JP4834844B2 - Information processing apparatus, information processing method, and program - Google Patents

Description

  The present invention relates to an information processing apparatus, an information processing method, and a program, and in particular, distinguishes malicious alteration from non-malicious changes such as compression and noise, accurately restores digital watermark information, and accurately alters the information. The present invention relates to an information processing apparatus, an information processing method, and a program that enable detection.

  In recent years, as various types of data such as character data, image data, and audio data are handled in computers and networks, copyright information and user information are used to prevent unauthorized use (falsification) of the data. Has been developed for embedding as digital watermark information.

  Since embedding digital watermark information changes data to be embedded, if the embedding strength is increased, the quality of content expressed by the data may be deteriorated. On the other hand, in order to accurately detect tampering, it is necessary to increase the tolerance of digital watermark information. Therefore, as a technique for enhancing resistance to attacks on digital watermark information without increasing the embedding strength, that is, without causing deterioration in content quality, conventionally, a plurality of predetermined coefficients among wavelet transformed coefficients are used. On the other hand, an invention is known in which a plurality of pixels constituting digital watermark information are embedded and each pixel value is determined by majority decision when digital watermark information is extracted (for example, Patent Document 1).

JP 2000-106624 A

  By the way, in the falsification detection, it is necessary to accurately restore the digital watermark information, and to detect and distinguish between malicious changes such as data editing, compression, expansion, noise, and the like, and falsification as a malicious attack. .

  Here, as the characteristic of the coefficient in the wavelet region of the image data, it can be cited that the deeper the level, the stronger the resistance to compression and noise. Further, since the amount of change of the coefficient is not so large for compression, noise, and the like, the damage of the embedded digital watermark information tends to be distributed, but the damage tends to be concentrated in the falsification.

  However, in the invention described in Patent Document 1, since the majority decision is uniformly performed without considering these features, the digital watermark information is damaged when strong compression or noise is applied to the image data. There has been a problem that the majority vote does not work and the digital watermark information cannot be restored, and malicious tampering cannot be detected.

  The present invention has been made in view of such circumstances, and distinguishes between malicious alterations and non-malicious changes such as compression / noise, accurately restores the digital watermark information, and accurately detects alterations. Is to be able to.

The information processing apparatus according to the first aspect of the present invention is an information processing apparatus that detects falsification of target information that has been subjected to wavelet transform and embedded with digital watermark information, conversion means that performs wavelet transform on the target information, and the digital watermark An embedding coefficient detecting means for detecting a plurality of embedding coefficients in which a plurality of identical pixels constituting information are respectively embedded; and the subbands to which the embedding coefficients belong to the plurality of embedding coefficients detected by the embedding coefficient detecting means. In the target information subjected to wavelet transform by the wavelet transform unit, the embedding coefficient value defeated by majority vote is set as a breakage coefficient based on the counting result obtained by weighting according to For each group of coefficients related across the band, the embedding A calculation means for calculating the number of coefficients and the number of breakage coefficients; and the number of embedding coefficients and the number of breakage coefficients calculated by the calculation means are set to the level of the subband to which the embedding coefficient and the breakage coefficient belong. It is determined whether or not the coefficient group has been tampered with based on a ratio of weighting means weighted accordingly, the number of the broken coefficients weighted by the weighting means, and the embedding coefficient weighted by the weighting means. Determining means for performing the operation, and operating means for operating the coefficient values of the coefficient group based on the determination result by the determining means .

  The information processing apparatus according to the first aspect may further include a determining unit that determines an embedding coefficient value that has won the majority decision as a pixel value constituting the digital watermark information based on a counting result by the counting unit.

  The operation means deletes the breakage coefficient included in the coefficient group when the ratio is equal to or less than a predetermined threshold, and if the ratio is larger than the predetermined threshold, the embedding included in the coefficient group The factor can be changed to a failure factor.

  The plurality of identical pixels constituting the digital watermark information is based on a second subband related coefficient associated with an embedding coefficient randomly determined in advance from a first subband coefficient in wavelet transformed target information. It can be modulated and embedded in the embedding coefficient.

  The first subband may be a subband other than the lowest band subband, and the second subband may be the lowest band subband.

  At the same time as performing wavelet transforms of a plurality of stages, whenever a wavelet transform of each stage is performed, a related coefficient of a second subband related to an embedding coefficient randomly determined in advance from a coefficient of the first subband is obtained. Can be detected.

  The first subband may be a subband other than the highest band subband, and the second subband may be the highest band subband.

  The information processing apparatus according to the first aspect further includes demodulation means for performing demodulation based on the related coefficient, and the counting means includes the embedding coefficient for each of the embedding coefficients demodulated by the demodulation means. Weighting can be performed according to the subband to which the subband belongs.

The first information processing method or program according to the present invention is an information processing method for detecting falsification of target information embedded with digital watermark information after wavelet conversion, or a target embedded with digital watermark information after wavelet conversion In a program for causing a computer to execute a process for detecting falsification of information, a transform step for performing wavelet transform on the target information, and an embedding coefficient for detecting a plurality of embedding coefficients each embedding a plurality of identical pixels constituting the digital watermark information A counting step for counting the plurality of embedding coefficients detected in the embedding coefficient detecting step by weighting according to a subband to which each embedding coefficient belongs, and a counting result by the counting step Based on the majority A calculation step of calculating the number of embedding coefficients and the number of breakage coefficients for each coefficient group related over subbands in the target information wavelet transformed by the transforming step as a lossy embedding coefficient value. The weighting step of weighting the number of embedding coefficients calculated by the calculating step and the number of breakage coefficients according to the level of the embedding coefficient and the subband to which the breakage coefficient belongs, and weighted by the weighting step Based on the ratio of the number of breakage coefficients and the embedding coefficient weighted in the weighting step, a determination step for determining whether or not the coefficient group has been tampered with, and a determination result by the determination step, And an operation step of operating coefficient values of the coefficient group .

In the information processing apparatus, the information processing method, or the program according to the first aspect as described above, the target information is subjected to wavelet transform, and a plurality of embedding coefficients in which a plurality of identical pixels constituting the digital watermark information are embedded respectively. The detected embedding coefficients are weighted and counted according to the subband to which each embedding coefficient belongs. Further, based on the count result, the embedding coefficient value lost to the majority decision is set as a breakage coefficient, and in the target information subjected to wavelet transform, the number of the embedding coefficients and the breakage coefficient for each related coefficient group over the subbands. A number is calculated, the calculated number of embedding coefficients and the number of break coefficients are weighted according to the level of the embedding coefficient and the subband to which the break coefficient belongs, and the number of weighted break coefficients, It is determined whether or not the coefficient group has been tampered with based on the ratio with the weighted embedding coefficient, and the coefficient value of the coefficient group is manipulated based on the determination result.

  According to the first aspect of the present invention, digital watermark information can be embedded or extracted efficiently and safely.

It is a block diagram which shows the structural example of the image processing apparatus to which this invention is applied. It is a figure explaining wavelet transformation. It is a flowchart explaining the digital watermark embedding process of the embedding part 13 of FIG. It is a figure explaining the process of step S4 of FIG. It is another figure explaining the process of step S4 of FIG. It is another figure explaining the process of step S4 of FIG. It is a figure explaining the process of step S5 of FIG. 3, and step S6. It is a block diagram which shows the structural example of the image processing apparatus 41 to which this invention is applied. It is a flowchart explaining the digital watermark extraction process of the falsification detection part 53 of FIG. It is a figure explaining the process of step S23 thru | or step S26 of FIG. It is a figure explaining the process of step S27 of FIG. 9, and step S28. It is a figure which shows the example of the image for a falsification detection. It is a figure which shows the failure rate according to a weight. It is a flowchart explaining the image process in the image process part 54 of FIG. It is a figure explaining the process of step S52 of FIG. It is another figure explaining the process of step S52 of FIG. It is a figure explaining the process of step S55 of FIG. It is a figure which shows the example of a target image. It is a figure which shows the example of a target image. It is a block diagram which shows the other structural example of the image processing apparatus 1 to which this invention is applied. 20 is a flowchart illustrating digital watermark embedding processing in the embedding unit 101 of FIG. It is a figure explaining the process of step S84 and step S85 of FIG. It is another figure which shows the failure rate according to a weight. It is a figure explaining the embedding method of a digital watermark image. It is another figure explaining the embedding method of a digital watermark image. It is another figure explaining the embedding method of a digital watermark image. It is a block diagram which shows the structural example of a computer.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 Image processing apparatus, 12 Wavelet transformation part, 13 Digital watermark embedding part, 14 Inverse wavelet transformation part, 52 Wavelet transformation part, 53 Tamper detection part, 101 Digital watermark embedding part

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  FIG. 1 shows a configuration example of an image processing apparatus 1 to which the present invention is applied. The image processing apparatus 1 can embed a digital watermark image W of a binary image as digital watermark information in a target image F (for example, an image captured by a digital camera) to be embedded. .

  The input unit 11 receives the target image F, the digital watermark image W, and the coefficient selection key C necessary for embedding the digital watermark image W. The coefficient selection key C indicates the number of embedded pixels (the number of copies) constituting the digital watermark image W, the coefficient of the target image F in which the digital watermark image W is embedded (hereinafter referred to as an embedded coefficient), and the embedding strength. Quantization parameters are included.

  The embedding coefficient is randomly determined in advance from the subbands HL1, HH1, LH1, HL2, HH2, LH2, HL3, HH3, or LH3 excluding the subband LL3. For example, in the example of FIG. 4, coefficient P1 and coefficient P2 from level 1 subband HL1 and subband LH1, coefficient P3 from level 2 subband HH2 and coefficient P4 from level 3 subband LH3 are embedded, respectively. Determined as a coefficient.

  The input unit 11 supplies the input target image F to the wavelet transform unit 12, and supplies the input digital watermark image W and coefficient selection key C to the digital watermark embedding unit 13.

  The wavelet transform unit 12 performs wavelet transform on the target image F supplied from the input unit 11, and supplies the frequency-converted coefficient of the target image F to the digital watermark embedding unit 13.

  In the wavelet transform unit 12, the two-dimensional level distribution of the image is frequency-transformed into data that can be weighted and is easily compressed.

  Specifically, the target image F is decomposed into a plurality of frequency bands by repeating the process of dividing the pixel data of the target image F into a high frequency component and a low frequency component.

  For example, when performing the process of dividing the high frequency component into the low frequency component in three stages, first, for example, the processing is performed on the pixel data of the target image F in FIG. Subband LL1 of "low range | low range", subband LH1 of "low range | high range", subband HL1 of "high range | low range", and "high range | high range" To subband HH1. The subbands LL1, LH1, HL1, or HH1 obtained by this processing are appropriately referred to as level 1 subbands.

  Next, the second processing is performed on the subband LL1 in the lowest band. As shown in FIG. 2C, the subband LL1 is subband LL2 of “low band | low band”, “low band | It is decomposed into a subband LH2 of “high frequency”, a subband HL2 of “high frequency | low frequency”, and a subband HH2 of “high frequency | high frequency”. The subbands LL2, LH2, HL2, or HH2 obtained by this processing are referred to as level 2 subbands as appropriate.

  Then, the third processing is performed on the subband LL2 in the lowest band, and the subband LL2 is subband LL3 in “low band | low band”, “low band | high band” as shown in D of FIG. The subband LH3 of “band”, the subband HL3 of “high band | low band”, and the subband HH3 of “high band | high band” are decomposed. The subbands LL3, LH3, HL3, or HH3 obtained by this processing are appropriately referred to as level 3 subbands.

  Returning to FIG. 1, the digital watermark embedding unit (hereinafter abbreviated as an embedding unit) 13 adds the digital watermark image W supplied from the input unit 11 to the coefficient of one frame of the target image F supplied from the wavelet transform unit 12. Are similarly embedded according to the coefficient selection key C supplied from the input unit 11, and the coefficient obtained as a result is supplied to the inverse wavelet transform unit 14. The embedding unit 13 also supplies the output unit 15 with a coefficient selection key C necessary for extracting the digital watermark image W.

  The inverse wavelet transform unit 14 performs inverse wavelet transform on the coefficients supplied from the embedding unit 13 (performs the reverse of the process shown in FIG. 2), and the target image F in which the digital watermark image W is embedded. (Target image F ′) is generated and supplied to the output unit 15.

  The output unit 15 supplies the target image F ′ supplied from the inverse wavelet transform unit 14 and the coefficient selection key C supplied from the embedding unit 13 to an external device (for example, the image processing device 41 in FIG. 8). .

  Next, the digital watermark embedding process in the embedding unit 13 of the image processing apparatus 1 will be described with reference to the flowchart of FIG.

  In step S1, the embedding unit 13 inputs the coefficient (D in FIG. 2) of the target image F for one frame from the wavelet transform unit 12.

  In step S <b> 2, the embedding unit 13 selects one pixel of the digital watermark image W supplied from the input unit 11.

  Next, in step S3, the embedding unit 13 copies the pixel value of the pixel of the digital watermark image W selected in step S2 (hereinafter referred to as a watermark bit) indicated by the coefficient selection key C supplied from the input unit 11. Duplicate the number.

  In step S4, the embedding unit 13 detects a coefficient (related coefficient) on the subband LL3 related to the embedding coefficient given by the coefficient selection key C.

  In the wavelet transform coefficient, the coefficient of the coordinate (x, y) on the subband of level r (r = 1, 2) and the coordinate (x / 2, y / 2) of the subband of level r + 1 The coefficient is known to have a close property (that is, high spatial correlation) (this relationship is hereinafter referred to as a parent-child relationship).

  Therefore, in the present invention, this parent-child relationship is used, and as shown in FIG. 5, the level 3 subband LL3 coordinates (x1 / 4, y1) are calculated from the embedding coefficients of the level 1 subband coordinates (x1, y1). / 4) from the embedding coefficients of the subband coordinates (x2, y2) of the level 2 sub-band, the coefficients of the subband LL3 coordinates (x2 / 2, y2 / 2) and the subband of the level 3 ( From the embedding coefficients of the coordinates (x3, y3) of the subband LL3), the coefficients of the coordinates (x3, y3) of the subband LL3 are respectively detected as the coefficients of the subband LL3 related to the embedding coefficients.

  This parent-child relationship can be represented in space as shown in FIG.

  In the example of FIG. 4, the coefficient P1 is the coefficient Q1, the coefficient P2 is the coefficient Q2, the coefficient P3 is the coefficient Q3, and the coefficient P4 is the coefficient Q4 as the coefficient of the associated subband LL3. Shall be detected.

  Next, in step S5, the embedding unit 13 detects, for example, three coefficients adjacent to the coefficient of the subband LL3 detected in step S4, and the three coefficients and step An average value of coefficient values of a total of four coefficients (hereinafter, these four coefficients are appropriately referred to as corresponding coefficients) with the coefficients of the subband LL3 detected in S4 is calculated, and quantized to be binary Convert to value (1 or 0).

  For the coefficient Q1 in FIG. 4 (for example, coordinates (xq1, yq1)), as shown in FIG. 7, the coordinates (xq1, yq1 + 1), (xq1 + 1, yq1) adjacent to the coefficient Q1 and (xq1 + 1, yq1 + 1) Three coefficients are detected, an average value of the coefficient Q1 and the coefficient value of the three coefficients is calculated, and quantized to obtain a binary value r1. For coefficient Q2 (for example, coordinates (xq2, yq2)), three coefficients of coordinates (xq2, yq2 + 1), (xq2 + 1, yq2), and (xq2 + 1, yq2 + 1) are detected, and coefficient Q2 and its three An average value of coefficient values is calculated and quantized to obtain a binary value r2.

  For the coefficient Q3 (for example, coordinates (xq3, yq3)), three coefficients of coordinates (xq3, yq3 + 1), (xq3 + 1, yq3), and (xq3 + 1, yq3 + 1) are detected. The average value of the coefficient values is calculated and quantized to obtain a binary value r3. For coefficient Q4 (for example, coordinates (xq4, yq4)), three coefficients of coordinates (xq4, yq4 + 1), (xq4 + 1, yq4), and (xq4 + 1, yq4 + 1) are detected, and coefficient Q4 and its three The average value of the coefficient values of the coefficients is calculated and quantized to obtain a binary value r4.

  Next, in step S6, the embedding unit 13 performs an exclusive OR operation (XOR) on each of the watermark bits copied in step S3 and each of the binary values of the average values obtained in step S5 (that is, The watermark bit is modulated with the binary value of the average value obtained in step S5), and the resulting value (hereinafter referred to as modulation bit) is the strength of the quantization step included in the coefficient selection key C. Embed according to.

  In the example of FIG. 7, the modulation bit wa1 obtained as a result of the exclusive OR operation (XOR) of the watermark bit wa and the value r1 is the coefficient value of the coefficient P1, and the result of the XOR of the watermark bit wa and the value r2 The obtained modulation bit wa2 is the coefficient value of the coefficient P2, the modulation bit wa3 obtained as a result of the XOR of the watermark bit wa and the value r3 is the coefficient value of the coefficient P3, and the XOR of the watermark bit wa and the value r4 The modulation bit wa4 obtained as a result of is used as the coefficient value of the coefficient P4.

  In step S7, the embedding unit 13 determines whether or not all the pixels of the digital watermark image W have been selected, and if it is determined that there are still pixels that have not been selected, the process returns to step S2 to return to the next pixel. Is selected, and the processing after step S3 is similarly executed.

  If it is determined in step S7 that all the pixels have been selected, the embedding unit 13 ends the digital watermark embedding process.

  The above processing is performed every time the target image F in which the digital watermark image W is embedded is input.

  As described above, since the embedding coefficient is randomly determined when embedding the digital watermark information (step S3), it becomes difficult to specify the embedding coefficient by a third party. For example, in the method of Patent Document 1, the coefficient in which the digital watermark information is embedded is limited to the coefficient whose absolute value is the nth largest, so that the coefficient in which the digital watermark information is embedded can be easily specified.

As described above, since the embedding process is performed on the embedding coefficient determined at random (steps S4 to S6), the embedding process can be performed efficiently.
For example, in the method of Patent Document 1, since it is necessary to scan all the coefficients in order to detect the n-th coefficient having an absolute value, the processing takes time.

  In the so-called Collage Attack, which manipulates the coefficient value based on the relationship between the digital watermark information and the coefficient in which the digital watermark information is embedded, the digital watermark information is disguised as if the digital watermark information is embedded. Since the coefficient value is manipulated based on the relevance of the coefficient in which the digital watermark information is embedded and tampering is performed, as a countermeasure, the coefficient in which the digital watermark information is embedded and It is effective to associate the coefficients with some relationship. For example, the coefficient in which the digital watermark information is embedded and the adjacent coefficient are checked, and if the coefficient in which the digital watermark information is embedded is larger, it is set to 0, and if the adjacent coefficient is larger, the value is embedded. It is a method to make it.

  Therefore, as described above, the value (modulation bit) to be embedded is determined by associating the embedding coefficient with the associated lowest band subband (in this case, subband LL3) (step S4 to step S4). S6), Collage Attack can be defended.

  Next, an image processing device 41 that extracts the digital watermark image W from the target image F (target image F ′) in which the digital watermark image W is embedded by the image processing device 1 of FIG. 1 will be described with reference to FIG. To do.

  The input unit 51 receives the target image F ′ and the coefficient selection key C for extracting digital watermark information output from the image processing apparatus 1 of FIG.

  The input unit 51 supplies the input target image F ′ to the wavelet transform unit 52 and supplies the input coefficient selection key C to the falsification detection unit 53 and the image processing unit 54.

  The wavelet transform unit 52 performs the same wavelet transform as the wavelet transform unit 12 shown in FIG. 1 on the target image F ′ supplied from the input unit 51 (FIG. 2), and the target for one frame obtained as a result thereof The coefficient of the image F ′ is supplied to the falsification detection unit 53 and the image processing unit 54.

  The falsification detection unit 53 extracts the digital watermark image W from the coefficient of the target image F ′ supplied from the wavelet transform unit 52 based on the coefficient selection key C, and the falsification information obtained at that time is subjected to image processing. Supplied to the unit 54.

  The image processing unit 54 applies coefficients to the coefficients of the target image F ′ supplied from the wavelet transform unit 52 according to the coefficient selection key C supplied from the input unit 51 and the falsification information supplied from the falsification detection unit 53. Perform the operation.

  Next, extraction processing of the digital watermark image and the falsification detection image in the falsification detection unit 53 will be described with reference to the flowchart of FIG.

  In step S <b> 21, the falsification detection unit 53 inputs the coefficient of the target image F ′ for one frame from the wavelet transform unit 52.

  Next, in step S <b> 22, the falsification detection unit 53 reads the coefficient selection key for one pixel of the digital watermark image W from the coefficient selection key C supplied from the input unit 51.

  In step S23, the falsification detection unit 53 embeds the embedding coefficient (the watermark bit of one pixel selected in step S22 from the coefficients for one frame input in step S21 based on the read coefficient selection key. Detection).

  For example, when the digital watermark image W is extracted from the target image F in which the digital watermark image W is embedded as shown in FIG. 7, as shown in FIG. 10, the coefficients of the level 1 subband HL1 are the same as in FIG. Coefficient P2 of P1 and subband LH1, coefficient P3 from level 2 subband HH2, and coefficient P4 from level 3 subband LH3 are detected as embedding coefficients, respectively.

  In step S24, the falsification detection unit 53 detects the coefficient of the subband LL3 related to the detected embedding coefficient based on the parent-child relationship of the wavelet transform.

  In the case of the example of FIG. 10, as in the case of FIG. 7, the subband LL3 associated with the coefficient P1 to the coefficient Q1, the coefficient P2 to the coefficient Q2, the coefficient P3 to the coefficient Q3, and the coefficient P4 to the coefficient Q4, respectively. It is detected as a coefficient.

  In step S25, the falsification detection unit 53 detects, for example, three coefficients adjacent to the coefficient for each of the coefficients of the subband LL3 detected in step S24, and the three coefficients and step S24. The average value of the coefficient values of a total of four coefficients (corresponding coefficients) with the coefficients of the subband LL3 detected in (5) is calculated, quantized, and converted into a binary value.

  In the case of the example of FIG. 10, as in the case of FIG. 7, the coordinates (xq1, yq1 + 1), (xq1 + 1, yq1), and (xq1 + 1, yq1 + 1) are applied to the coefficient Q1 (coordinates (xq1, yq1)). Three coefficients are detected, an average value of the coefficient Q1 and the coefficient value of the three coefficients is calculated, and quantized to obtain a binary value r1 ′. For coefficient Q2 (coordinates (xq2, yq2)), three coefficients of coordinates (xq2, yq2 + 1), (xq2 + 1, yq2), and (xq2 + 1, yq2 + 1) are detected, and coefficient Q2 and its three coefficients An average value of the coefficient values is calculated and quantized to obtain a binary value r2 '.

  Also, for the coefficient Q3 (coordinates (xq3, yq3)), three coefficients of coordinates (xq3, yq3 + 1), (xq3 + 1, yq3), and (xq3 + 1, yq3 + 1) are detected, and the coefficient Q3 and its three The average value of the coefficient values of the coefficients is calculated and quantized to obtain a binary value r3 ′. For coefficient Q4 (coordinates (xq4, yq4)), three coefficients of coordinates (xq4, yq4 + 1), (xq4 + 1, yq4), and (xq4 + 1, yq4 + 1) are detected, and coefficient Q4 and its three coefficients The average value of the coefficient values is calculated and quantized to obtain a binary value r4 '.

  In step S26, the falsification detection unit 53 calculates each of the embedding coefficient coefficient values (modulation bits (step S6 in FIG. 3)) detected in step S23 and the binary value of the average value obtained in the corresponding step S25. XOR with each other (that is, the modulation bit is demodulated with the binary value of the average value obtained in step S25), and the resulting value (hereinafter referred to as the demodulation bit) is selected in step S22 The pixel value (watermark bit) of the pixel of the digital watermark image W is a candidate.

  In the case of the example of FIG. 10, the demodulated bit wb1 obtained as a result of the XOR between the modulation bit wa1 'and the value r1', the demodulated bit wb2 obtained as the result of the XOR between the modulation bit wa2 'and the value r2', and the modulation bit wa3 The demodulated bit wb3 obtained as a result of XOR between 'and the value r3' and the demodulated bit wb4 obtained as a result of the XOR between the modulated bit wa4 'and the value r4' are set as watermark bit candidates.

  Next, in step S27, the falsification detection unit 53 counts the demodulated bits as the watermark bit candidates obtained in step S26 with weighting according to the level of the subband to which the demodulated bits belong, and determines the majority based on the result. Then, a winning demodulated bit (hereinafter referred to as a winning bit) and a losing demodulated bit (hereinafter referred to as a losing bit) are determined.

  For example, a weight for a demodulated bit of a subband belonging to level 1 is set to 1, a weight for a demodulated bit of a subband belonging to level 2 is set to 6, and a weight of a demodulated bit of a subband belonging to level 3 is set to 8. , The number of demodulated bits multiplied by the weight is prepared, among which many bits and few bits are detected.

  In the case of the example of FIG. 10, when the demodulated bits wb1, wb4, wb3, and wb2 are 0, 0, 0, and 1 as shown in FIG. 11, one value 0 as the demodulated bit wb1 of level 1 is one. 8 values 0 as level 3 demodulation bits wb4, 6 values 0 as level 2 demodulation bits wb3, and 1 value 1 as level 1 demodulation bits wb2, that is, 15 values 0 One value 1 is prepared.

  Therefore, in this example, since the value 0 is 15 and the value 1 is 1, the value 0 is detected as a winning bit and the value 1 is detected as a losing bit.

  Next, in step S28, the falsification detection unit 53 uses the winning bit (0) detected in step S27 as the pixel value of the pixel of the digital watermark image W selected in step S22 as shown in FIG. 1) is a coefficient value of a coefficient P2 ′ corresponding to a coefficient P2 of the target image F ′ of a white image (hereinafter referred to as a falsification detection image) M ′ that has been subjected to three stages of wavelet transform processing prepared in advance. To do.

  In step S29, the falsification detection unit 53 determines whether or not the coefficient selection key for all the pixels of the digital watermark image W has been read in step S22, and determines that there is a coefficient selection key that has not been read. Returning to step S22, the coefficient selection key for the next pixel is read out, and the processes in and after step S23 are performed.

  If it is determined in step S29 that the coefficient selection keys for all the pixels have been read, the process proceeds to step S30, where the digital watermark image W is restored, and an alteration detection image M ′ is generated. The falsification detection unit 53 supplies the falsification detection image M ′ to the image processing unit 54. Note that the falsification detection image M obtained by performing the inverse wavelet transform process on the falsification detection image M ′ is displayed as shown in FIG. 12, for example.

  The digital watermark information is extracted as described above.

  As a characteristic of the image wavelet transform coefficient, the deeper the level, the stronger the resistance to compression and noise, so that the digital watermark information embedded at the deep level is resistant to compression and noise. Therefore, if the digital watermark image W and the falsification detection image M ′ embedded at a deep level are broken, it can be considered that this is not due to compression or noise but due to falsification such as cutting and pasting processing.

  Accordingly, the watermark information embedded at a deep level as described above has a higher weight than the watermark information embedded at a shallow level (the weight for the demodulated bits of subbands belonging to level 1 is set to 1, The weight of the demodulated bit of the subband belonging to 2 is set to 6 and the weight of the demodulated bit of the subband belonging to level 3 is set to 8) so that the influence of the digital watermark information embedded in the deep level becomes large. Since the watermark bits are detected, the digital watermark information can be detected more accurately.

  FIG. 13 shows the case where the weight applied to the level 2 watermark shown on the X axis and the weight applied to the level 3 watermark shown on the Y axis when the target image F is compressed by JPEG compression with a compression rate of 60% are used. Shows the damage rate. In this example, when the level 2 weight is set to 6 and the level 3 weight is set to 8 to 10, the lowest digital watermark information damage rate can be obtained.

  Next, the processing of the image processing unit 54 of the image processing apparatus 41 will be described with reference to the flowchart of FIG.

  In step S51, the image processing unit 54 converts each of the level 3 subbands LH3 and HL3 in the coefficient of the target image F ′ for one frame supplied from the wavelet transform unit 52 into, for example, a 4 × 4 pixel block. To divide.

  Next, in step S52, the image processing unit 54, for each of the subband LH3 and subband HL3 blocks obtained in step S51, corresponds to the level 2 subband LH2 and subband HL2 and the level 1 subband LH3. The subband LH1 and the block of the subband HL1 are determined based on the parent-child relationship of the wavelet transform.

  For example, the level 3 subband LH3 or the block of the subband HL3 can be identified by a predetermined block number, and the level 2 subband LH2 and subband HL2 and the level 1 subband LH1 and subband corresponding to the block can be identified. The block of the band HL1 can also be identified by the same block number as the corresponding subband LH3 or the block of the subband HL3.

  That is, each block can be identified by, for example, a code bk (i) having a level k and a block number i, and a block group represented by the same code bk (i) is represented by a code Bk (i). It can be expressed as a block belonging to.

  For example, the block of level 3 subband LH3 and subband HL3 shown in FIG. 15 is block b3 (1), and the corresponding block of level 2 subband LH2 and subband HL2 is block b2 (1). The block of level 1 subband LH1 and subband HL1 is assumed to be block b1 (1), and as shown in FIG. 16, the block group represented by level 1 subband LH1 and block b1 (1) of HL1 Is a block group B1 (1), a block group represented by block b2 (1) of level 2 subbands LH2 and HL2 is block group B2 (1), and subbands LH3 and HL3 of level 3 A block group represented by the block b3 (1) is assumed to be a block group B3 (1).

  Next, in step S53, the image processing unit 54 selects one block number i, and in step S54, the block group B1 (i), B2 (i), B3 (i) is assigned based on the coefficient selection key C. For each block to which it belongs, the number of embedding coefficients included in it is calculated. Further, the image processing unit 54, based on the falsification detection image M ′, for each block belonging to the block group B1 (i), B2 (i), B3 (i), a coefficient in which the losing bit included therein is embedded. The number is calculated (hereinafter referred to as breakage coefficient).

  In step S55, the image processing unit 54 sums the number of embedding coefficients and the number of breakage coefficients for each block for each of the block groups B1 (i), B2 (i), and B3 (i). Multiply the weight according to.

  For example, as shown in FIG. 17, each of the total number of embedding coefficients included in the blocks belonging to the block group B3 (i) and the total number of breakage coefficients included in the blocks belonging to the block group B3 (i) 8 is multiplied.

  Each of the total number of embedding coefficients included in the blocks belonging to the block group B2 (i) and the total number of breakage coefficients included in the blocks belonging to the block group B2 (i) are multiplied by 6.

  Then, 1 is multiplied to each of the total number of embedding coefficients included in the blocks belonging to the block group B1 (i) and the total number of breakage coefficients included in the blocks belonging to the block B group 1 (i).

  In step S56, the image processing unit 54 divides the sum of the breakage coefficients obtained by the weighting in step S55 by the sum of the embedding coefficients obtained by the weighting in step S55, as shown in Expression (1). .

  Next, in step S57, the image processing unit 54 determines whether or not a value obtained as a result of the calculation in step S56 (hereinafter referred to as a tampering rate) is equal to or less than a predetermined threshold, and is equal to or less than the threshold. If it is determined that the block group with the block number i has not been tampered with, the coefficient value (loss bit) of the break coefficient included in the target block is deleted in step S58 (hereinafter, this process is performed). Called processing).

  On the other hand, if it is determined in step S57 that it is larger than the predetermined threshold value, the block group with the block number i is assumed to have been tampered with, and the process proceeds to step S59, where the image processing unit 54 breaks all the coefficients belonging to that block. The coefficient is changed (hereinafter, this processing is referred to as enhancement processing).

  One threshold may be provided as described above, or an upper threshold and a lower threshold are provided. If the threshold is lower than the lower threshold, a sieving process is performed. May perform an emphasis process. In this case, when the tampering rate is between the upper limit threshold and the lower limit threshold, the sieving process and the enhancement process are not performed.

  When the break coefficient is deleted in step S58 or when the coefficient of the block group having the block number i is changed in step S59, the process proceeds to step S60, and the image processing unit 54 selects all the block numbers i in step S53. If it is determined that there is a block number that has not yet been selected, the process returns to step S53, the next block is selected, and the processing from step S54 onward is similarly executed.

  If it is determined in step S60 that all block numbers i have been selected, the process ends.

  Image processing is performed as described above.

  As described above, since the sieving process and the enhancement process are performed based on the tampering rate, when the target image F is FIG. 18A, the image corresponding to the tampered block is enhanced as shown in FIG. 18B. Can be displayed.

  For compression and noise, the correction amount of the pixel coefficient is not so large, and the damage of the digital watermark information tends to be dispersed. However, if tampering such as cutting or pasting occurs, the image coefficient of the tampering is concentrated. Tend to be damaged. Therefore, as described above, the density (falsification rate) of the damaged digital watermark information is checked and compared with a threshold value, so that it is possible to appropriately determine whether the damage is due to compression or noise or due to falsification.

  FIG. 19 shows another configuration example of the image processing apparatus 1. In this image processing apparatus, a digital watermark embedding unit 101 is provided instead of the digital watermark embedding unit 13 of FIG. The other parts are the same as in FIG.

  The embedding process in the embedding unit 13 in FIG. 1 associates the embedding coefficient with the coefficient of the lowest band subband (subband LL3). However, the embedding unit 101 replaces the lowest band subband with the same embedding coefficient. The embedding process is performed in association with the coefficient of the level subband HH.

  The digital watermark embedding process in the embedding unit 101 will be described with reference to the flowchart of FIG.

  In step S81, the embedding unit 101 obtains a result obtained when the first wavelet transform is performed on the target image F of one frame from the wavelet transform unit 12, and the second wavelet transform is further performed. Enter a coefficient (C in FIG. 2).

  In step S82, the embedding unit 101 selects one pixel of the digital watermark image (binary image) W.

  In step S83, the embedding unit 101 duplicates the pixel value (watermark bit) of the pixel of the digital watermark image W selected in step S82 by the number of copies indicated by the coefficient selection key C supplied from the input unit 11. To do.

  Next, in step S84, the embedding unit 101 detects the coefficient of the level 2 subband HH2 related to the embedding coefficient of the level 2 subband HL2 and the subband LH2 given by the coefficient selection key C.

  For example, if the coefficient P11 (coordinates (xq11, yq11)) of the subband LH2 of level 2 in FIG. 21 is an embedding coefficient, the coefficient Q11 of the coordinates (xq11, yq11) of the subband HH2 is related to the coefficient P11. It is detected as a coefficient of the band HH2.

  Next, in step S85, the embedding unit 101 detects, for example, three coefficients adjacent to the coefficient of the subband HH2 detected in step S84, and the three coefficients and the coefficient in step S84. An average value of coefficient values of a total of four coefficients (corresponding coefficients) with the detected coefficient of the subband HH2 is calculated, quantized, and converted into a binary value (1 or 0).

  For the coefficient Q11 (coordinates (xq11, yq11)) in FIG. 21, three coefficients of coordinates (xq11, yq11 + 1), (xq11 + 1, yq11) adjacent to the coefficient Q11, and (xq11 + 1, yq11 + 1) are detected. An average value of the coefficient Q11 and the coefficient values of the three coefficients is calculated, and is quantized to obtain a binary value.

  Next, in step S86, the embedding unit 101 performs an exclusive OR operation (XOR) of the watermark bit copied in step S83 and the binary value of the average value obtained in step S85 (that is, the watermark bit is Modulation is performed with the binary value of the average value obtained in step S85), and the value (modulation bit) obtained as a result is embedded according to the strength of the quantization step included in the coefficient selection key C.

  In step S87, the embedding unit 101 determines whether or not all the pixels of the digital watermark image W have been selected. If it is determined that there are still pixels that have not been selected, the embedding unit 101 returns to step S82 and returns to the next pixel. Is selected, and the processing after step S83 is similarly executed.

  Since it is not necessary to embed all of the watermark bits in the level 2 subband, when a watermark bit that is not embedded in the level 2 subband is selected, the processing in steps S83 to S86 is skipped as appropriate.

  If it is determined in step S87 that all the pixels have been selected, the embedding unit 101 proceeds to step S88, determines whether or not all the coefficients for one frame of the target image F have been input, and inputs all. If it is determined that it is not, the process returns to step S81.

  In this case, in step S81, the embedding unit 101 uses the coefficient (D in FIG. 2) obtained when the wavelet transform unit 12 performs the third wavelet transform on the target image F of one frame. input. Processing when this coefficient is input will be described.

  That is, in step S82, one pixel of the digital watermark image W is selected.

  Next, in step S83, the pixel value (watermark bit) of the pixel of the digital watermark image W selected in step S82 is copied by the number of copies indicated by the coefficient selection key C supplied from the input unit 11.

  Next, in step S84, the level 3 subband HL3 and the level 3 subband HH3 coefficient associated with the embedding coefficient of the subband LH3 given by the coefficient selection key C are detected.

  For example, when the coefficient P21 (coordinates (xq21, yq21)) of the subband HL3 of level 3 in FIG. 21 is an embedding coefficient, the coefficient Q21 of the coordinates (xq21, yq21) of the subband HH3 is detected.

  Next, in step S85, for example, three coefficients adjacent to the coefficient of the subband HH3 detected in step S84 are detected, and these three coefficients and the coefficient detected in step S84 are detected. An average value of coefficient values of a total of four coefficients (corresponding coefficients) with the coefficients of the subband HH3 is calculated, and is quantized and converted into a binary value (1 or 0).

  For the coefficient Q21 (coordinates (xq21, yq21)) in FIG. 21, three coefficients of coordinates (xq21, yq21 + 1), (xq21 + 1, yq21) and (xq21 + 1, yq21 + 1) adjacent to the coefficient Q21 are detected. An average value of the coefficient Q21 and the coefficient values of the three coefficients is calculated, and is quantized to obtain a binary value.

  Next, in step S86, an exclusive OR operation (XOR) of the watermark bit copied in step S83 and the binary value of the average value obtained in step S85 is performed (that is, the watermark bit is changed in step S85). The obtained average value is modulated with a binary value), and the resulting value (modulation bit) is embedded according to the strength of the quantization step included in the coefficient selection key C.

  In step S87, it is determined whether or not all the pixels of the digital watermark image W have been selected. If it is determined that there are still pixels that have not been selected, the process returns to step S82 to select the next pixel. The processes after step S83 are similarly executed.

  Since it is not necessary to embed all of the watermark bits in the level 3 subband, when a watermark bit that is not embedded in the level 3 subband is selected, the processing in steps S83 to S86 is skipped as appropriate.

  If it is determined in step S87 that all the pixels have been selected, the process proceeds to step S88, where it is determined that all the coefficients for one frame of the target image F have been input, and the process ends.

  In the embedding unit 13 in FIG. 1, the embedding processing is performed so as to associate the embedding coefficient with the lowest band subband (in this example, subband LL3) associated therewith. Further, as shown in FIG. 2D, the lowest band subband is formed after the wavelet transform process of all stages is performed.

  That is, the embedding process in the embedding unit 13 in FIG. 1 has to be performed after the wavelet process in the wavelet transform unit 12 is completed.

  On the other hand, the embedding unit 101 in FIG. 19 associates the coefficient of the subband HH at the same level as the embedding coefficient in place of the subband of the lowest band, and as described above, the wavelet coefficient of each level Since the embedding process is performed when obtained (because the wavelet transform process and the embedding process are performed in parallel), the embedding process can be performed more quickly than the embedding process in the case of FIG.

  Note that the subband HH used here is the weakest band against tampering, and causes an increase in the damage rate. For example, even if the embedding coefficient of the subband HL or LH is not broken, if the coefficient of the subband HH associated with the subband HL or the LH is significantly changed, the subband HL or the LH is broken. Therefore, in this case, level 1 which is vulnerable to attack is not used for embedding, and level 2 and level 3 are embedded.

  The operation of the image processing apparatus 41 when extracting the digital watermark image W from the target image F (target image F ′) in which the digital watermark image W is embedded by the image processing apparatus 1 of FIG. 19 is shown in FIGS. Since it is as shown, its description is omitted.

  FIG. 22 shows a case where the target image F has a compression rate of 60% when the digital watermark image W is extracted from the target image F (target image F ′) embedded with the digital watermark image W by the image processing apparatus 1 of FIG. This shows the damage rate when using the weight applied to the level 2 watermark shown on the X axis and the weight applied to the level 3 watermark shown on the Y axis when compressed by JPEG compression. In this example, when the level 2 weight is 1, the level 3 weight is 5, or the level 2 weight is 2, and the level 3 weight is 9 or 10, the lowest failure rate is obtained.

  In the above, embedding of the digital watermark image W into the target image F is performed by, for example, quantizing the modulation bit obtained as a result of the exclusive OR (XOR) of the average value of the corresponding coefficient of the subband LL3 and the watermark bit. Although embedding is performed according to the strength of the activation parameter (steps S4 to S6 in FIG. 3), the embedding can be performed as described below.

Here, it is assumed that a target image F obtained by wavelet transform is expressed by Expression (2). In Expression (2), k is expressed by Expression (3), l is a level, and (m, n) indicates the position (coordinates) of the pixel.

The digital watermark image W is embedded by, for example, mapping f _{l, k} (m, n) (formula (2)) with a binary value using the quantization function Q defined by formula (4). The embedding described here is performed so that _{fl, k} (m, n) after embedding becomes the median value of the section represented by the equation (5).

In Expression (4), Δ is a quantization parameter. The i-th pixel of the digital watermark image W is expressed by Expression (6).

For example, for the quantization function Q (equation (4)), when equation (7) holds, f _{l, k} (m, n) satisfying equation (5) is at the center of the section using the following rule: Be changed.

Specifically, when Expression (8) is established, f _{l, k} (m, n) is obtained by Expression (9).

FIG. 23 schematically shows the change of _{fl, k} (m, n) based on this rule.

Further, when Expression (10) is established, _{fl, k} (m, n) is obtained by Expression (11).

For the quantization function Q (equation (4)), when equation (12) is established, f _{l, k} (m, n) is expressed by the following rule so that equation (13) is established. Be changed.

Specifically, when Expression (14) is established, f _{l, k} (m, n) is obtained by Expression (15).

When the equation (16) is established, f _{l, k} (m, n) is obtained by the equation (17).

In the case under this rule, f _l, the change of _k (m, n), as shown in FIGS. 24A and 24B is represented schematically when a _{f l, k (m, n} )> 0 . Note that FIG. 24A is a case where equation (18) is satisfied, and FIG. 24B is a case where equation (19) is satisfied.

In this way, the digital watermark image W is embedded in the target image F so that fl _{l, k} (m, n) (equation (2)) after embedding becomes the median value of the section represented by equation (5). By doing so, it is possible to reduce the influence on the image quality of the target image F by embedding the digital watermark image W, and to be strong against attacks such as compression.

  The series of processes described above can be executed by hardware or can be executed by software. When a series of processing is executed by software, a program constituting the software executes various functions by installing a computer incorporated in dedicated hardware or various programs. For example, it is installed from a program recording medium in a general-purpose personal computer or the like.

  FIG. 23 is a block diagram showing an example of the configuration of a personal computer that executes the above-described series of processing by a program. A CPU (Central Processing Unit) 201 executes various processes according to a program stored in a ROM (Read Only Memory) 202 or a storage unit 208. A RAM (Random Access Memory) 203 appropriately stores programs executed by the CPU 201 and data. The CPU 201, ROM 202, and RAM 203 are connected to each other via a bus 204.

  As shown in FIG. 23, a program recording medium that stores a program that is installed in a computer and can be executed by the computer includes a magnetic disk (including a flexible disk), an optical disk (CD-ROM (Compact Disc-Read Only). Memory, DVD (Digital Versatile Disc), a magneto-optical disk, a removable medium 211 that is a package medium composed of a semiconductor memory, or the like, a ROM 202 in which a program is temporarily or permanently stored, or a storage unit 208 It is comprised by the hard disk etc. which comprise The program is stored in the program recording medium using a wired or wireless communication medium such as a local area network, the Internet, or digital satellite broadcasting via a communication unit 209 that is an interface such as a router or a modem as necessary. Done.

  In the present specification, the step of describing the program stored in the program recording medium is not limited to the processing performed in time series in the described order, but is not necessarily performed in time series. Or the process performed separately is also included.

  Further, the image processing apparatus 1 and the image processing apparatus 41 may be integrally configured by, for example, a personal computer, the image processing apparatus 1 is mounted on a digital camera, and the image processing apparatus 41 is mounted on a personal computer. Etc. may be configured separately. In particular, when the image processing apparatus 1 is mounted on a digital camera, it is required to speed up the process of embedding digital watermark information. From this point of view, the wavelet is simply embedded without embedding a plurality of identical pixels in the digital watermark image. Conversion and digital watermark information embedding may be processed in parallel.

Claims (10)

In an information processing apparatus that detects falsification of target information that has been wavelet transformed and embedded with digital watermark information,
A transforming means for wavelet transforming the target information;
An embedding coefficient detecting means for detecting a plurality of embedding coefficients in which a plurality of the same pixels constituting the digital watermark information are respectively embedded;
Counting means for weighting and counting the plurality of embedding coefficients detected by the embedding coefficient detecting means according to the level of the subband to which each embedding coefficient belongs ,
Based on the counting result by the counting means, the embedding coefficient value lost to the majority vote is a broken coefficient, and in the target information wavelet transformed by the wavelet transforming means, the embedding coefficient value Calculating means for calculating the number and the number of breakage coefficients;
Weighting means for weighting the number of the embedding coefficients calculated by the calculating means and the number of the breakage coefficients according to the level of the embedding coefficient and the subband to which the breakage coefficient belongs;
Determining means for determining whether or not the coefficient group has been tampered with based on a ratio between the number of the broken coefficients weighted by the weighting means and the embedding coefficient weighted by the weighting means;
An information processing apparatus comprising: an operation unit that operates a coefficient value of the coefficient group based on a determination result by the determination unit. The information processing apparatus according to claim 1, further comprising: a determination unit that determines an embedding coefficient value that has won the majority decision as a pixel value constituting the digital watermark information based on a counting result by the counting unit. The operation means includes
When the ratio is less than or equal to a predetermined threshold, the break coefficient included in the coefficient group is deleted, and when the ratio is greater than the predetermined threshold, the embedding coefficient included in the coefficient group is set as a break coefficient. The information processing apparatus according to claim 1 or 2 . The plurality of identical pixels constituting the digital watermark information is based on a second subband related coefficient associated with an embedding coefficient randomly determined in advance from a first subband coefficient in wavelet transformed target information. The information processing apparatus according to any one of claims 1 to 3 , wherein the information processing apparatus is modulated and embedded in the embedding coefficient. The first subband is a subband other than the lowest band.
The information processing apparatus according to claim 4 , wherein the second subband is the lowest band subband. At the same time performing multi-stage wavelet transform,
5. The information processing apparatus according to claim 4 , wherein each time wavelet transform is performed, an associated coefficient of the second subband associated with an embedding coefficient that is randomly determined in advance from the coefficient of the first subband is detected. . The first subband is a subband other than the highest frequency subband;
The information processing apparatus according to claim 6 , wherein the second subband is the highest frequency subband. Further comprising demodulation means for performing demodulation based on the related coefficient,
Said counting means, for the embedding coefficient demodulated by the demodulating means, as claimed in any one of claims 4 to 7, each of the embedding coefficient counted by weighting in accordance with the sub-band belonging Information processing device. In an information processing method for detecting falsification of target information embedded with digital watermark information by wavelet transformation,
A transforming step for wavelet transforming the target information;
An embedding coefficient detection step for detecting a plurality of embedding coefficients in which a plurality of identical pixels constituting the digital watermark information are embedded;
A counting step of weighting and counting the plurality of embedding coefficients detected in the embedding coefficient detecting step according to the level of the subband to which each embedding coefficient belongs ,
Based on the counting result of the counting step, the embedding coefficient value lost to the majority is a broken coefficient, and in the target information wavelet transformed by the converting step, the number of embedding coefficients for each related coefficient group over subbands And a calculating step for calculating the number of breakage coefficients,
A weighting step of weighting the number of embedding coefficients and the number of breakage coefficients calculated by the calculating step according to the level of the embedding coefficient and the subband to which the breakage coefficient belongs;
A determination step of determining whether or not the coefficient group has been tampered with based on a ratio between the number of the broken coefficients weighted by the weighting step and the embedding coefficient weighted by the weighting step;
And an operation step of operating a coefficient value of the coefficient group based on a determination result of the determination step . In a program for causing a computer to execute processing for detecting falsification of target information that has been wavelet transformed and embedded with digital watermark information,
A transforming step for wavelet transforming the target information;
An embedding coefficient detection step for detecting a plurality of embedding coefficients in which a plurality of identical pixels constituting the digital watermark information are embedded;
A counting step of weighting and counting the plurality of embedding coefficients detected in the embedding coefficient detecting step according to the level of the subband to which each embedding coefficient belongs ;
Based on the counting result of the counting step, the embedding coefficient value lost to the majority vote is a broken coefficient, and in the target information wavelet transformed by the converting step, the number of embedding coefficients for each related coefficient group over subbands And a calculating step for calculating the number of breakage coefficients,
A weighting step of weighting the number of embedding coefficients and the number of breakage coefficients calculated by the calculating step according to the level of the embedding coefficient and the subband to which the breakage coefficient belongs;
A determination step of determining whether or not the coefficient group has been tampered with based on a ratio between the number of the broken coefficients weighted by the weighting step and the embedding coefficient weighted by the weighting step;
A program for causing a computer to execute a process including an operation step of operating a coefficient value of the coefficient group based on a determination result of the determination step .

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