WO2007010624A1 - Coordinate conversion method, data compression method using the same, information hiding method, and device thereof - Google Patents

Abstract

[PROBLEMS] To provide a technique for coordinate conversion in which the coordinate conversion of object data such as an arbitrary image has the maximum conversion efficiency. [MEANS FOR SOLVING PROBLEMS] Since a first axis is decided according to a distribution shape of object data, it is possible to perform coordinate conversion not only for an ideal function such as a convex function but also object data having a partially peculiar distribution shape without being significantly affected in the peculiar distribution shape portion.

Description

 Specification

 Coordinate transformation method, data compression method and information hiding method using the same, and apparatus thereof

 Technical field

 [0001] The present invention relates to coordinate transformation that shows the position of a point in a space shown on one coordinate system on another coordinate system, and more particularly to coordinate transformation suitable for data compression and information hiding. Related.

 Background art

 [0002] Principal component transformation is used to compress target data. For example, principal component conversion is used in the compression encoding method for color images disclosed in Japanese Patent Laid-Open No. 1-264092. This background art color image compression coding method divides a color image into small regions, performs principal component analysis on the RGB signals of the pixels contained in each small region, and obtains the first of each pixel obtained as a result. Each small area is approximated with two colors by dividing each pixel into two classes based on the principal component score. Thus, according to the color image compression encoding method of the background art, color image data compression can be realized with a small amount of memory and calculation time.

[0003] Information and idling are generic names for transparent technology and steganography technology. Information that appears outside is called original data (original image), and information that doesn't appear outside is called secret data. Information hiding methods can be broadly divided into a method of embedding secret data in the real space of the original image and a method of embedding secret data in the frequency space of the original image. Compared to the former from the viewpoint that it is possible to embed secret data in a specific frequency band that is relatively unaffected by the original image even if processing such as compression is applied to the embedded distribution image. The latter is capable of concealing secret data information. The former requires a device to embed secret data by manipulating the edge portion of the original image. In the latter case, it is necessary to determine the frequency band of the original image in which the secret data is to be embedded. An information hiding method using RGB 'color original images has also been proposed. From the viewpoint of the amount of information in the original image, information hiding using a color original image is information hiding using a powerless original image. Compared to, it has the ability to conceal the information of secret data. Information hiding using a color original image uses a method of embedding secret data in a certain component of the original image. For example, a method of embedding secret data in the G component of the original image is used. Therefore, when embedding secret data in the G component of the original image, the R and B component information of the original image is not used.

 [0004] Information hiding based on wavelet multi-resolution analysis is also a conventional method. When multi-resolution analysis is applied to an image, the vertical and horizontal high-frequency components (HH), vertical high-frequency components, horizontal low-frequency components (HL), vertical and horizontal low-frequency components (LL), and vertical low-frequency components' horizontal high-frequency components (LH) It can be decomposed into images and this decomposition can be repeated up to any stage, and conversely, the original image can be reconstructed from these decomposition images, but at any level (stage) in this multi-resolution analysis. By embedding component images as secret images and secret data, and then reconstructing them, an image that is almost the same as the original image can be generated. If this is used as a distribution image, for example, a copyright display image is used as a secret image, the copyright of the original image can be claimed. At that time, if the position (level and decomposition component) where the secret image is embedded is detected, the copy light as the secret image may be erased or tampered with. In order to cope with this, principal component transformation is applied as preprocessing for information hiding, and only the author who owns the original image can know the principal component coordinates of the original image, so the copyright is protected. A method has also been invented.

 Patent Document 1: Japanese Patent Laid-Open No. 1-264092

 Disclosure of the invention

 Problems to be solved by the invention

[0005] The background technology is configured as described above. Principal component transformation is used as a coordinate transformation used for data compression and information hiding to achieve a certain effect. The principal component coordinates are coordinate axes of the three primary colors of the color original image. If the distribution of pixels in is a distribution expressed by a convex function such as a multidimensional normal distribution, the most efficient coordinate conversion is possible by principal component conversion, but generally an image showing a distribution that can be expressed by a convex function For functions other than a few convex functions, there is a problem that it is difficult to realize coordinate transformation that matches the target data by principal component transformation. [0006] An object of the present invention is to provide a technique related to coordinate conversion that maximizes the conversion efficiency in the coordinate conversion of target data such as an arbitrary image. Another object of the present invention is to provide a data compression method using this coordinate transformation. Furthermore, for the purpose of overcoming the drawbacks of the method of embedding secret data in one of the band images of the original multi-band image, information high-definition using a multi-band image based on multi-resolution analysis with appropriate coordinate transformation is used. The purpose is to provide an inning method.

 Means for solving the problem

[0007] When coordinate transformation is performed based on the first principal component axis as a result of the principal component analysis, the amount of information contained in the first principal component image is optimal for a distribution in which the proportion of the total information is not sufficient. Perform coordinate transformation based on the target axis so that the first axis component after conversion has the maximum amount of information.

 [0008] (1) In the coordinate conversion method according to the present invention, the first axis is based on the distribution shape of the target data so that the information amount of the first axis component data after coordinate conversion occupies the maximum. Is determined. Thus, in the present invention, since the first axis is determined based on the distribution shape of the target data, the target data has not only an ideal function such as a convex function but also a partially unique distribution shape. However, coordinate transformation can be performed without being significantly affected by the unique distribution shape. Specifically, the first axis is the straight line passing through the data element set having the maximum distance among the data elements of the target data. In this case, the isolated point removal process is first performed so that the determination of the first axis is not appropriate due to the influence of the isolated data elements of the target data. It is preferable to determine the first axis after

 [0009] (2) The information hiding method according to the present invention is based on a multi-resolution analysis using, as necessary, the coordinate transformation for determining the first axis as preprocessing. Thus, in the present invention, since information hiding is performed using the coordinate transformation, component data with concentrated energy can be obtained, and target data in which secret data is appropriately concealed can be reconstructed.

[0010] (3) The information hiding method according to the present invention is based on multi-resolution analysis using coordinate transformation for arbitrarily setting a reference axis as preprocessing. [0011] (4) The data compression method according to the present invention is claim 4. The distribution force of the target multidimensional data in the multidimensional space The first principal component corresponding to the maximum eigenvalue is obtained based on the assumption that it is a convex function even though it is not a convex function, and sequentially corresponds to the nth eigenvalue The data compression that performs dimensional reduction according to the ratio of the amount of information up to the m-th principal component to the original amount of information, called the cumulative contribution rate, is the optimal for an actual distribution that exhibits a concave function. It is not a dimensional reduction method. The dimensional reduction method according to the present invention is a method in which the maximum dispersion axis in an actual distribution is obtained and used as the first principal component axis, and the axis having the next largest variance perpendicular to it is used as the second principal component axis. It is characterized by determining the coordinate axes after conversion and performing dimensional reduction according to the cumulative contribution rate.

 [0012] (5) A data compression method according to the present invention is claim 5. A data compression apparatus and method characterized by enhancing the data compression efficiency by emphasizing the bias of the target multidimensional distribution and increasing the redundancy of the target data by converting to oblique coordinates. By converting to oblique coordinates, re-quantization is required, and the power that increases the quantization error is expected to increase the compression ratio much higher than its influence.

[0013] (6) In the data compression method according to the present invention, the computer considers a data element whose distance from the nearest data element is larger than the first threshold among the data elements constituting the target data as an isolated point. A step in which the computer obtains eigenvalues and eigenvectors from the target data after removal, and a computer obtains each principal component data by removing at least one principal component data from the target data using the eigenvalues and eigenvectors. Is included. As described above, in the present invention, eigenvalues and eigenvectors are obtained by removing the isolated points from the target data, and each principal component data excluding at least one principal component data using the eigenvalues and eigenvectors for the target data is obtained. Therefore, the conversion formula is obtained by removing the singular part of the target data, and the necessary principal component data is obtained, and the target data can be generated by dimension compression with little influence of the singular part. It is becoming possible to compress the entire principal component data with a smaller number of principal components than the time limit. In order to reconstruct the target data also with this principal component data force, the target data can be reconstructed from the obtained principal component data and the conversion formula used when obtaining the principal component data. Needless to say, there is no principal component data! It cannot be reconfigured.

 [0014] (7) In the data compression method according to the present invention, the computer specifies the data element set having the largest distance between the data elements from the target data! / And passes through the specified data element set. Determining the s-axis using the first to (s1) axes obtained from the target data by the computer, and the t-th axis using the t-th axis obtained by the computer for the target data force. Obtaining the component data, and the number of obtained axial components is smaller than the number of dimensions of the target data. As described above, in the present invention, the first axis passing through the data element set having the largest distance between the data element of the target data (same as the coordinate value in the coordinate space) and the data element is obtained, and the necessary axis is obtained sequentially. Since the required axis component data is obtained from the obtained axis and target data, and the target data is reconstructed from the obtained axis component data and the axis, the data realizing the data quality and compression ratio desired by the user is obtained. Compression can be provided. For example, in the case of 3D target data, the first axis is obtained, the second axis that is orthogonal to the first axis and passes through the center of gravity of the target data, for example, is obtained, and the first and second axes are converted. Substituting the target data as an equation to obtain the first axis component data and the second axis component data, and reconstructing the target data from the first axis component data and the second axis component data, and the first axis and the second axis can do. Here, the data compression is performed by removing the third axis component data, but the data compression can also be performed by removing the second axis component data. Finds the third axis that is orthogonal to the first and second axes and passes through the center of gravity of the target data, determines the first axis component data from the first axis and the target data, the third axis and the target data force third axis Component data can be obtained, and target data can be reconstructed from the first axis component data and the third axis component data, and the first axis and the third axis.

[0015] (8) In the data compression method according to the present invention, a data element whose distance from the nearest data element among the data elements constituting the target data is greater than the first threshold is regarded as an isolated point. Removing from the data, the computer identifying the data element set with the largest distance between the data elements after removal, determining the first axis passing through the identified data element set, and the computer The steps of obtaining the s-axis using the first to (s-1) axes obtained from the data and obtaining the t-axis component data using the t-axis obtained by the computer for the target data force. Included and sought The number of axis components is smaller than the number of dimensions of the target data. Thus, in the present invention,

In addition to the data compression method of (7) above, in order to determine the first axis by removing the data element of the singular part from the target data in advance, the first axis where the information is concentrated except for the data element of the singular part. The first axis component data can be configured with a high contribution rate, the contribution of axis component data other than the first axis component data is reduced, and the target data is reconstructed using at least the first axis component data It is possible to generate compressed data with a high compression rate and good data quality.

 [0016] (9) In the information hiding method according to the present invention, the computer specifies a data element set having the largest distance between the target data force data elements, and the first axis passing through the specified data element set is determined. Calculating the s-axis using the first to (s-1) axes calculated from the target data by the computer, and the t-axis component using the t-axis determined from the target data by the computer. A step of obtaining data, a step in which the computer performs reversible wavelet transform on at least one of the axis component data, and embedding the secret data in the high-frequency component of the axis component data; Including inverse wavelet transform of component data, and computer reconstructing target data from each axis component data A. As described above, in the present invention, the first axis passing through the data element set having the largest distance between the data element of the target data (same as the coordinate value in the coordinate space) and the data element is obtained, and the number of dimensions is sequentially increased. Axis equal to is obtained, all the axis component data of the obtained axis and target data force are obtained, and one axis component data of the obtained axis component data is subjected to one or more wavelet transforms and secret data is obtained as a high frequency component. The data is reconstructed with the same number of times as the number of times wavelet transform is performed by inverse wavelet transformation, and the distribution target data is generated from the other axis component data and each axis. In order to extract the target data, which is the original data, each axis and axis component must be obtained in the same way, one axis component must be selected, and wavelet transformation must be performed as many times as necessary. Gu In addition, the data quality is good when compared with the target data that is the original data.

[0017] (10) In the information hiding method according to the present invention, the distance between the computer and the nearest data element that constitutes the target data is greater than the first threshold. Is considered as an isolated point and is removed from the target data, and the target data force after removal is identified. The data element set with the largest distance between the data elements is specified, and the first axis passing through the specified data element set is obtained. Calculating the s-axis using the first to (s-1) axes from which the computer also determined the removal target data force, and the t-axis component using the t-axis determined by the computer from the target data A step of obtaining data, a step in which the computer performs reversible wavelet transform on at least one of the axis component data, and the secret data is embedded in the high frequency component of the axis component data; and a computer after the secret data is embedded A step of inverse wavelet transformation of the axis component data and a step in which the computer reconstructs each axis component data force target data. And As described above, in the present invention, in order to determine the first axis by removing the data element of the singular part in advance of the data hiding method of the information (9), the data element of the singular part is determined. The first axis where information is concentrated can be determined, and the first axis component data can be constructed with a high contribution rate.By embedding secret data in such a first axis component, the data quality can be improved. It is possible to generate distribution target data that is well confidential.

(11) In the information hiding method according to the present invention, a computer specifies a data element set having the largest target data force and a distance between data elements, and obtains a first axis passing through the specified data element set. The step of obtaining the s-axis using the first axis or the (s-1) axis obtained from the target data by the computer and the t-axis component data using the t-axis obtained from the target data by the computer. A step in which the computer performs oblique coordinate transformation on at least one of the axis component data, and a reversible wavelet transformation is performed on the axis component data subjected to the oblique coordinate transformation to obtain axis component data. Embedding secret data in the high-frequency components of the computer, a computer performing inverse wavelet transform of the axis component data after embedding the secret data, and a computer There are those comprising a step of performing oblique coordinate reverse conversion axis component data of the wavelet Gyakuhen 換後; and computer to reconstruct the respective axis components de one Taka ゝ Luo target data. As described above, in the present invention, in consideration of the information hiding method of the above (9), after obtaining at least the axis component data to be wavelet transformed, the axis component data is subjected to oblique coordinate transformation at a specified angle. This oblique coordinate transformed data is wavelet transformed, embedded with secret data, Inverse transformation of the bullet, inverse transformation of the oblique coordinates at the same specified angle, reconstruction of the axis component data, and generation of distribution target data from the other axis component data and each axis. If the results of the coordinate transformation are different and the specified angle is not known, for example, it is difficult to extract confidential data even if a third party illegally acquires the target data that is the original data. High nature.

 [0019] (12) In the information hiding method according to the present invention, the computer considers a data element whose distance from the nearest data element is larger than the first threshold among the data elements constituting the target data as an isolated point. The removal from the target data, the computer identifies the data element set with the largest distance between the target data forces after the removal, determines the first axis that passes through the identified data element set, and the computer removes The step of obtaining the s-axis using the first to (s-1) axes from which the target data force is also obtained, the step of obtaining the t-axis component data using the t-axis obtained from the target data by the computer, A step in which the computer performs oblique coordinate transformation on at least one of the axis component data, and a reversible wavelet for the axis component data subjected to the oblique coordinate transformation. Transform and embed the secret data in the high-frequency component of the axis component data; the computer performs the wavelet inverse transform of the axis component data after the embedded secret data; and the computer converts the axis component data after the wavelet inverse transform. The method includes a step of performing an oblique coordinate reverse transformation and a step of reconstructing each axis component data force target data by the computer. As described above, in the present invention, in addition to the information hiding method of (11) above, in order to determine the first axis by removing the data element of the singular part in advance as well, the data element of the singular part is excluded. The first axis on which information is concentrated can be determined, and the first axis component data can be constructed with a high contribution rate, and by embedding secret data in such a first axis component, the data quality is good and concealed It is possible to generate distribution target data with high characteristics.

[0020] (13) In the information hiding method according to the present invention, the computer obtains eigenvalues and eigenvectors from the target data after removal, and the computer uses at least one principal component data using the eigenvalues and eigenvectors from the target data. Steps for obtaining each principal component data except for, performing oblique coordinate transformation on the obtained one principal component data, and performing reversible wavelet transformation on the one principal component data obtained by oblique coordinate transformation.ヽ The step of embedding the secret data in the high frequency component, the step of the computer performing the wavelet inverse transform on the data after embedding the secret data, and the computer performing the oblique coordinate inverse transform of the one principal component data after the wavelet inverse transform. And a step in which the computer performs inverse transformation of principal component from each principal component data. As described above, in the present invention, the target data is principal component transformed into each principal component data, one principal component data is subjected to oblique coordinate transformation at a specified angle, and the oblique coordinate transformed data is wavelet transformed, Embedded secret data, inverse wavelet transform, oblique coordinate inverse transform at the specified angle to reconstruct one principal component data, other principal component data and coefficient force used in principal component transformation also generate distribution target data Therefore, even in an information hiding method using principal component transformation, confidentiality can be improved by adopting oblique coordinate transformation.

 [0021] (14) This corresponds to an apparatus to which the above (4) is applied.

 (15) Corresponds to an apparatus to which the above (5) is applied.

 (16) Corresponds to an apparatus to which the above (6) is applied. An example of this apparatus is a computer in which a program to which the above (4) is applied is installed and can be read out to the main memory.

 [0022] (17) This corresponds to an apparatus to which the above (7) is applied.

 (18) Corresponds to an apparatus to which the above (9) is applied.

 (19) Corresponds to an apparatus to which the above (11) is applied.

 (20) Corresponds to an apparatus to which the above (13) is applied.

 [0023] It should be noted that a computer as a processing entity of steps may be processed by one computer, and each step may be processed by using a plurality of computers. Further, it can be paraphrased as a power processor whose computer is the main processing element. The outline of the invention described above is not an enumeration of characteristics essential to the present invention, and a sub-combination of a plurality of characteristics can also be an invention.

 Brief Description of Drawings

FIG. 1 is a flowchart when an information hiding method according to a first embodiment of the present invention is executed by a computer. 2) An example of a hardware configuration of a computer that executes the method of the first embodiment of the present invention.

圆 3] is a flowchart in the case of causing a computer to execute a method for decrypting distribution target data generated by the information hiding method according to the first embodiment of the present invention. 圆 4] Second embodiment of the present invention 6 is a flowchart when the information hiding method according to the above is executed by a computer.

[5] FIG. 5 is an explanatory diagram of detection of an isolated point in the information hiding method according to the second embodiment of the present invention.

圆 6] is a flowchart in the case of causing a computer to execute a method for decrypting distribution target data generated by the information hiding method according to the second embodiment of the present invention.

FIG. 7 is a flowchart in which steps for oblique coordinate transformation and oblique coordinate inverse transformation are added to FIG.

 FIG. 8 is a flowchart in which the steps of oblique coordinate conversion are added to FIG.

[9] This is a flow chart in the case where the computer executes the data compression method and decompression method according to the third embodiment of the present invention.

 [FIG. 10] RGB color original data of the example.

 [FIG. 11] Secret data of the example.

 [FIG. 12] This is the R component of the RGB color original data of the example.

 [FIG. 13] This is the G component of the RGB color original data of the example.

 [FIG. 14] This is the B component of the RGB color original data of the example.

 [Fig.15] Scattering of R component and G component of RGB color original data of Example.

 [Fig. 16] This is the result of principal component transformation of R component and G component dispersion of RGB color original data of the example.

 [Fig.17] Example of dispersion after oblique coordinate transformation in the example (Θ = 90 °, 110 °)

 FIG. 18 is an example of distribution data in the example (0 = 110 °).

FIG. 19 is a graph of RMS error with respect to parameter Θ of an example. Explanation of symbols

 [0025] 20 computers

 21 CPU

 22 Main memory

 23 Hard disk

 24 CD—ROM drive

 25 display

 26 keyboard

 27 mouse

 28 LAN card

 BEST MODE FOR CARRYING OUT THE INVENTION

Here, the present invention can be implemented in many different forms. Therefore, it should not be interpreted only by the description of the following embodiments. Further, the same reference numerals are given to the same elements throughout the embodiments.

 In each embodiment, the method will be mainly described. However, as is apparent to those skilled in the art, the present invention can also be implemented as a program, system, and apparatus that can be used by a computer. Furthermore, the present invention can be implemented in hardware, software, or software and hardware embodiments. The program can be recorded on any computer-readable medium such as a hard disk, CD-ROM, DVD-ROM, optical storage device or magnetic storage device. In addition, the program can be recorded on other computers via the network.

 [0027] (First embodiment of the present invention)

 An information hiding method according to the first embodiment of the present invention will be described with reference to the drawings.

 FIG. 1 is a flowchart when the information hiding method according to the present embodiment is executed by a computer. In FIG. 1, the information method and the idea method according to the present embodiment are C

The PU21 calculates the eigenvalues and eigenvectors of the multiband original image that is the target data (step 101), and the CPU21 safely stores the calculated eigenvalues and eigenvectors in the hard disk. 23 (step 102), the principal component of the multiband original image is converted by the eigenvalue and eigenvector computed by CPU21 (step 110), and CPU21 is designated for the first principal component image after the principal component transformation. The oblique coordinate transformation at the angle Θ (step 120), the CPU 21 performs the reversible wavelet transformation on the data obtained by the oblique coordinate transformation (step 130), and the CPU 21 is the secret data in the high frequency component after the reversible wavelet transformation. The secret image is embedded (step 140), CPU 21 performs reversible wavelet inverse transformation after embedding (step 150), CPU 21 performs oblique coordinate inverse transformation with the specified Θ (step 160), and CPU 21 performs eigenvalues and eigenvectors. Thus, the principal component is inversely transformed together with other principal component images (step 170) to generate a distribution multi-band image which is distribution target data.

 FIG. 2 is an example of a hardware configuration of the computer 20 that executes the method of the present embodiment. In this embodiment, a CPU (Central Processing Unit) 21, a main memory 22, a hard disk (HD: Hard Disk) 23, a CD-ROM drive 24, a display 25, a keyboard 26, a mouse 27, and a LAN card 28 are configured as a node. A general personal computer is used.

The general flow of information and idling is: first, wavelet decomposition is performed on the shifted band image of the multiband original image, and second, a secret image is inserted into the high-frequency component after wavelet decomposition, Third, when an information hiding image is generated by wavelet reconstruction. The important point here is the first “for any band image of the multiband original image”. In this embodiment, confidentiality can be improved by using oblique coordinate transformation that uses not only principal component transformation but also pre-processing for realizing energy concentration of multiband original images. Principal component transformation is a type of orthogonal transformation and can be inversely transformed. The oblique coordinate transformation can also be reversed. In addition, the present invention can be applied to a multi-band original image that is not a 3-band original image, and Sarako can also be applied to a 1-band original image. However, when applied to a 1-band original image, the 1-band original image itself becomes the first principal component image. Therefore, the principal component transformation can flexibly handle multiband original images compared to transformations applicable only to three-band original images such as HSI transformation. The reason for hiding the secret image in the first principal component image is that the first principal component image is the image that concentrates the energy of the multi-band original image most, and it is highly confidential and distributed. for This is because target data can be generated.

 [0029] The eigenvalues and eigenvectors are eigenvalues and eigenvectors in principal component analysis, which are obtained by multiband original image force, and are obtained using a variance covariance matrix or a correlation matrix force characteristic equation. It is obvious that other known calculation methods for obtaining eigenvalues and eigenvectors can be applied.

 To safely record eigenvalues and eigenvectors is to record eigenvalues and eigenvectors calculated from multiband original images in such a way that they are not known to third parties. It is desirable to record with encryption rather than recording directly on the hard disk 23. This is because when eigenvalues and eigenvectors are known to a third party, principal component transformation is easily performed on multiband images for distribution using these eigenvalues and eigenvectors. Similarly, the multi-band original image itself should not be known to third parties. This is because eigenvalues and eigenvectors can be calculated from the multiband original image. In the present invention, the oblique coordinate transformation is adopted, and since the content of the transformed data differs depending on Θ in this oblique coordinate transformation, even if the eigenvalue and eigenvector are known by a third party, Θ must be known. Secret image data cannot be extracted. Therefore, the eigenvalue, eigenvector, and 0 are keys for extracting the secret image data.

 [0030] Principal component transformation obtains a conversion equation from the eigenvalue and eigenvector to the first principal component, substitutes multiband target data into the conversion equation to the first principal component, and obtains the first principal component data. The How to perform principal component transformation is "Mathematical of spatial data" (Kanaya)

 Written by Asakura Shoten), "Image Processing Algorithm" (by Saito, Modern Science Co., Ltd.), "Data and Data Analysis" (by Kurihara, The Japan Broadcasting Corporation Education Promotion Association), and has become a well-known technology in this field. . For example, in order to obtain the coefficient of the conversion equation from the target data, there are a method using a correlation matrix, a method using a variance covariance matrix, and the like. The contribution ratio of each principal component is obtained by dividing the variance of each principal component by the sum of the variances of the variables.

 The orthogonal coordinate representation and the oblique coordinate representation in the two-dimensional space have the following relationship.

 [0031] W = X + Ycos (Θ)

 Z = Ysin (θ)

Therefore, it is possible to perform oblique coordinate transformation of a specified angle using this equation. This By specifying the force u and entering the values of X and Y, W and Z can be obtained. Conversely, by specifying the values of W and Z, X and Y can be obtained. Therefore, as described above, the oblique coordinate transformation is also a transformation that can be inversely transformed.

[0032] A reversible wavelet transform is used to frequency-divide a signal. This frequency division is called subband division. The functions used for the reversible wavelet transform include Daubechies function and Haar function. How to perform these reversible wavelet transforms can be found in the “Wavelet Beginners Guide” (Hagiwara

 Author, Tokyo Denki University Press), "Wavelet Image Analysis" (by Niijima, Science and Technology Publishing), "Basic Theory of Wavelet Analysis" (Arai

 Written by Morikita Publishing), "Use of Earth Observation Satellite Data by Wavelet Analysis" (Arai / L. Jameson, Morikita Publishing), "Signal Processing and Image Processing by Wavelets" (by Nakano Z Yamamoto Z Yoshida, Kyoritsu Publishing) , "Wavelet Analysis and Filter Bang, (G. Strung Z T. Nguyen, Baifukan), and is well known in the image processing technology field. Note that Fourier transform is observed from the definition of Fourier transform. It is calculated using only the signal and the sin function / cos function, and the wavelet transform can be operated using functions other than these. Analyzing what functions are used by third parties This is a transform with high secrecy, but it can be applied if both Fourier transform and wavelet transform are reversible. Transform is a kind of reversible wavelet transform, whereas orthogonal wavelet transform has the same coefficient as transform and inverse transform, whereas reversible wavelet transform does not always have the same coefficient. The reversible wavelet transform is preferable from the viewpoint of protecting the secret data, and at least the reversible wavelet transform is sufficient as the transform applicable to the present invention, and one of them is the bi-orthogonal wavelet transform. The reversible wavelet transform used and the reversible wavelet transform using the Haar function are the reversible wavelet transform and the orthogonal wavelet transform.

[0033] The hiding of the secret image has been described above. Next, a method for decoding the multiband data card for distribution in which the secret data is embedded will be described. FIG. 3 shows a method for decrypting distribution target data generated by the information hiding method according to this embodiment. It is a flowchart in the case of making a computer perform a method. In the background art, it has been realized simply by performing wavelet decomposition on a specific component of a multiband image in which confidential data is hidden. In the decoding for information hiding according to the present embodiment, the coefficients when principal component transformation is performed on the multiband original data before the secret data is hiding (both parameters, and eigenvectors are used as coefficients). CPU21 reads out (Step 201), and CPU21 uses this coefficient to perform principal component conversion (Step 210). CPU21 performs oblique coordinate conversion of the first principal component data at the specified Θ (Step 220). ), The CPU 21 performs reversible wavelet decomposition on the converted first principal component data (step 230), and the CPU 21 extracts the high frequency component force and secret data (step 240). Decoding for information hiding according to the present embodiment is combined only when the coefficient when performing principal component transformation on the multiband original data before hiding the secret data and Θ in the oblique coordinate transformation are known. It becomes possible. In other words, the principal component transformation coefficients differ depending on the multiband target data before hiding the secret data. Θ can be specified by the user. Since coefficients such as HSI conversion are well known, there is a possibility that a third party may obtain information on confidential data. In addition, in the background art, since secret data is hiding only in a specific component of multiband target data, there is a possibility that a third party can obtain the secret data by performing wavelet decomposition on the specific component. . In other words, a third party may obtain confidential data by performing wavelet decomposition on each band data.

 [0034] In the decoding method, the reversible wavelet transform conversion coefficient used at the time of information hiding, the eigenvalues and eigenvectors of the multiband original image are important and can be decoded by an unauthorized person who can decrypt the secret image data. It is necessary to be managed. Here, the eigenvalues and eigenvectors used at the time of decoding are only calculated from the multiband original image, not the multiband image force for distribution. Since eigenvalues and eigenvectors can be calculated from the multiband original image, it is necessary to manage the multiband original image as a result. Therefore, it is not a good idea to adopt a well-known image as the multiband original image.

[0035] Thus, according to the information hiding method of the present embodiment, the multiband original image is fixed. Calculates the value and eigenvector, records the calculated eigenvalue and eigenvector safely, converts the multiband original image into principal components using the calculated eigenvalue and eigenvector, and performs the oblique coordinate conversion with the specified Θ, Reversible wavelet transform on the first principal component data afterwards, embedded secret data in high frequency components after reversible wavelet transform, and then reversible wavelet inverse transform after embedding, and oblique coordinates at specified Θ Inverse transformation and inverse principal component transformation together with other principal component data using eigenvalues and eigenvectors to generate a multiband image for distribution, so even if either eigenvalues and eigenvectors or multiband original data are known If Θ is not known, it is difficult to decrypt the secret data, which is excellent in secrecy and the energy is most concentrated. When hiding a secret image for one principal component data, it is particularly excellent in secrecy.

 [Supplement of wavelet transform] When wavelet decomposition is performed on a two-dimensional signal, four components [1 low frequency component (LL1 component) and 3 high frequency components (LH1 component, HL1 component ΗΗ1 component)] are generated. When wavelet decomposition is performed on the LL1 component, four components (LL2 component 'LH2 component • HL2 component · ΗΗ2 component) are further generated. If a reversible wavelet is used and there are four components after wavelet decomposition, the two-dimensional signal given with zero error is restored. An orthogonal wavelet is a type of reversible wavelet. An overview of information noiding technique based on multi-resolution analysis is shown. Information noiding

 1. Perform wavelet decomposition on any band image of the multi-band original image

2. Insert secret data into high-frequency components after wavelet decomposition

 3. Generate distribution image by wavelet reconstruction

It is performed in the procedure. It is also possible to insert secret data into HL1, HH1 and ΗΗ2 components. The fact that the component that inserts secret data can be changed means that information hiding based on multiple resolution analysis has the ability to protect the information of secret data. The problem here is that information hiding procedure 1 “for any band image of the multi-band original image”. In the proposed method, principal component transformation is used as preprocessing to achieve energy concentration in the multiband original image, and further, oblique coordinate transformation is performed to secret data into the first principal component image. The proposed method can also be applied to cases where the original image is not 3 bands. In other words, the proposed method is hiding. In order to suppress degradation of image quality due to image quality, principal component transformation is performed on the multi-band original image, and secret data is hidden in the first principal component image. At that time, oblique coordinate transformation is performed. Further, a method for decrypting secret data will be described. The first principal component image is constructed for the distribution image using the coefficients obtained when the principal component transformation is applied to the multiband original image before the confidential data is hidden, and the first principal component image This is achieved by performing wavelet decomposition. Decryption of the secret data by the proposed method can be performed only when the principal component transformation of the multiband original image before hiding the secret data is known. That is, the coefficient of main component conversion differs depending on the multiband original image before hiding the secret data. Coefficients such as HSI conversion are well known. If the conversion factor is well-known, there is a possibility that a third party may obtain information on confidential data.

 [Recalculation of Eigenvalues and Eigenvectors from Original Data] In this embodiment, eigenvalues and eigenvectors are obtained from the target data, and if the force target data recorded in the storage unit is recorded, the eigenvalues are stored. And eigenvectors can be recalculated, and secret data can be extracted by recalculation without being recorded in the storage unit.

 [Second Embodiment of the Present Invention]

 The information hiding method according to the present invention will be described with reference to the drawings. Also in this embodiment, the information hiding method is executed by the computer 20 in FIG.

FIG. 4 is a flowchart when the information hiding method according to the present embodiment is executed by a computer. In FIG. 4, in the information hiding method according to this embodiment, the data element whose distance from the closest data element among the data elements constituting the target data by the CPU 21 is larger than the first threshold is regarded as an isolated point. As a result, the CPU 21 identifies the data element set having the largest distance between the data elements after the removal, and obtains the first axis that passes through the identified data element set. Each axis is obtained in order from one axis (step 310), CPU21 also obtains axial component data for each axial force (step 320), and CPU21 performs a reversible wavelet transform on at least one of each axial component data (step) 330), CPU 21 embeds secret data in the high frequency component (step 340), CPU 21 performs inverse wavelet transformation after embedding the secret data (step 350), and CCU 21 obtains the target data from each axis component data. (Step 360). [0039] In other words, the detection of the isolated point in the step 301 is to detect whether or not another data element exists in a region centered on each data element and having a first threshold as a distance. Is the same. If it is 2D, it will be the power of other data elements in the circle. If it is 3D, it will be the power of other data elements in the sphere. FIG. 5 is an explanatory diagram of detection of isolated points in the information hiding method according to the present embodiment. The black dots in Fig. 5 are data elements (coordinate values). Solid circles are circles that contain other data elements, and dotted circles are circles that do not contain other data elements. In other words, the data element at the center of the dotted circle is an isolated point.

 [0040] The determination of the first axis in step 310 is performed on the data element in the target data from which the isolated points have been removed, and in FIG. 5, the end point of the alternate long and short dash line is the data element set. When the first axis is determined, the axis that is orthogonal to the first axis and passes through the center of gravity of the target data is the second axis, and the axis that is orthogonal to the first and second axes and passes through the center of gravity of the target data is As the third axis, the axis that is orthogonal and passes through the center of gravity of the target data is obtained in the same manner. In the case of 3-band target data, find the first to third axes. The centroid of the target data may be a centroid that does not include isolated points.

 [0041] Here, the center of gravity is used, but the axis may be obtained based on the magnitude of the variance, which is orthogonal according to the principal component transformation. For example, the first axis is specified by the maximum dispersion axis, the second axis is orthogonal to the first axis, and is specified according to the condition that the variance is next to the first axis, and the third axis is specified by the first axis and the first axis. It can be specified according to the condition that it is orthogonal to the two axes and has the second largest variance after the second axis. Similarly, it can be specified under the same conditions up to the nth axis. In this case, it is possible to determine whether or not the determination of the first axis is performed based on the target data from which isolated points are removed, and whether or not the determination on the first axis and after is performed based on the target data from which isolated points are removed.

 When the axis is determined, the coefficient of the conversion formula is determined for each axis, and by inputting the target data into the powerful conversion formula, the axis component data is obtained.

[0042] The wavelet transformation without! / And the wavelet inverse transformation (step 330, step 340, step 350) are executed in the same manner as in the first embodiment. For example, the first axis component data in which the secret data is embedded can be reconstructed by executing step 330 or step 350 on the first axis component. The reconstruction of the target data in Step 360 is to obtain the reconstructed target data by solving simultaneous equations using the respective conversion equations for the first axis component data, the second axis component data, and the third axis component data. Can do.

FIG. 6 is a flowchart in the case of causing a computer to execute a method for decrypting distribution target data generated by the information hiding method according to the present embodiment. In the decryption for the information / decoding according to the present embodiment, the coefficients of the conversion formulas for each axis (both parameters, and the target data exist) in the multi-band original data before the secret data is de-identified. CPU21 reads (step 401), and CPU21 inputs the target data into the conversion equation using this coefficient (step 41).

0) The CPU 21 performs reversible wavelet decomposition on the converted first axis component data (step 420), and the CPU 21 extracts the high-frequency component force and secret data (step 430).

 [Adoption of oblique coordinate transformation] In this embodiment, the oblique coordinate transformation applied in the first embodiment can also be applied. In the information hiding method, as shown in FIG. As shown in FIG. 8, oblique coordinate transformation is performed between 320 and step 330 (step 370), and oblique coordinate transformation is performed between step 350 and step 360 in FIG. 7 (step 380). Further, it is possible to adopt a configuration in which oblique coordinate transformation is performed between the step 410 and the step 420 (step 440), and high confidentiality of confidential data is realized by a designated angle Θ that can be designated by the oblique coordinate transformation. Can do.

 [0045] (Third embodiment of the present invention)

 A data compression method according to the third embodiment of the present invention will be described with reference to the drawings. Also in this embodiment, the data compression method is executed by the computer 20 in FIG.

 FIG. 9 is a flowchart when the data compression method and decompression method according to this embodiment are executed by a computer. In FIG. 9 (a), the data compression of the present embodiment assumes that the data element whose distance from the nearest data element of the CPU 21 constituting the target data is larger than the first threshold is regarded as an isolated point. Remove from target data (Step 50

1) The CPU21 identifies the data element set with the largest data element distance after removal, and obtains the first axis that passes through the specified data element set. The configuration is such that an axis is obtained (step 510), and the CPU 21 obtains other axis component data for each axial force by excluding at least one axis component data (step 520).

In FIG. 9B, the CPU 21 reads the coefficient of the conversion formula (step 601), and the target data can be reconstructed from the axis component data and the conversion formula obtained by the CPU 21 (step 610). The conversion formula coefficients together with the axis component data form, for example, a single file as header information. When the CPU 21 reads such a file, the conversion formula coefficients are read from the header information catalog, and after step 610, normal For example, the image data format may be displayed on the display 25. Oblique coordinate transformation can also be applied to this data compression method, and the user can conceal Θ so that only those who know Θ can reconstruct the target data. It is possible to achieve confidentiality while fulfilling the purpose of data compression.

 [0047] The removal of isolated points in step 501 is the same process as the removal of isolated points in the second embodiment. The determination of the axis in step 510 is the same as the process for determining the axis, but the axis is not determined for an unnecessary axis. Also, in the calculation of the axis component in step 520, the calculation is not performed for the unnecessary axis component. Here, the unnecessary axis component is an axis component that is not used in step 530, and may be obtained, but is not used in step 530, and thus processing is wasted. An unnecessary axis is an axis related to an unnecessary axis component, but an axis related to an unnecessary axis component is not necessarily an unnecessary axis. That is, the first axis is obtained, the second axis is obtained from the first axis, the third axis is obtained from the first axis and the second axis, and the axis component of the second axis is not used because it is not used. However, since the third axis is required, the second axis must be obtained.

[0048] In step 520, in the case of the three-dimensional target data, two axis component data is obtained and one axis component is not obtained, and dimensional compression is realized. In order to reconstruct the target data as shown in step 610 from the code information that has been subjected to such dimensional compression, the target data is obtained from the remaining obtained axis component data and the axis. Here, in the simultaneous equations, the force that increases the number of norameters. For example, the target data can be obtained by applying singular value decomposition. Like the principal component transformation, when there are the 1st axis component, 2nd axis component, ..., nth axis component, the energy is concentrated as the lower order axis component data. Dimensional compression is desired except high order axis component data.

 [0049] (Other Embodiments)

 [Application to Moving Image] In the first embodiment, a multi-band original image as a hiding target, that is, a dynamic image that is a multi-band image, can also be a hiding target. In addition, it is possible to embed other types of hiding, not just secret images. Generally, data that can be hidden is considered secret data. There are several methods for embedding secret data in a moving image. There are a method of applying hiding to an image as it is, a method of hiding a secret image with respect to a specific frame, and the like. The method of applying hiding to an image as it is and the method of hiding a secret image to a specific frame, respectively, apply the information node and the idling according to the first embodiment as they are to the frame. can do. The present invention can also be applied to a method of embedding secret data by performing wavelet transform for each video object used as a compression unit in MPEG4 and operating its coefficient. Note that moving image data is not always “continuous in the time axis direction” (same for 3D moving images). Specifically, it is assumed that there are nine hours of moving image data, and are Frame 1, Frame 2, Frame 3, Frame 4, Frame 5, Frame 6, Frame 7, Frame 8, and Frame 9. For example, data can be extracted in the order of frame 3, frame 4, frame 1, frame 8, and frame 7 and subjected to five-dimensional principal component conversion. In addition, frame 3, frame 4, frame 1, frame 8 Also, the data can be extracted in the order of frame 7 and frame 3, and three-dimensional principal component transformation can be performed on frame 4, frame 1, and frame 8. The high-speed moving image data can be distributed in the order of frame 1, frame 2, frame 3, frame 4, frame 5, frame 6, frame 7, frame 8, and frame 9. By embedding secret data by changing the frame order in this way, it becomes difficult for a third party to analyze the secret data. In addition, third party analysis becomes more difficult by applying oblique coordinate transformation.

[0050] In the first embodiment! It can also be applied to a 1S dynamic original image that has been hiding using a static original image. For example, the still image in band 1 of sensor TM is regarded as the image at time 1, and the still image in band 2 of sensor TM is regarded as the image at time 2. Just do it. Similarly, it can be applied to 3D still images.

[Embedding in Other Principal Component Data] In the first embodiment, the first main component image is reversibly wavelet transformed and the secret image is embedded in the high frequency component. It is also possible to embed a secret image in a high-frequency component by reversible wavelet transform of the principal component image. Since energy is concentrated on the first principal component image, as a general rule, embedding a secret image in the first principal component image improves the quality of the multiband image for distribution and provides high confidentiality. The secrecy can be improved by making it possible to embed a secret image in addition to the first principal component image. Furthermore, it is possible to divide and embed the secret image in each principal component image instead of embedding the secret image in all the single principal component images.

 [0052] [Application of number of bands other than 3 bands to target data] In addition, in the examples described later, the force used in the experiment using 3 bands in 3 band images is used. It is also possible to perform hiding. In other words, C hiding set m n

 Because there is a match, the proposed method is superior in the ability to protect secret image information compared to the existing method. The existing method uses only one band in the m-band original image. It is difficult for third parties to obtain information on how many bands in the m-band original image are used for hiding.

 [Application to other target data] [0053] Although the image and the moving image have already been described, data compression and information hiding can be performed by applying the present invention to time series data.

 Although the present invention has been described by the above embodiments, the technical scope of the present invention is not limited to the scope described in the embodiments, and various modifications or improvements can be added to these embodiments. is there. Embodiments to which vigorous changes or improvements are added are also included in the technical scope of the present invention. This is clear from the claims and the means to solve the problems.

 Example

In accordance with the information hiding method according to the first embodiment, FIG. 10 is used as original data (multiple spectral image), and FIG. 11 is used as secret data. That is, in FIG. Hiding the data to the data shown in Fig. 10. 12 to 14 show the data of each wavelength band in FIG. From Fig. 15, it can be seen that the B components in Fig. 10 are all zero (Fig. 12 and Fig. 13 are both binarized on the drawing! In the actual image, it is possible to grasp the animal face image for both components). Figure 15 shows the dispersion of the R and G components in Figure 10. Figure 16 shows the result of principal component transformation performed on Figure 15. The vertical axis in FIG. 16 is the first principal component axis, and the horizontal axis in FIG. 16 is the second principal component axis.

FIG. 17 shows an example of a result obtained by performing oblique coordinate transformation on the scatter shown in FIG. 16 using the parameter Θ.

 Fig. 18 shows the result of hiding secret data in Fig. 17 (b). In other words, the third party estimates the secret data from FIG. The purpose of this embodiment is to show that the protection of secret data is improved by the parameter Θ. Therefore, we try to estimate the secret data from the first main component image in Fig. 18 using wavelet transform. It is assumed that the third party does not know the information of the original data, and can know the information of the component (for example, HH1 component) in which the wavelet base and secret data are embedded by some method. In other words, the third party does not know the information such as eigenvectors held by the parties and the parameter Θ.

 The average vector for conversion from the scatter of FIG. 15 to the scatter of FIG. 16 is (137.7724, 129.2966), and the conversion coefficients are as follows.

[0056] [Equation 1]

Where i is the first eigenvector and ξ ₂ is the second eigenvector.

 It is. The information for converting from the scatter shown in Fig. 15 to the scatter shown in Fig. 16 is known only to the parties concerned.

[0057] [Experimental results]

Figure 19 shows the RMS error when a third party tries to estimate the data power for distribution for each distribution data in which the secret data is embedded by changing the parameter Θ. [0058] [Discussion]

 From Fig. 19, it can be seen that the RMS error depends on the parameter Θ when a third party tries to estimate the data power for distribution. In other words, it can be seen that the protection of the secret data is improved by the parameter Θ. In addition, it can be seen that by protecting the information in the original data, it is possible to protect the secret data.

[0059] The present invention relates to an information hiding technique using multiple spectral images. We examined the case where a third party tried to extract confidential data only for distribution data. In the method according to the present invention, only the party who knows the characteristics of the multiple spectral image that is the original data can restore the confidential data. In other words, it is applicable when it is necessary to protect the information of the original data. Furthermore, in the proposed method, secret data information is protected by the existence of eigenvectors and oblique coordinate transformation. In other words, the secret information cannot be restored unless at least the true original image information is known. The coefficient of principal component conversion differs for each original data, and consists of eigenvectors of the original data. For 3-band color images, a method involving HSI conversion is also conceivable, but conversion coefficients such as HSI conversion are well-known coefficients. The effectiveness of the proposed method was confirmed from the viewpoint of protecting confidential information. In this embodiment, secret information can be restored if a force reversible wavelet adopting a Daubechies basis as a wavelet. Secret data can also be protected by hiding what to use as a reversible wavelet.

Claims

The scope of the claims

 [1] A coordinate conversion method that determines the first axis based on the distribution shape of the target data so that the information amount of the first axis component data after coordinate conversion occupies the maximum.

 [2] An information hiding method based on a multi-resolution solution using the coordinate transformation for determining the first axis according to claim 1 as preprocessing.

 [3] An information hiding method based on multi-resolution analysis using coordinate transformation that arbitrarily sets the reference axis as preprocessing.

 [4] Even when the multidimensional target data is not a convex function in multidimensional spatial coordinates, the computer determines the maximum dispersion axis in the actual distribution and sets it as the first principal component axis, and the computer The step of setting the axis with the s-th principal component axis as the s-th principal component axis, which is orthogonal to the (s-1) principal component axis and orthogonal to the (s-1) principal component axis. A data compression method including a step of principal component transformation using the s-th principal component axis. Here, s is a natural number greater than or equal to 2 and less than the number of dimensions of the target data.

 [5] A data compression method characterized by emphasizing the bias of the target multidimensional distribution and increasing the redundancy of the target data by converting to oblique coordinates.

 [6] The computer removes the data element from the target data by considering the data element as an isolated point when the distance from the nearest data element among the data elements constituting the target data is greater than the first threshold, and the computer removes A method of compressing data including a step of obtaining eigenvalues and eigenvectors from the later target data, and a computer obtaining each principal component data by removing at least one principal component data from the target data using the eigenvalues and eigenvectors.

[7] The computer identifies the data element set with the largest distance between the target data forces, finds the first axis that passes through the identified data element set, and the first axis that the computer also obtains the target data force It includes the steps of obtaining the s-axis using the (s-1) axis and obtaining the t-axis component data using the t-axis obtained from the target data by the computer. A data compression method in which the number of axis components is smaller than the number of dimensions of the target data. Here, s is a natural number greater than or equal to 2 and less than or equal to the number of dimensions of the target data, and t is a natural number greater than or equal to 1 and less than or equal to the number of dimensions of the target data.

[8] The computer removes the data element from the target data by considering the data element as an isolated point when the distance from the nearest data element among the data elements constituting the target data is greater than the first threshold. Post-target data force The step of identifying the data element set having the longest distance between the data elements and obtaining the first axis passing through the identified data element set is not the first axis obtained by the computer from the data to be removed. It includes the step of obtaining the s-axis using the (s-1) axis and the step of obtaining the t-axis component data using the t-axis obtained by the computer to obtain the target data force. Less than the number of data dimensions! / ヽ Data compression method. Here, s is a natural number of 2 or more and less than or equal to the number of dimensions of the target data, and t is a natural number of 1 or more and less than or equal to the number of dimensions of the target data.

 [9] The computer identifies the data element set having the largest distance between the target data forces and obtains the first axis passing through the identified data element set, and the first axis from which the computer also obtains the target data force. The step of obtaining the s-th axis using the (s-1) axis, the step of obtaining the t-th axis component data using the t-axis obtained from the target data by the computer, and the computer Performing a reversible wavelet transform on at least one of the component data and embedding the secret data in the high-frequency component of the axis component data; the computer performing an inverse wavelet transform on the axis component data after embedding the secret data; And a computer reconstructing target data from each axis component data. Here, s is a natural number greater than or equal to 2 and less than or equal to the number of dimensions of the target data, and t is a natural number greater than or equal to 1 and less than or equal to the number of dimensions of the target data.

[10] The computer removes the data element from the target data by considering the data element as an isolated point when the distance from the nearest data element among the data elements constituting the target data is greater than the first threshold. Post-target data force The step of identifying the data element set having the longest distance between the data elements and obtaining the first axis passing through the identified data element set is not the first axis obtained by the computer from the data to be removed. Determining the s-axis using the (s-1) -axis, determining the t-axis component data using the t-axis obtained by the computer for the target data force, and at least 1 of each axis component data for the computer. A reversible wavelet transform is performed on the data, and the secret data is embedded in the high-frequency component of the axis component data. The axis component data of An information hiding method comprising the steps of inverse bullet transformation and a computer reconstructing target data from each axis component data. Here, s is a natural number of 2 or more and less than or equal to the number of dimensions of the target data, and t is a natural number of 1 or more and less than or equal to the number of dimensions of the target data.

 [11] The step in which the computer identifies the data element set having the longest distance between the data elements and obtains the first axis passing through the identified data element set, and the first axis in which the computer also obtains the target data force The step of obtaining the s-axis using the (s-1) axis, the step of obtaining the t-axis component data using the t-axis obtained from the target data by the computer, and the computer Performing oblique coordinate transformation on at least one of the component data, performing reversible wavelet transformation on the oblique component transformed axis component data, and embedding secret data in the high frequency component of the axis component data; The computer performs a wavelet inverse transform on the axis component data after embedding the secret data, and the computer performs the axis component data after the wavelet inverse transform. A scan Tetsupu performing oblique coordinate inverse transformation step and the including information hiding method the computer to reconstruct the object data from each axis component data. Here, s is a natural number of 2 or more and less than or equal to the number of dimensions of the target data, and t is a natural number of 1 or more and less than or equal to the number of dimensions of the target data.

[12] The computer removes the data element from the target data by considering the data element as an isolated point when the distance from the nearest data element among the data elements constituting the target data is greater than the first threshold, and the computer removes Post-target data force The step of identifying the data element set having the longest distance between the data elements and obtaining the first axis passing through the identified data element set is not the first axis obtained by the computer from the data to be removed. Determining the s-axis using the (s-1) -axis, determining the t-axis component data using the t-axis obtained by the computer for the target data force, and at least 1 of each axis component data for the computer. The step of performing oblique coordinate transformation on the two and the reversible wavelet transformation on the axis component data subjected to the oblique coordinate transformation are performed, and the high-frequency component of the axis component data is hidden. A step of embedding dense data, a step in which the computer performs inverse wavelet transformation on the axis component data after embedding the secret data, a step in which the computer performs inverse oblique coordinate transformation on the axis component data after wavelet inverse transformation, and a computer Reconstructing target data from each axis component data. Where s is 2 or more A natural number less than or equal to the original number, t is a natural number greater than or equal to 1 and less than or equal to the number of dimensions of the target data.

[13] The computer obtains eigenvalues and eigenvectors from the target data after removal, the computer obtains each principal component data by removing at least one main component data from the target data using the eigenvalues and eigenvectors, and the computer obtains Performing oblique coordinate transformation on one principal component data, performing reversible wavelet transformation on one principal component data that has been obliquely coordinate transformed, and embedding secret data in high-frequency components; The computer performs a wavelet inverse transform on the data after embedding the secret data, the computer performs an oblique coordinate inverse transform on one principal component data after the wavelet inverse transform, and the computer performs each principal component data conversion. Information heide including the step of inverse transformation of principal components Packaging method.

[14] Even when the multidimensional target data is not a convex function in the multidimensional spatial coordinates, the maximum dispersion axis in the actual distribution is obtained, and the first principal component axis is used. (s-1) Means of dispersion that is orthogonal to the principal component axis and next to the (s-1) principal component axis !, means for setting the axis as the s principal component axis, and these first principal component axis through s principal component axis A data compression apparatus including means for principal component transformation using a component axis. Here, s is a natural number greater than or equal to 2 and less than the number of dimensions of the target data.

 [15] A data compression apparatus characterized by emphasizing the bias of the target multidimensional distribution and increasing the redundancy of the target data by converting to oblique coordinates.

 [16] Means to remove the target data force by regarding the data element that constitutes the target data the distance from the nearest data element that is greater than the first threshold as an isolated point, and the eigenvalue and A data compression apparatus, comprising: means for obtaining eigenvectors; and means for obtaining each principal component data by removing at least one principal component data from the target data using an eigenvalue and an eigenvector.

[17] Target data force Means to identify the data element set with the longest distance between data elements, find the first axis passing through the identified data element set, and the first axis V derived from the target data, Including means for obtaining the s-axis using the (s-1) axis and means for obtaining the t-axis component data using the t-axis for which the target data force is also obtained. Data compression device smaller than the number of dimensions. Where s is a natural number greater than or equal to 2 and less than or equal to the number of dimensions of the target data, t Is a natural number between 1 and the number of dimensions of the target data.

 [18] Target data force Means to identify the data element set with the longest distance between data elements, find the first axis passing through the identified data element set, and the first axis V derived from the target data, For at least one of the means for obtaining the s-th axis using the (s-1) axis, the means for obtaining the t-axis component data using the t-axis for which the target data force has also been obtained, A reversible wavelet transform is performed to embed secret data in the high-frequency component of the axis component data, a means for inverse wavelet transform of the axis component data after embedding the secret data, and each axis component data force. And an information hiding device comprising means for configuring. Here, s is a natural number of 2 or more and less than or equal to the number of dimensions of the target data, and t is a natural number of 1 or more and less than or equal to the number of dimensions of the target data.

 [19] Target data force Means to determine the data element set having the longest distance between data elements, find the first axis passing through the specified data element set, and the first axis V derived from the target data, At least one of the means for obtaining the s-axis using the (s-1) axis, the means for obtaining the t-axis component data using the t-axis for which the target data force is also obtained, and at least one of each axis component data Means for performing oblique coordinate transformation, means for performing reversible wavelet transformation on the axis component data subjected to the oblique coordinate transformation, and embedding secret data in the high frequency component of the axis component data, and after embedding the secret data Information including: means for inversely transforming the axis component data of the axis; means for inversely transforming the axis component data after the inverse wavelet transform; and means for reconstructing the target data for each axis component data force, Iding device. Here, s is a natural number greater than or equal to 2 and less than or equal to the number of dimensions of the target data, and t is a natural number greater than or equal to 1 and less than or equal to the number of dimensions of the target data.

[20] Target data force after removal Means for obtaining eigenvalues and eigenvectors, means for obtaining each principal component data by removing at least one principal component data from the target data using the unique values and eigenvectors, Means for performing oblique coordinate transformation on the principal component data of the image, means for performing reversible wavelet transformation on the one principal component data subjected to oblique light coordinate transformation, and embedding the secret data in the high frequency component, and embedding the secret data Information including means for performing wavelet inverse transformation on the subsequent data, means for performing oblique coordinate inverse transformation on one principal component data after wavelet inverse transformation, and means for performing principal component inverse transformation from each principal component data. Information hiding device.