIG.

  The detailed processing shown in FIG. 18 is executed by the computer shown in FIG. 3, for example, from the first step S31 to the third step S33. In this case, the main memory 3 of the computer of FIG. 3 stores a program corresponding to the processing of FIG. 17 in advance or loaded from a program recording medium.

  Next, the expansion method will be described. First, in the first step S31, the compressed data compressed by the one-dimensional time-series data compression method according to the first embodiment and the number of data to be generated when this data is expanded are input by the input process P101.

  Next, in the second step S32, the data interpolation process P102 interpolates the compressed data with the same interpolation function used when compressing the data, and the data is made continuous, and the data calculation process P103 makes it continuous. The required number of data is calculated from the data, and the time calculation process P104 calculates the number of data that requires time from the initial time and the time interval. However, the interpolation function is a function having an index as an independent variable as in the case of compression, and an interpolation function is generated using the value of the index string of the compressed data.

Then, in the third stage S33, the output process P105 outputs the data calculated in the second stage S32 and the time as one-dimensional time-series data expanded.
As can be seen from the above decompression method, when restoring one-dimensional time-series data, the number of data can be decompressed to a number different from the original one. In other words, this means that it is possible to change the time of the one-dimensional time-series data, and that control can be performed according to the number of input data.

  As described above, according to the fifth embodiment, the one-dimensional time-series data compressed by the method of the first embodiment can be expanded, and the number of data generated when the expansion is performed is the original one-dimensional time. There is an advantage that a one-dimensional time-series data expansion method that can arbitrarily increase / decrease the series data and can increase / decrease the number of generated data without impairing the properties of the data is obtained.

Embodiment 6 FIG.
In the fifth embodiment, the one-dimensional time-series data expansion process is realized by software. However, this data expansion process may be realized by dedicated hardware.
FIG. 19 shows a time-series data decompression device in which the processing flow of FIG. 17 is implemented as dedicated hardware. One-dimensional time-series data compressed by the compression device of the second embodiment, that is, FIG. 1 shows a data decompression apparatus when data compressed only in a format is supplied. In the figure, 50a is an input means for inputting compressed data compressed by the time-series data compression apparatus according to the second embodiment, 20a is a data expansion means for interpolating and expanding compressed data by an interpolation function, and 50b is an expanded 1 It is an output means for outputting dimension time series data.

  Next, the operation will be described. The input means 50a inputs the compressed data compressed by the time-series data compression apparatus according to the second embodiment and the number of data to be generated when this data is expanded. Next, the data decompression means 20a interpolates and decompresses the compressed data using the same interpolation function used when compressing the data. Then, the output means 50b outputs the one-dimensional time series data expanded by the data expansion means 20a.

FIG. 20 shows in more detail the configuration of the expansion device of FIG.
In the figure, reference numeral 50a denotes an input means configured similarly to the input means 50a of FIG. Reference numeral 21 denotes data interpolation means for performing data interpolation processing on input data, 22 denotes data calculation means for calculating data expanded from the interpolated data, and 23 denotes time calculation means for calculating a time corresponding to the data. . Reference numeral 50b denotes output means configured similarly to the output means 50b of FIG.

Next, the operation will be described. First, the input means 50a inputs the compressed data compressed by the time-series data compression apparatus according to the second embodiment and the number of data to be generated when the data is expanded.
Next, the data interpolation means 21 interpolates the compressed data with the same interpolation function that was used when compressing the data to make the data continuous, and the data calculation means 22 requires the data from the continuous data. The number of data is calculated, and the time calculation means 23 calculates the number of data requiring time from the initial time and the time interval. However, the interpolation function is a function having an index as an independent variable as in the case of compression, and an interpolation function is generated using the value of the index string of the compressed data.

Then, the output means 50b outputs the calculated data and time as decompressed one-dimensional time series data.
As described above, according to the sixth embodiment, the one-dimensional time series data compressed by the apparatus of the second embodiment can be decompressed at high speed by the dedicated hardware, and the number of data to be generated when performing the decompression is reduced. The original one-dimensional time-series data can be arbitrarily increased or decreased, and the number of generated data can be increased or decreased without impairing the properties of the data.

Embodiment 7 FIG.
Next, a method for decompressing the one-dimensional time series data compressed by the compression method of the third embodiment will be described.
In the seventh embodiment, a case will be described in which data in the format of FIG. 16A and data in the format of FIG.

FIG. 21 shows one-dimensional time-series data compressed by the compression method of the third embodiment, that is, the case where data is supplied in a mixture of the format of FIG. 16 (a) and the format of FIG. 16 (b). It shows a data decompression method. This decompression method is composed of four stages, and in the figure, the same reference numerals as those in FIG. 17 denote the same or corresponding elements.
P101b is a data format determination process for determining the format of the compressed data, and P101c is a 0 data expansion process for expanding the compressed data when it is determined that all the compressed data is “0”.

Next, the expansion method will be described. When data is supplied in the format of FIG. 16 (a), the data format determination process P101b passes the data to the data expansion process P101a, and then expands the data in the same manner as in FIG. 17 and outputs it by the output process P5b. To do.
On the other hand, when data is supplied in the format shown in FIG. 16B, the data format determination process P101b passes the data to the 0 data decompression process P101c, and generates all “0” data over a predetermined period. This is output by the output process P5b as in FIG.

FIG. 22 shows the expansion method of FIG. 21 in more detail.
The process of FIG. 21, whose details are shown in FIG. 22, is executed by the computer of FIG. 3, for example. In this case, the computer of FIG. 3 stores a program corresponding to the processing of FIG. 22 in advance or loaded from a program recording medium.

  In the figure, the first step S41 includes an input process P101 similar to the input process P101 of FIG. The second stage S42 includes a data format discrimination process P106, a 0 data calculation process P107, and a time calculation process P108. The third stage S43 includes a data interpolation process P102, a data calculation process P103, and a time calculation process P104, as in the second stage S32 of FIG. The third stage S44 includes an output process P105 similar to the output process P105 of FIG.

  Next, the expansion method will be described. First, in the first step S41, the compressed data compressed by the one-dimensional time series data compression method and the number of data when decompressed are input by the input process P101.

  Next, in the second step S42, in the data format discrimination process P106, the format of the compressed data is discriminated, and in the case of the format of FIG. 16B, that is, an identifier indicating that all the compressed data is “0”. In this case, “0” corresponding to the number of data is calculated by the 0 data calculation process P107, and the time is calculated by the number of data from the initial time and the time interval by the time calculation process P108. The calculated “0” data and its time are output as one-dimensional time series data by the output process P105 in the fourth step S44.

  On the other hand, the third stage S43 is a case where it is determined in the second stage S42 that the compressed data are not all “0” identifiers, that is, in the case of the format of FIG. At the same time as in the second step S32 of FIG. 18, the compressed data is interpolated by the interpolation function used at the time of compression, the data is made continuous, and the data corresponding to the number specified by the input processing is obtained from the continuous data. The time is calculated from the initial time and the time interval by the same number as the data. However, the interpolation function is a function having an index as an independent variable as in the case of compression, and an interpolation function is generated using the value of the index string of the compressed data.

  Then, in the fourth stage S44, similarly to the second stage S32 in FIG. 18, the data and time calculated in the second stage S42 or the third stage S43 are output as one-dimensional time-series data expanded.

  As can be seen from the above decompression method, when restoring one-dimensional time-series data, the number of data can be decompressed to a number different from the original one. In other words, this means that it is possible to change the time of the one-dimensional time-series data, and that control can be performed according to the number of input data.

  As described above, according to the seventh embodiment, the one-dimensional time-series data compressed by the method of the third embodiment can be decompressed, and the number of data generated when the decompression is performed is the original one-dimensional time. There is an advantage that a one-dimensional time-series data expansion method that can arbitrarily increase / decrease the series data and can increase / decrease the number of generated data without impairing the properties of the data is obtained.

Embodiment 8 FIG.
In the seventh embodiment, the one-dimensional time-series data expansion process is realized by software. However, the data expansion process may be realized by dedicated hardware.
FIG. 23 shows a time-series data decompression apparatus in which the processing flow of FIG. 21 is made into dedicated hardware. One-dimensional time-series data compressed by the compression apparatus of the fourth embodiment, that is, FIG. FIG. 17 shows a data decompression apparatus when data is supplied in a mixed format and the format of FIG. In the figure, the same reference numerals as those in FIG. 19 denote the same or corresponding parts. Reference numeral 20b denotes data format discrimination means for discriminating the format of the compressed data, and 20c denotes zero data decompression means for decompressing the compressed data when it is determined that all the compressed data is "0".

  Next, the decompression operation will be described. When data is supplied in the format of FIG. 16 (a), the data format discrimination means 20b passes the data to the data decompression means 20a, and thereafter decompresses the data in the same manner as in FIG. 19 and outputs it by the output means 50b. To do.

On the other hand, when data is supplied in the format of FIG. 16 (b), the data format discrimination means 20b passes the data to the 0 data decompression means 20c and generates all “0” data over a predetermined period. This is output by the output means 50b as in FIG.

FIG. 24 shows the expansion device of FIG. 23 in more detail. In the figure, the same reference numerals as those in FIG. 20 denote the same or corresponding parts. Reference numeral 24 denotes data format discrimination means for discriminating the format of input data, reference numeral 25 denotes zero data calculation means for calculating “0” data, and reference numeral 26 denotes time calculation means for calculating a time corresponding to “0” data.
Next, the decompression operation will be described. First, the input means 50a inputs the compressed data compressed by the time-series data compression device and the number of data when decompressed.

  Next, the data format discriminating means 24 discriminates the format of the compressed data. In the case of the format of FIG. 16B, that is, in the case of an identifier indicating that all the compressed data is “0”, 0 The data calculation means 25 calculates “0” corresponding to the number of data, and the time calculation means 26 calculates the time by the number of data from the initial time and the time interval. The calculated “0” data and its time are output as one-dimensional time series data by the output means 50b.

On the other hand, when the data format discriminating unit 24 discriminates that the compressed data is not an identifier indicating that all of the compressed data is “0”, that is, when data in the format of FIG. As in FIG. 20, the compressed data is interpolated by the interpolation function used at the time of compression, the data is made continuous, the number of data designated by the input means 50a is calculated from the continuous data, and the initial time The time is calculated from the time interval by the same number as the data. However, the interpolation function uses an index as an independent variable as in the compression, and generates an interpolation function using the value of the index string of the compressed data.
Then, the output means 50b outputs the calculated data and time as one-dimensional time-series data obtained by decompressing data, as in FIG.

  As described above, according to the eighth embodiment, the one-dimensional time-series data compressed by the apparatus of the fourth embodiment can be decompressed at high speed by dedicated hardware, and the number of data generated when the decompression is performed. Can be arbitrarily increased / decreased from the original one-dimensional time-series data, and the number of generated data can be increased / decreased without impairing the properties of the data.

Embodiment 9 FIG.
Note that the present invention is not applicable only to one-dimensional time series data, and the same compression, decompression method, and compression / decompression are applicable to compression and decompression of multidimensional, that is, a plurality of one-dimensional time series data. It can be realized by applying the device.
For example, compression for a plurality of one-dimensional time series data can be performed by repeatedly using the compression method according to the first and third embodiments of the present invention and the compression device according to the second and fourth embodiments.

In the ninth embodiment, a case where such multidimensional time-series data is compressed will be described using Motion Data Compression as an example.
This Motion Data Compression is a technique for compressing the data amount of multi-dimensional time-series data that expresses the movement of a person when the movement is expressed by regarding the person as a rigid articulated object as described above. .

  Motion Data is a translation vector of representative point positions of a rigid and articulated object modeled on a person, a rotation amount of a posture vector with respect to a coordinate axis in a three-dimensional space, a translation vector of each joint (joint), and each coordinate axis of a local coordinate system. The amount of rotation for

That is, if the number of joints of the rigid articulated object is m and the length of the time series is n, the Motion Data is {M _i = (Cx _i, Cy _i, Cz _i, θ _i ^Cx , θ _i ^Cy , θ _i ^Cz , X _i ^jt0 , y _i ^jt0 , z _i ^jt0 , θ _i ^jtx0 , θ _i ^jty0 , θ _i ^jtz0 ,..., X _i ^jtm−1 , y _i ^jtm−1 , z _i ^jtm−1 , θ _i ^{jtxm −1} , θ _i ^jtym−1 , θ _i ^jtzm−1 ) | i = 0, 1,..., N−1}
Given in. However, in this example, the order of rotation is set in the order of x-axis, y-axis, and z-axis, and Cx _i, Cy _{i, and} Cz _i are the coordinate values of the root, that is, the reference point of the position on the rigid body, θ _i ^Cx , θ _i ^Cy , θ _i ^Cz are joint attitude control angles, x _i ^jt0 , y _i ^jt0 , z _i ^jt0 are joint slide amounts, θ _i ^jtx0 , θ _i ^jty0 , θ _i ^jtz0,. x _i ^jtm-1 , y _i ^jtm-1 , z _i ^jtm-1 , θ _i ^jtxm-1 , θ _i ^jtym-1 , θ _i ^jtzm-1 are the x, y, and z axes of the m joints Is the rotation angle.

FIG. 25 shows this Motion Data compression method. In FIG. 25, P200 is Motion Data input processing for inputting Motion Data, and P201 is Motion Data that is multi-dimensional time-series data. Multidimensional time-series data decomposition processing that decomposes into time-series data, P202 is a one-dimensional time-series data compression processing that compresses the decomposed one-dimensional time-series data using the compression method of the first or third embodiment. P203 is a determination process for determining whether or not the compression of the same number of one-dimensional time-series data as the number of dimensions has been completed, and P204 is an output process for outputting the compressed multi-dimensional time-series data.
The process in FIG. 25 is executed by, for example, the computer in FIG. In this case, the main memory 3 of the computer in FIG. 3 stores a program corresponding to the processing in FIG. 25 in advance or loaded from a program recording medium.

  Next, the process will be described. First, in the input process P200, Motion Data as multidimensional time series data is input. Next, by the decomposition process P201, Motion Data is decomposed into one-dimensional time-series data for each element, and an index number is given to each one-dimensional time-series data.

The processes after the decomposition process P201 are the same as the one-dimensional time-series data compression method according to the first or third embodiment.
That is, the one-dimensional time-series data compression process P202 after the decomposition process P201 performs compression processing on each one-dimensional time-series data after decomposition by the same compression method as in the first or third embodiment. .
Then, when it is determined by the determination process P203 that compression processing has been performed on all the one-dimensional time series data, each of the compressed one-dimensional time series data, that is, the compressed multidimensional data is output by the output process P204. Outputs Motion Data.

Thus, according to the ninth embodiment, multidimensional time series data is compressed into a plurality of one-dimensional time series data, and each one-dimensional time series data is the same as in the first or third embodiment. Since compression is performed by applying the compression method, there is an interval in which, with respect to certain one-dimensional time-series data, there is little error between the original one-dimensional time-series data and the interpolation function, and data compression is not performed. Even if it exists, in many cases, the remaining one-dimensional time-series data can be compressed with respect to the same section as this section. Therefore, when viewed as the whole multi-dimensional time-series data, the original 1/4 to 1 / Data compression can be performed to about 5.
As an example of this multi-dimensional time-series data, for example, in the case of using the time-series data of the joint angle of a rigid multi-joint object (human), the compression rate is 0.168 to 0.264, depending on the approximation accuracy. I was able to get it.

Note that in the case of such one-dimensional time-series data representing the motion of each joint angle of a rigid multi-joint, errors accumulate toward the tip of the motion. Therefore, in order to make the approximation accuracy constant, it is necessary to make it smaller than the value used for the one-dimensional time-series data having no such relationship, but in this case, the overall compression rate is reduced. Become. In order to avoid such problems, the approximation accuracy is not constant and the approximation accuracy of the original joint of the rigid and articulated object is made smaller than usual, and the approximation accuracy is gradually increased toward the top. Therefore, the compression rate can be prevented from lowering than when the approximation accuracy is kept constant.
In addition, for one-dimensional time-series data with unequal intervals with respect to time, the multi-dimensional time-series data compression method according to the ninth embodiment is applied to time and data as independent one-dimensional data, What is necessary is just to compress independently.

Embodiment 10 FIG.
In the ninth embodiment, the compression processing of multi-dimensional time series data is realized by software. However, this data compression processing may be realized by dedicated hardware.
FIG. 26 shows a multi-dimensional time-series data compression apparatus in which the processing flow of FIG. 25 is made into dedicated hardware. In the figure, 100a is a Motion Data input means for inputting Motion Data, and 51 is multi-dimensional time-series data. Multidimensional time-series data decomposing means for decomposing a certain Motion Data into the same number of one-dimensional time-series data, 52 is the compression apparatus of the second or fourth embodiment for decomposing one-dimensional time-series data 1-dimensional time-series data compressing means for compressing using the same configuration as the above, 53 is a determining means for determining whether or not the compression of the same number of one-dimensional time-series data as the number of dimensions has been completed, 100b is compressed, It is an output means for outputting multidimensional time series data.

Next, the operation will be described. First, Motion Data as multidimensional time series data is input by the input means 100a. Next, the multi-dimensional time series data decomposition means 51 decomposes the Motion Data into one-dimensional time series data for each element, and gives an index number to each one-dimensional time series data.
The operation after the decomposing means 51 is the same as the one-dimensional time-series data compression operation in the second or fourth embodiment.
That is, the one-dimensional time-series data compression means 52 after the decomposition means 51 performs compression processing on each one-dimensional time-series data after decomposition by the same compression operation as in the second or fourth embodiment. .

  When the determination unit 53 determines that all the one-dimensional time series data has been compressed, the output unit 100b compresses each one-dimensional time series data, that is, compressed multi-dimensional Motion. Data is output.

Thus, according to the tenth embodiment, multidimensional time series data is compressed into a plurality of one-dimensional time series data, and each one-dimensional time series data is the same as in the second embodiment or the fourth embodiment. Therefore, the compression operation can be performed at high speed by using dedicated hardware, and the original one-dimensional time series data and the interpolation function can be obtained with respect to certain one-dimensional time series data. Even if there is a section where data is not compressed and data is not compressed, the remaining one-dimensional time-series data for the same section as this section often contains data that can be compressed. When viewed as the entire time-series data, data compression can be performed to about 1/4 to 1/5 of the original time series data.
As an example of this multi-dimensional time-series data, for example, in the case of using the time-series data of the joint angle of a rigid multi-joint object (human), the compression rate is 0.168 to 0.264, depending on the approximation accuracy. I was able to get it.

Note that in the case of such one-dimensional time-series data representing the motion of each joint angle of a rigid multi-joint, errors accumulate toward the tip of the motion. Therefore, in order to make the approximation accuracy constant, it is necessary to make it smaller than the value used for the one-dimensional time-series data having no such relationship, but in this case, the overall compression rate is reduced. Become. In order to avoid such a problem, the approximation accuracy is not constant, but the approximation accuracy of the original joint of the rigid articulated object is made smaller than usual, and the approximation accuracy is increased toward the top. By using this, it is possible to prevent the compression rate from being lowered than when the approximation accuracy is kept constant.
In addition, for one-dimensional time-series data with unequal intervals with respect to time, the multi-dimensional time-series data compression apparatus according to the tenth embodiment is applied to time and data as independent one-dimensional data. What is necessary is just to compress independently.

Embodiment 11 FIG.
In the eleventh embodiment, the multidimensional time-series data decompression method compressed according to the ninth embodiment is handled. FIG. 27 shows an example of decompression of Motion Data compressed by the compression method of FIG. 25. In FIG. 27, P300 is a multidimensional compressed data input process for inputting compressed Motion Data, and P301 is a compression. Multi-dimensional compressed data decomposition processing for decomposing the multi-dimensional time-series data into a plurality of compressed one-dimensional time-series data, and P302 represents the decomposed one-dimensional time-series data in Embodiment 5 or One-dimensional time-series data decompression process that decompresses using the decompression method of aspect 7, P303 is a determination process that determines whether or not a series of one-dimensional time-series data has been decompressed, and P304 is a series of decompressed one-dimensional data This is an output process for outputting time series data.
The processing in FIG. 27 is executed by, for example, the computer in FIG. In this case, the main memory 3 of the computer of FIG. 3 stores a program corresponding to the processing of FIG. 27 in advance or loaded from a program recording medium.

Next, the processing flow will be described. First, in the input process P300, the compressed Motion Data is input. Next, in the decomposition process P301, the compressed Motion Data is decomposed into one-dimensional compressed time series data for each element, and an index number is given to each compressed one-dimensional time series data.
The processes after the decomposition process P301 are the same as the one-dimensional time-series data expansion method according to the fifth or seventh embodiment.
That is, by the one-dimensional time-series data expansion process P302 after the decomposition process P301, the expansion process is performed on each one-dimensional time-series data after decomposition by the same expansion method as in the fifth or seventh embodiment. .

When it is determined that the decompression process has been performed on all the one-dimensional time series data by the determination process P303, each of the compressed one-dimensional time series data, that is, the decompressed multidimensional Motion is output by the output process P304. Data is output.
As described above, according to the eleventh embodiment, the compressed multidimensional time-series data is decomposed into a plurality of one-dimensional time-series data, and the five-dimensional or fifth embodiment is obtained for each one-dimensional time-series data. Since the decompression method similar to 7 is applied, the decompression process can be performed even on multi-dimensional compressed time-series data.

  When the decompression is performed, the number of data to be generated can be set to a number different from that of the original data. Therefore, particularly when decompressing Motion Data, the number of data to be generated is increased compared to the original data. Therefore, by generating images of rigid articulated objects that move slower than the original rigid articulated object, or by reducing the number of data to be generated in reverse, the rigid body moving faster than the original rigid articulated object It is possible to generate an image of a joint object, and it is possible to easily edit the motion of the object.

Embodiment 12 FIG.
In the eleventh embodiment, the expansion processing of multidimensional time series data is realized by software, but this data expansion processing may be realized by dedicated hardware.
FIG. 28 shows a multidimensional time-series data decompression apparatus in which the processing flow of FIG. 27 is implemented as dedicated hardware. In FIG. 28, 200a is multidimensional compressed data input means for inputting compressed Motion Data, and 61 is compressed. Multidimensional compressed data decomposing means for decomposing the multidimensional time-series data into a plurality of compressed one-dimensional time-series data, and 62 is the sixth embodiment or the sixth embodiment. 1 is a one-dimensional time-series data decompression unit that decompresses using the same configuration as the decompression apparatus 8; 63 is a determination unit that determines whether or not a series of one-dimensional time-series data has been decompressed; and 200b is a decompressed series. Output processing for outputting the one-dimensional time-series data.

Next, the operation will be described. First, the compressed motion data is input by the input means 200a. Next, the decomposition unit 61 decomposes the compressed Motion Data into one-dimensional compressed time series data for each element, and gives an index number to each compressed one-dimensional time series data.
The processing after the decomposing means 61 is the same as that of the one-dimensional time-series data expansion apparatus of the sixth embodiment or the eighth embodiment.
That is, the one-dimensional time-series data expansion means 62 after the decomposition means 61 performs expansion processing on each one-dimensional time-series data after decomposition by the expansion device similar to that of the sixth embodiment or the eighth embodiment. .

When the determining unit 63 determines that all the one-dimensional time series data has been decompressed, the output unit 200b compresses each compressed one-dimensional time series data, that is, decompressed multidimensional Motion. Data is output.
Thus, according to the twelfth embodiment, the compressed multi-dimensional time series data is decomposed into a plurality of one-dimensional time series data, and the sixth embodiment or the sixth embodiment is obtained for each one-dimensional time series data. Since the decompression device similar to 8 is applied to perform decompression, the decompression processing can be performed at high speed even for multi-dimensional compressed time-series data using dedicated hardware.

  When the decompression is performed, the number of data to be generated can be set to a number different from that of the original data. Therefore, particularly when decompressing Motion Data, the number of data to be generated is increased compared to the original data. Therefore, by generating images of rigid articulated objects that move slower than the original rigid articulated object, or by reducing the number of data to be generated in reverse, the rigid body moving faster than the original rigid articulated object It is possible to generate an image of a joint object, and it is possible to easily edit the motion of the object.

  As described above, the time-series data compression method, the recording medium on which the time-series data compression program is recorded, and the time-series data compression apparatus according to the present invention are multidimensional representing a rigid articulated object expressed as a three-dimensional CG image. It is suitable for use for compressing one-dimensional time series data obtained by decomposing time series data.

The processing block diagram of the time series data compression method in Embodiment 1 of this invention. The processing block diagram of the time series data compression method in Embodiment 1 of this invention. The figure which shows the computer used for execution of the time series data compression method in each embodiment of this invention, and a time series data expansion | extension method. The block diagram of the time series data compression apparatus in Embodiment 2 of this invention. The block diagram of the time series data compression apparatus in Embodiment 2 of this invention. The processing block diagram of the time series data compression method in Embodiment 3 of this invention. The processing block diagram of the time series data compression method in Embodiment 3 of this invention. The block diagram of the time series data compression apparatus in Embodiment 4 of this invention. The block diagram of the time series data compression apparatus in Embodiment 4 of this invention. Explanatory drawing of the 1st determination method of a suboptimal node candidate. Explanatory drawing of the 2nd determination method of a suboptimal node candidate. Explanatory drawing of 1-dimensional time series data. Explanatory drawing of the node candidate of 1-dimensional time series data. Explanatory drawing of the interpolation by the node candidate of 1-dimensional time series data. Explanatory drawing of the selection method of a suboptimal node candidate. Explanatory drawing of a compression data format. The processing block diagram of the time series data expansion | extension method in Embodiment 5 of this invention. The processing block diagram of the time series data expansion | extension method in Embodiment 5 of this invention. The block diagram of the time series data expansion | extension apparatus in Embodiment 6 of this invention. The block diagram of the time series data expansion | extension apparatus in Embodiment 6 of this invention. The processing block diagram of the time series data expansion | extension method in Embodiment 7 of this invention. The processing block diagram of the time series data expansion | extension method in Embodiment 7 of this invention. The block diagram of the time series data expansion | extension apparatus in Embodiment 8 of this invention. The block diagram of the time series data expansion | extension apparatus in Embodiment 8 of this invention. The processing block diagram of the multidimensional time series data compression method in Embodiment 9 of this invention. The block diagram of the multidimensional time series data compression apparatus in Embodiment 10 of this invention. The processing block diagram of the multidimensional time series data compression method in Embodiment 11 of this invention. The block diagram of the multidimensional time series data compression method in Embodiment 12 of this invention.

Explanation of symbols

P1a, P1b, P1c, P1d, P1e, P1f, P4a, P5a, P4b, P5b, P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12, P13, P14, P21, P22, P23, P24, P25, P26, P27, P28, P29, P30, P31, P32, P33, P34, P35, P41, P42, P43, P44, P45, P46, P47, P48, P49, P50, P51, P52, P53, P54, P55, P56, P57, P58, P59, P61, P62, P63, P64, P65, P66, P67, P68, P69, P70, P71, P72, P73, P74, P75, P76, P77, P78, P79, P101, P101a, P102, P103, P104, P105, P10 , P107, P108, P200, P201, P202, P203, P204 processing,
S1, S2, S3, S4, S5, S6, S7, S8, S9, S11, S12, S13, S14, S15, S16, S17, S18, S19, S20 Stage 1 CPU
2 Data memory 3 Main memory 4 Input / output device 5 Bus 6 External storage device 40a, 50a Input means 10a Node candidate calculation means 10b Node position optimization means 10c Judgment means 10d Node number optimization means 10e Judgment means 10f Judgment means 20a Data expansion Means 20b Data format discrimination means 20c 0 Data expansion means 21 Data interpolation means 22 Data calculation means 23 Time calculation means 24 Data format discrimination means 25 0 Data calculation means 26 Time calculation means 40b, 50b Output means 11 Index addition means 12 Initial node number Calculation means 13 Node candidate determination means 14 Interpolation means 15 Error calculation means 16 First objective function calculation means 17 Suboptimal node candidate determination means 18 Interpolation execution means 19 Error calculation means 20 Second objective function calculation means 21 Threshold determination means 22 Number of nodes Change hand Stage 23 Means for determining within approximate accuracy

Claims (3)

A compression method for one-dimensional time series data in the field of CG image processing,
A first step of inputting the one-dimensional time series data and approximate accuracy;
A second step of calculating node candidates of an interpolation function approximating the one-dimensional time series data;
Calculates the error between the one-dimensional time series data generated by the interpolation function based on the node candidates and the original one-dimensional time series data, and calculates the weighted addition of the maximum error value, the average error value, and the error variance. A third step of calculating a value of the first objective function to be performed;
A fourth step of repeatedly changing the nodal candidate so as to minimize the value of the first objective function and determining a suboptimal nodal candidate;
Fifth step of changing the number of node candidates and returning to the second step when it is determined that the minimum value of the objective function calculated in the fourth step exceeds a threshold value determined based on the approximation accuracy When,
When it is determined that the minimum value of the objective function calculated in the fourth step does not exceed the threshold value determined based on the approximation accuracy, the suboptimal node candidate data and the corresponding time data are obtained. A sixth step of outputting as compressed information,
A time-series data compression method. A recording medium recording a one-dimensional time-series data compression program in the CG image processing field,
A first step of inputting the one-dimensional time series data and approximate accuracy;
A second step of calculating node candidates of an interpolation function approximating the one-dimensional time series data;
Calculates the error between the one-dimensional time series data generated by the interpolation function based on the node candidates and the original one-dimensional time series data, and calculates the weighted addition of the maximum error value, the average error value, and the error variance. A third step of calculating a value of the first objective function to be performed;
A fourth step of repeatedly changing the nodal candidate so as to minimize the value of the first objective function and determining a suboptimal nodal candidate;
Fifth step of changing the number of node candidates and returning to the second step when it is determined that the minimum value of the objective function calculated in the fourth step exceeds a threshold value determined based on the approximation accuracy When,
When it is determined that the minimum value of the objective function calculated in the fourth step does not exceed the threshold value determined based on the approximation accuracy, the suboptimal node candidate data and the corresponding time data are obtained. A sixth step of outputting as compressed information,
A recording medium on which a time-series data compression program for causing a computer to execute each step is recorded. A compression apparatus for one-dimensional time-series data in the field of CG image processing,
Input means for inputting the one-dimensional time-series data and approximate accuracy;
Node candidate calculation means for calculating node candidates of an interpolation function approximating the one-dimensional time series data;
Calculates the error between the one-dimensional time series data generated by the interpolation function based on the node candidates and the original one-dimensional time series data, and calculates the weighted addition of the maximum error value, the average error value, and the error variance. Determining means for calculating a value of the first objective function to be performed;
Node position optimizing means for repeatedly changing node candidates so as to minimize the value of the first objective function, and determining sub-optimal node candidates;
When the determination means determines that the minimum value of the first objective function exceeds a threshold determined based on the approximation accuracy, the number of node candidates is changed, and the one-dimensional time when the number of nodes is changed Node number changing means for inputting series data to the node candidate calculating means;
When it is determined by the determination means that the minimum value of the objective function does not exceed a threshold value determined based on the approximation accuracy, the suboptimal node candidate data and the corresponding time data are compressed. Output means for outputting the information as
A time-series data compression apparatus characterized by the above.

Images