Method for achieving digital watermarking of an image and associated detecting method

Abstract

The present invention relates to a method (10) for achieving digital watermarking of an image Im with at least one watermark WMi and to an associated method (20) for detecting one or more watermarks WMi in a watermarked image WMlm. Potentially, the watermarked image WMlm may have been modified by intentional or unintentional transformations, or for example as a result of its transmission via a communication channel (1020) following implementation of the watermarking method (10) and before implementation of the associated detecting method (20). The present invention is comparable to watermarking encrypted with a private key. It is resistant to modification of the brightness of the pixels of the watermarked image WMlm and / or introduction of noise into the watermarked image WMlm and / or filtering of the watermarked image WMlm.

Description

[0001] “Method for digitally watermarking an image and associated detection method”

[0002] TECHNICAL FIELD OF THE INVENTION

[0003] The present invention relates to a method for digitally watermarking an image and the associated method for detecting the watermark in the watermarked image. It is particularly applicable in the field of computer security for the authentication or identification of an image or a document in image form, and / or protection against unauthorized copies of an image or a document in image form, and for the authentication or identification of the author, owner or authorized user of the image or document in image form.

[0004] STATE OF THE ART

[0005] Digital watermarking consists of introducing, into a digital document in the form of an image, certain information, data or particular marks, which can be grouped under the name "watermark".

[0006] The introduced watermark can be visible or invisible, or take any intermediate level of visibility or invisibility.

[0007] In every watermarking system, there are two steps: introducing the watermark into the content to be protected and detecting whether or not the watermark is present in the content. Beyond simple detection, this can involve extracting the watermark from a given content.

[0008] Depending on the intended use and objectives, there are several types of watermarking (see P. Miloslav, Z. Banjac, et al. “Overview and classification of digital watermarking algorithms”, International Scientific Conference on Information Technology and Data Related Research - Sinteza 2019, pp. 537-545. Belgrade, Serbia, 2019): a. blind watermarking, in which the watermark can be extracted from the image without the presence of the original document; b. non-blind watermarking, in which the original document is compared with the document to be analyzed and the watermark is extracted. In this case, the presence of the original document is necessary; and c. zero-bit watermarking, which allows checking whether a given (known) watermark exists in a document or not. Accessibility to the original document is not necessary.

[0009] The watermark or information can be directly inserted into the image. In this case, we have a "public" system. Alternatively, it is also possible to encrypt the watermark or information with an encryption algorithm based on a private key. This is a "private" tattoo that can only be detected or extracted by someone who knows the key.

[0010] Watermarking can be robust, fragile, or semi-fragile. Robust watermarking is resistant, to some extent, to image transformations—compression, resizing, cropping part of the image, adding noise, or filtering. This type of watermarking is used for copy protection and image modifications. Fragile watermarking is destroyed if the image is modified. It is also used to authenticate the originality of the content. Semi-fragile watermarking allows certain image processing, but disappears for certain types of image modifications—for example, adding noise or compression.

[0011] Watermarking information can be added directly to the image. In this case, we are dealing with spatial domain processing (see Frank Y. Shih, "Digital Watermarking and Steganography - Fundamentals and Techniques", CRC Press, Taylor & Francis Group LLC, pp. 35-38, 2017). A typical example includes the perceptible or imperceptible change in the intensity or color of certain pixels or areas of the image. The watermark can be concentrated in a particular area of ​​the image. Another approach is to use an image transformation (Fourier transform, wavelet transform, discrete cosine transform or DCT (for "Discrete Cosine Transform" according to English terminology) or any type of transformation into orthogonal functions) and to introduce the watermark into the coefficients of the chosen transformation. In this case, it is a watermark in the frequency domain (Cf. IJ Cox, J. Kilian, FT Leighton and T.Shamoon, “Secure spread spectrum watermarking for multimedia,” in IEEE Transactions on Image Processing, vol. 6, no. 12, pp. 1673-1687, Dec. 1997).

[0012] A mixed spatial-frequency approach is also possible. Watermarking in the frequency domain is more complicated to perform, but it is more robust to image transformations compared to spatial watermarking.

[0013] The present invention aims to provide a tattooing method and its associated detection method which offer an advantageous alternative to existing methods.

[0014] The present invention aims more particularly to provide a watermarking method which is preferably: a. invisible, and / or b. of the zero-bit type, and / or c. in the frequency domain, and / or d. intended to protect and identify digital content, and / or e. encrypted with a private key, and / or f. resistant to certain transformations of the image, such as, for example, at least one, preferably each, of the transformations chosen from compression, addition of noise and filtering.

[0015] Another object of the present invention is to propose a watermarking method and its associated detection method which make it possible to integrate and detect in the image several watermarks, potentially simultaneously, each watermark being where appropriate intended for a specific use, in particular so as to broaden the possibilities of applications of the watermarking.

[0016] SUMMARY OF THE INVENTION

[0017] Before introducing the present invention, let us note the following writing conventions: a. matrices or vectors (one-dimensional matrix) are represented by bold symbols, for example Im; b. Im(i, j) represents the element of the matrix (integer or real number) with indices i and j; c. indices are represented by lowercase letters (i, j, k, I ...) and start at 1; d. the size of a matrix is ​​represented by uppercase letters; according to the example considered the size of the matrix Im of N rows and M columns is N x M.

[0018] Furthermore, regarding the representation of images, note that: a. a black and white image is represented by a two-dimensional matrix Im; b. the dimensions of the image Im are: N (number of rows) and M (number of columns); c. the element lm(1, 1) of the image Im is located at the top left of the image; d. the element lm(N, M) of the image Im is located at the bottom right of the image; e. each element lm(i, j) of the image Im, which is an integer or real number, is also called a pixel; f. a color image Im is represented by 3 2-dimensional matrices ImR, ImG, ImB. Each matrix corresponds to a color - Red (R), Green (G) and Blue (B). The same image Im can also be represented by 3 2-dimensional matrices ImY, ImCb and ImCr (also called luminance-chrominance representation YCbCr). The transition between RGB and YCbCr representation is carried out according to standardized and well-known transformations (see REC 709 or CIE RGB 1931 standards).

[0019] To achieve at least one of the objectives set, according to a first aspect of the invention, a method for digitally watermarking an image Im with a watermark is provided, the method implemented by a dedicated computing system or a computer comprising the following steps: a. providing the image Im to be watermarked, the image Im having a size NxM, b. applying, to the image Im, a frequency transformation FT to obtain a matrix FT_lm of elements FT_lm (i,j) and of the same size as the image Im provided, c. providing a user code Wi, d. implementing a (pseudo)random number generator based on a deterministic algorithm by initializing it with the user code Wi, so as to generate a sequence of (pseudo)random numbers AWMi(j) with j = 1, Li, where the size Li of the sequence is strictly less than the size NxM of the image Im, e.from the sequence of (pseudo)random numbers AWMi(j), generate the watermark WMi to be watermarked on the image Im, the watermark WMi having the size Li of the sequence of (pseudo)random numbers AWMi(j), f. integrate the watermark WMi in the matrix FT_lm: i. by defining, in the matrix FT_lm, an integration zone EA of elements EA(ij) and of size PxQ smaller than the size NxM of the matrix FT_lm and from a determined element FT_lm(ni, mi) of the matrix FT_lm such that (P-mi+1) < M and (Q-ni+1) < N, then ii. by converting the integration zone EA into a vector LV of length K equal to or smaller than the size PxQ of the integration zone EA, the conversion consisting of:.

[0020] 1. assign, to a first element LV(1)= EA(1,1) of the vector LV, the value of the element FT_lm(ni, mi) determined from the matrix FT_lm, then

[0021] 2. assigning respectively, to each of the following elements of the vector LV, the value of each of the elements FT_lm(i,j) following the determined element FT_lm(ni, mi) of the matrix FT_lm by traversing the integration zone EA according to a so-called predetermined extraction scheme, iii. by combining, with the watermark WMi, a part of the vector LV which is between a starting element LV(kStart) and an arrival element LV(kEnd), with kStart>1, kEnd <k-1 , kend-kstart="Li-1" et avec k>Li+2(kStart-1), so as to generate a WMV vector of size K composed of the first kStart-1 elements of the vector LV, of elements WMV(kStart) to WMV(kEnd) resulting from the combination of the elements of LV(kStart) to LV(kEnd) with the elements of WMi(1) to WMi(Li) of the watermark WMi and of the last K- kEnd elements of the vector LV, then iv. by introducing the vector WMV into the matrix FT_lm in place of the integration zone EA, by traversing the integration zone EA according to a so-called insertion scheme identical to said predetermined extraction scheme, to generate a matrix FT_WMIm which represents, in the frequency domain, the image Im combined with the watermark WMi, and g. applying, to the matrix FT_WMIm, an inverse transformation IT to the frequency transformation FT, to obtain a watermarked image WMlm.

[0022] A second aspect of the invention relates to a method for detecting at least one WMi watermark in a WMlm image, the method being implemented by a dedicated computing system or a computer storing, in association with each WMi watermark to be detected, a (pseudo)random number generator based on a deterministic algorithm, a so-called predetermined extraction scheme and identification data for each WMi watermark to be detected, the latter comprising, or even consisting of, a user code Wi, a size Li of the WMi watermark and coordinates (ni, mi) of an element WMIm(ni, mi) of the WMlm image from which the WMi watermark is to be searched, the method comprising the following steps: a. provide the WMlm image in which the WMi watermark is to be detected, the WMlm image having a size NxM strictly greater than the size Li of the WMi watermark to be detected, preferably a size NxM greater than 2 times the size Li of the WMi watermark to be detected, b.apply, to the image WMlm, a frequency transformation FT to obtain the matrix FT_WMIm of elements FT_WMIm(i,j) and of the same size as the provided image WMlm, c. depending on the size Li of the watermark WMi and the user code Wi, implement the (pseudo)random number generator by initializing it with the user code Wi, to generate a sequence of (pseudo)random numbers AWMi(j) having the size Li, d. from the sequence of (pseudo)random numbers AWMi(j), generate the watermark WMi, the latter having the size Li of the sequence of (pseudo)random numbers AWMi(j), e.from the size Li of the watermark WMi, the coordinates (ni, mi) of the element WMIm(ni, mi) of the image WMlm from which the watermark WMi is to be searched and the predetermined extraction scheme, extracting, from the matrix FT_WMIm, a vector LVm of length K=P*Q strictly greater than the size Li of the watermark WMi and strictly less than the size NxM of the image WMlm, the extraction consisting of: i. assigning, to a first element LVm(1) of the vector LVm, the value of the element FT_WMIm(ni, mi) of the matrix FT_WMIm, then ii. assigning respectively, to each of the following elements of the vector LVm, the value of each of the elements FT_WMIm(i, j) following the determined element FT_WMIm(ni, mi) of the matrix FT_WMIm by partially scanning it according to the so-called predetermined extraction scheme, then f.based on the generated WMi watermark and a portion of the extracted LVm vector that is comprised between a starting element LVm(kStart) and an ending element LVm(kEnd), where kEnd-kStart=Li -1 and K>Li+2(kStart-1), calculating the values ​​Cxy(k) of a cross-correlation function Cxy between the generated WMi watermark and the extracted LVm vector, for a plurality of values ​​k of the starting index kStart comprised between 1 and K-Li+1, and g. verifying that the calculated Cxy(k) values ​​of the cross-correlation function Cxy comprise a maximum value that is representative of an effective correlation between the generated WMi watermark and the extracted LVm vector, h. so as to detect, in the event of a positive verification, the WMi watermark in the WMlm image.A third aspect of the invention relates to a method for authenticating and / or identifying an Im image and / or the author, owner or authorized user of an Im image implementing the digital tattooing method according to the first aspect of the invention and the detection method according to the second aspect of the invention.

[0023] A fourth aspect of the invention relates to a computer program product comprising instructions which, when implemented by a dedicated computing system or a computer, executes the steps of at least one of the digital watermarking method according to the first aspect of the invention and the detection method according to the second aspect of the invention.

[0024] BRIEF DESCRIPTION OF THE FIGURES

[0025] The aims, objects, as well as the characteristics and advantages of the invention will emerge more clearly from the detailed description of an embodiment thereof which is illustrated by the following accompanying drawings in which:

[0026] Figure 1 schematically represents an overview of the method for digitally watermarking an image Im according to an embodiment of the first aspect of the invention and of the method for detecting a watermark WMi in an image WMlm according to an embodiment of the second aspect of the invention, and illustrates in particular the possibility offered by these methods of watermarking and detecting, respectively, a plurality of watermarks on the same image Im.

[0027] Figure 2 schematically represents the steps of generating a WMi watermark according to an embodiment of each of the first and second aspects of the invention.

[0028] Figure 3A schematically represents an embodiment of the application of a frequency transform FT to an image Im to be watermarked to obtain a representation FT_lm of the image Im in the frequency space.

[0029] Figure 3B schematically represents an embodiment of a conversion, into an LV vector, of an integration area EA of a watermark generated in the manner illustrated in Figure 2 in an image in order to combine the LV vector with the WMi watermark.

[0030] Figure 4A schematically represents an embodiment of a combination of the vector LV resulting from the conversion illustrated in Figure 3B with the watermark WMi generated in the manner illustrated in Figure 2 and an integration of the watermark WMi in the integration area EA illustrated in Figure 3B.

[0031] Figure 4B schematically represents an embodiment of an application of an inverse frequency transform IT to the representation FT_WMIm of the image in the frequency space following the integration illustrated in Figure 4A.

[0032] Figure 5 schematically represents an example of an FT_WMIm representation of the image in frequency space following the integration of a plurality of watermarks, each watermark having been integrated in the manner illustrated in Figure 4A.

[0033] Figure 6A schematically represents an embodiment of the application of a frequency transform FT to a WMlm image in which the watermark is to be detected, to obtain a representation FT_WMIm of the WMlm image in the frequency space.

[0034] Figure 6B schematically represents an embodiment of an extraction, from the FT_WMIm representation of the WMlm image in the frequency space illustrated in Figure 6A, of an LVm vector and of correlation calculations between the extracted LVm vector and different parts of the LVm vector.

[0035] Figure 7 is a graph illustrating an example of representation in the frequency space of a watermark WMi to be tattooed on an image Im by implementing an embodiment of the digital tattooing method according to the first aspect of the invention and / or to be detected in a WMlm image by implementing an embodiment of the detection method according to the second aspect of the invention.

[0036] Figure 8 illustrates an example of an image Im to be tattooed by implementing an embodiment of the digital tattooing method according to the first aspect of the invention.

[0037] Figure 9A illustrates a frequency space representation of the image Im shown in Figure 8. In this case, a discrete cosine transform (DCT) is used.

[0038] Figure 9B illustrates a representation in the frequency space of the image Im illustrated in Figure 8 once this image Im has been watermarked by implementing an embodiment of the watermarking method according to the first aspect of the invention with the watermark WMi illustrated in Figure 7, with a weighting coefficient a equal to 0.1.

[0039] Figure 10A illustrates a representation in frequency space of the image Im illustrated in Figure 8; it is therefore identical to Figure 9A.

[0040] Figure 10B illustrates a representation in the frequency space of the image Im illustrated in Figure 8 once this image Im has been watermarked by implementing an embodiment of the watermarking method according to the first aspect of the invention with the watermark WMi illustrated in Figure 7, with a weighting coefficient a equal to 2.0.

[0041] Figure 11 A illustrates the watermarked image WMlm obtained by inverse frequency transformation IT of the representation illustrated in Figure 9B.

[0042] Figure 11 B illustrates the watermarked image WMlm obtained by inverse frequency transformation IT of the representation illustrated in Figure 10B.

[0043] Figure 12A illustrates the difference between the watermarked image WMlm shown in Figure 11A and the image Im shown in Figure 8. This is in fact the watermark introduced into the image in the case where a = 0.1; for this value of a, the watermark is invisible or almost invisible.

[0044] Figure 12B illustrates the difference between the watermarked image WMlm shown in Figure 11B and the image Im shown in Figure 8. This is in fact the watermark introduced into the image in the case where a = 2.0; for this value of a, the watermark is visible.

[0045] Figure 13A graphically illustrates the cross-correlation function Cxy whose values ​​Cxy(k) are calculated by implementing an embodiment of the detection method according to the second aspect of the invention, the presence of a maximum value of the cross-correlation function Cxy for a value kStart of the parameter k being interpreted as representative of the detection of the watermark WMi illustrated in Figure 7 in the image WMlm illustrated in Figure 11A.

[0046] Figure 13B graphically illustrates the cross-correlation function Cxy whose values ​​Cxy(k) are calculated by implementing an embodiment of the detection method according to the second aspect of the invention, the presence of a maximum value of the cross-correlation function Cxy for a value kStart of the parameter k being interpreted as representative of the detection of the watermark WMi illustrated in Figure 7 in the image WMlm illustrated in Figure 11B.

[0047] The drawings are given by way of example and are not limiting of the invention. They constitute schematic representations of principle intended to facilitate the understanding of the invention and are not necessarily to the scale of practical applications. DETAILED DESCRIPTION OF THE INVENTION

[0048] Before commencing a detailed review of embodiments of the invention, optional features which may optionally be used in combination or alternatively are set out below:

[0049] According to an example of the first and second aspects of the invention, the frequency transform FT is chosen from: a Fourier transform, a discrete cosine transform (DCT), a wavelet transform and a transformation into orthogonal functions.

[0050] According to another example of the first and second aspects of the invention, the (pseudo)random number generator is configured to generate (pseudo)random numbers whose mean value is substantially zero and whose standard deviation is substantially equal to 1, preferably according to a Gaussian distribution.

[0051] According to another example of the first and second aspects of the invention, the size PxQ of the integration zone EA is such that P=Q.

[0052] According to another example of the first and second aspects of the invention, a. the image Im being a black and white image, the frequency transformation FT is applied to the image Im, or b. the image Im being a color image, the frequency transformation FT is applied: i. either to a luminance Y of the image Im in a luminance-chrominance representation

[0053] (Y, Cb, Cr), ii. or at least one of the three red, green and blue components of the image Im in a red-green-blue color representation.

[0054] According to the preceding example and where appropriate, the identification data of the WMi watermark to be detected further comprising data determining to which of the black and white WMlm image, the luminance Y of the WMlm image and said at least one of the three red, green and blue components of the WMlm image the frequency transform FT is to be applied.

[0055] According to another example of the first and second aspects of the invention, the generation of the watermark WMi to be watermarked on the image Im comprises a filtering of the sequence of (pseudo)random numbers AWMi(j) by a low-pass filter. Preferably, the low-pass filter comprises a finite impulse response filter. Other types of filter of the “low-pass” type can be used. The finite impulse response filter is advantageously the simplest to implement. Where appropriate, the identification data of the watermark WMi to be detected further comprise data determining the low-pass filter associated with the watermark WMi to be detected.

[0056] According to another example of the first and second aspects of the invention, the generation of the watermark WMi to be watermarked on the image Im comprises a multiplication by a weighting function F(j) of each number of the sequence of (pseudo)random numbers AWMi(j). Preferably, the weighting function F(j) is given by the following equation: F(j)=(Li-j) / (Li-1 ) with j=1 , ... , Li, where Li is the size of the sequence of (pseudo)random numbers AWMi(j). Other decreasing functions F(j) can be used provided that F(1) = 1 and F(Li) = 0. The function chosen above is the simplest to implement. Where appropriate, the identification data of the watermark WMi to be detected further comprise data determining the weighting function F(j) associated with the watermark WMi to be detected.

[0057] According to another example of the first and second aspects of the invention, the extraction scheme is defined by a zig-zag traversal of the elements of the matrix FT_lm included in the integration zone EA, starting from the element FT_lm(ni, mi) and ending with the element FT_lm(ni+P-1, mi+Q-1).

[0058] According to an example of the first aspect of the invention, the integration of the watermark WMi in the matrix FT_lm is such that the elements WMV(kStart) to WMV(kEnd) of the vector WMV are given by the following equation: a. WMV(k)=LV(k)+a*DLV*WMi(j), with j=1, ..., Li, and k = kStart, ... kEnd, where DLV is the standard deviation of the elements of the vector LV(k), WMi(j) is the element j of the watermark WMi, and where a is a weighting coefficient taking a predetermined value.

[0059] According to the previous example, the value of the weighting coefficient a can be chosen according to a compromise between visibility of the watermark WMi in the watermarked image Im and reliability of detection of the watermark WMi, for example the value of the weighting coefficient a is substantially between 0.01 and 2.5, preferably substantially between 0.05 and 0.5, and for example substantially equal to 0.1.

[0060] According to another example of the first and second aspects of the invention, the index kStart is greater than 10, preferably greater than 50 and even more preferably substantially equal to 100, and / or the size Li of the sequence of (pseudo)random numbers AWMi(j) is greater than 500, preferably equal to or greater than 1000.

[0061] According to an example of the first aspect of the invention, the same image Im is watermarked with a plurality of watermarks WMi, WMj, etc. Each watermark being associated with an integration zone EA which is specific to it, the integration zone EAi of at least one watermark WMi can at least partially cover the integration zone EAj of at least one other watermark WMj.

[0062] According to an example of the second aspect of the invention, in case of negative verification, the WMi watermark is not detected in the WMI image.

[0063] According to another example of the second aspect of the invention, each value Cxy(k) of the cross-correlation function Cxy is defined by the following equation: with

[0064] And

[0065] According to the preceding example, the value Cxy(k) of the cross-correlation function Cxy between the generated WMi watermark and the extracted LVm vector can be calculated for each value of the starting index kStart between 1 and K-Li+1. According to another example of the second aspect of the invention, the dedicated calculation system or the computer further storing a value of the index kStart in association with the WMi watermark to be detected, the values ​​Cxy(k) of the cross-correlation function Cxy between the generated WMi watermark and the extracted LVm vector are calculated for only the values ​​of the index k which are between kStart-d and kStart+d, where d is a predetermined integer, strictly less than kStart and between 1 and 20, preferably between 2 and 10, and even more preferably equal to 4.

[0066] According to another example of the second aspect of the invention, the WMlm image has been watermarked by implementing the digital watermarking method according to the first aspect of the invention.

[0067] According to another example of the second aspect of the invention, the WMlm image as watermarked has been modified, following its watermarking, by filtering and / or adding noise and / or modifying the intensity of the pixels which compose it, before being provided.

[0068] According to another example of the second aspect of the invention, a plurality of watermarks WMi, WMj, etc. are to be detected in the image WMlm. At least one watermark WMi may at least partially cover at least one other watermark WMj.

[0069] A parameter that is "substantially equal to / greater than / less than" a given value means that this parameter is equal to / greater than / less than the given value, within plus or minus 20% or even 10% of this value. A parameter that is "substantially between" two given values ​​means that this parameter is at least equal to the smallest given value, within plus or minus 20% or even 10% of this value, and at most equal to the largest given value, within plus or minus 20% or even 10% of this value.

[0070] Here, the term "image" or "digital image" means any kind of digital document taking the form of a matrix Im of pixels.

[0071] The term "watermark" means data constituting a mark, preferably permanent, inserted by digital tattooing in a document taking the form of a digital image.

[0072] The present invention relates to a method for digitally watermarking an Im image with at least one WMi watermark and to an associated method for detecting one or more WMi watermarks in a watermarked WMlm image, in particular by implementing the digital watermarking method according to the present invention. Optionally, the watermarked WMlm image may have been modified by intentional or unintentional transformations, or due, for example, to its transmission via a communication channel following the implementation of the digital watermarking method according to the present invention and before the implementation of the associated detection method.

[0073] A preferred embodiment of the invention is described below with reference to the accompanying figures.

[0074] The digital watermarking method according to the preferred embodiment of the invention is, more or less invisible, of the zero-bit type in the frequency domain. It is in particular intended to protect and identify digital content in the form of an image Im, referenced 1 in Figures 1 and 8, the latter figure illustrating an example of an image Im to be watermarked to obtain a corresponding watermarked image WMlm, which may be as illustrated in any one of Figures 11 A and 11 B. The digital watermarking method according to the preferred embodiment of the invention is more particularly an encrypted watermark with a private key and resistant to a modification of the intensity of the pixels of the watermarked image WMlm and / or to the introduction of noise into the image Im and / or to a filtering of the image Im.

[0075] The operating principle of said preferred embodiment of the digital watermarking method 10 and the associated detection method 20 is illustrated in FIG. 1.

[0076] The information 2, or watermark WMi, to be watermarked 20 in the provided image Im 101 can be generated from a code Wi which is a sequence of numbers, if necessary obtained by converting an alphanumeric text defined by a user in the manner of a password. Each watermark WMi is watermarked 10 in the image Im using a technique of the “spread spectrum in the frequency domain” type which is described below.

[0077] Let us note here, with reference to figures 1 and 5, that several watermarks WM1, WM2, ..., WMN, preferably generated 107 (see figure 2) from different codes W1, W2, ..., WN, can be watermarked 10 in the same image Im by successive implementations of the digital watermarking method 10 according to the first aspect of the invention.

[0078] Still with reference to Figure 1, the watermarked WMlm image can be recorded, transmitted or used, in particular before the detection method 20 is implemented according to the second aspect of the invention. In the case where at least one modification is made to the watermarked WMlm image, in particular by techniques for modifying the intensity of the pixels of the WMlm image and / or filtering the WMlm image and / or adding noise to the WMlm image, the process then implemented can be considered equivalent to a modification 1020 of the watermarked WMlm image due to its passage through a transmission channel. The image to be tested is then seen as the result of the passage of the watermarked WMlm image through the transmission channel.

[0079] With reference to figures 1, 6A and 7, the second aspect of said preferred embodiment of the present invention relates to a method 20 for detecting a watermark 2 in a presumed watermarked, and possibly modified, WMlm image 1020, this WMlm image being referenced 3 in figures 1, 6A, 11A and 11B. The detection method 20 aims to determine 209 whether the WMi watermark is present or not in the image 3. For this, the digital device implementing the detection method 20 according to the second aspect of the invention must know each WMi watermark to be searched for in the image 3.

[0080] This type of digital watermarking 10 and associated detection 20 may typically have the objective of protecting copyright, as well as, where appropriate, identifying the author. Alternatively or in addition, it may also be used to authenticate and / or identify, potentially uniquely, an image or a copy of an original image.

[0081] One of the particularities of the methods according to the first aspect of the invention and according to the second aspect of the invention is that they make it possible to integrate 108 and detect 209, in the same image Im, several watermarks, if necessary successively, each watermark WMi being able to be intended for a specific use chosen in particular from those stated above. This considerably broadens their possibilities of applications / uses, as shown by the different use cases described below.

[0082] The preferred embodiment of the digital watermarking method 10 according to the first aspect of the invention is described below with reference to Figures 2 to 4B and 7 to 11B.

[0083] Generating a watermark

[0084] With reference to Figure 2, each watermark WMi to be watermarked 10 is generated 107 from the code (or key) Wi provided 104 by the user. This code Wi, which is a sequence of numbers or which can be expressed in this form, if necessary by conversion of an alphanumeric text, is used to initialize the implementation 105 of a (pseudo)random number generator based on a deterministic algorithm, that is to say a random number generator which generates the same sequence of (pseudo)random numbers when it is initialized with the same root.

[0085] The Wi code can actually be considered as a private key and the random number generation algorithm can be considered as equivalent to an encryption algorithm, so the random number sequence AWMi can be considered as an encrypted signal.

[0086] For example, if the user code Wi is the text "CLEF", each letter can for example be replaced by its ASCII code and we obtain the decimal numerical sequence "65 76 69 70". The number 65766970 initializes the random number generator to generate 106 a sequence or series of random numbers AWMi(j) with j = 1 , ... , Li.

[0087] The generator is preferably capable of generating 106 a sequence of random numbers with a mean value substantially zero and a standard deviation substantially equal to 1. Typically, the distribution of the sequence of random numbers generated is Gaussian.

[0088] The generated sequence of random numbers AWMi(j) 106 is preferably filtered 1061 by applying a low-pass filter. In this case, a finite impulse response (FIR) filter is preferably used, but other types of low-pass filters can be used. The finite impulse response filter can advantageously be the simplest to implement. Preferably, the finite impulse response filter can be a moving average filter with 11 coefficients, but a different number of coefficients can be used.

[0089] At the output of filtering 1061, we obtain a filtered sequence of random numbers, noted AWMFi(j) in figure 2.

[0090] As an alternative or in addition to filtering 1061 , each number in the sequence AWMi or AWMFi can be multiplied 1062 by a weighting function F(j). This weighting function F(j) can be given by the following formula:

[0091] F( / ) = (Li -j) / (Li - 1) with j = 1, ... ,Li

[0092] The WMi watermark is then given by one of the following formulas, depending on whether 1061 filtering is implemented or not:

[0093] No filter:

[0094] And with filter

[0095] According to the preferred embodiment of the invention, the filtering 1061 and the multiplication 1062 by the weighting function are implemented, the filtering 1061 preceding the multiplication 1062. The generation of a WMi watermark may optionally comprise other steps. Furthermore, not only is each step among the filtering 1061 and the multiplication 1062 only optional and can be ignored, but also the steps of generating a WMi watermark can be implemented in a different order than that indicated above as preferred.

[0096] The advantages of using filtering 1061 and / or using multiplication 1062 by a weighting function are explained below. Note here that a WMi watermark generated according to the preferred embodiment of the first aspect of the invention is graphically illustrated in Figure 7.

[0097] Watermark integration

[0098] To watermark 10 the generated WMi watermark 107 in the image Im, a frequency transformation, denoted FT, is applied 102 to the image Im. This frequency transformation FT can for example be chosen from a Fourier transform, a discrete cosine transform (DCT), a wavelet transform and a transformation into orthogonal functions.

[0099] In the case of a black and white Im image, the FT frequency transform is applied to the image itself.

[0100] In the case of a color Im image, the frequency transform FT can be applied to the luminance Y (or intensity) of the image.

[0101] Note here that the transformation of a red-green-blue (R, G, B) color image into a luminance-chrominance (Y, Cb, Cr) representation, as well as the inverse transformation, can be carried out by standardized and well-known procedures.

[0102] We therefore understand that any red-green-blue (R, G, B) color image can be converted into a luminance-chrominance (Y, Cb, Cr) representation.

[0103] The frequency transform FT can be applied 102 to the luminance Y of the image Im alone, and Cb and Cr are not affected by the watermarking method 10 according to the first aspect of the invention.

[0104] It is also possible to apply 102 the frequency transformation FT directly to a red-green-blue (R, G, B) color image. The frequency transformation FT can in this case be applied 102 to at least one of the three red, green and blue components of the image Im, to two of them or to all three.

[0105] According to the preferred embodiment described herein, a discrete cosine transform (or DCT) is used although, as already mentioned above, the use of other frequency transforms is possible. The use of a DCT is justified by the low complexity of the related calculations.

[0106] The frequency transformation FT makes it possible to generate a matrix FT_lm of elements FT_lm(i, j) of the same size as the original image Im. Such matrices are illustrated in each of Figures 9A and 9B which are strictly the same because they come from the same frequency transformation of the image Im illustrated in Figure 8. It is in such a matrix FT_lm that the watermark WMi is integrated, in the manner described below.

[0107] In the case where a Fourier transform is used, each element of the FT_lm matrix is ​​composed of a complex number that represents the modulus (amplitude) of the frequency component as well as the phase (angle) of the frequency component. The modulus of each frequency component corresponds to the intensity of the image.

[0108] With reference to Figure 3A, in the matrix FT_lm, which has the same dimension NxM as the image Im, an integration zone EA is chosen 1081 which is a sub-matrix of elements EA(i,j) of dimension PxQ, preferably PxP, having as first element the one located at the coordinates (mi, ni) of the matrix FT_lm, with (P-mi+1) < M and (Q-ni+1) < N. From the integration zone EA, a linear vector LV(k) of length K less than, and preferably equal to, the size PxQ of the integration zone EA is extracted 1082. In the case where a Fourier transformation is used, the vector LV is formed solely from the moduli of the frequency components. The phases of the frequency components are not modified by the procedure for integrating the watermark WMi.The linear vector LV can more particularly be formed by extracting one by one the elements EA(i,j) from the sub-matrix EA by traversing them according to a predetermined extraction scheme 30, for example a zigzag extraction scheme starting from EA(1,1) = FT_lm(ni, mi), in this way that: a. LV(1) = EA(1,1) = FT_lm(ni, mi) b. LV(2) = EA(1,2) = FT_lm(ni, mi+1) c. LV(3) = EA(2,1) = FT_lm(ni+1, mi) d. LV(4) = EA(3,1) = FT_lm(ni+2, mi) e. LV(5) = EA(2,2) = FT_lm(ni+1, mi+1) f. LV(6) = EA(1, 3) = FT_lm(ni, mi+2) g. .

[0109] Other extraction schemes can be chosen, which only pass once through each element EA(i,j) of the sub-matrix EA.

[0110] The zigzag extraction scheme 30 is advantageously chosen for the following reason: the coefficients of the frequency transform FT of an image Im decrease when the indices i and j increase; using the recommended extraction scheme 30 or an equivalent scheme, the elements LV(k) of the linear vector LV also decrease when k increases.

[0111] Once the integration zone EA is converted 1082 into a vector LV of length K, we calculate the standard deviation DLV of the elements of the vector:

[0112] DLV =

[0113] Where LVmean is the average value of the elements of the LV vector.

[0114] The previously generated WMi watermark 107 can then be integrated into the LV vector according to the procedure illustrated in Figure 4A.

[0115] Referring to Figure 4A, the elements WMi(j) of the watermark WMi are introduced into the vector LV from an index kStart and up to an index kEnd such that: kEnd = kStart + Li - 1 The length K of the vector LV must be such that:

[0116] K > Li + 2 * (kStart — 1) so that the first and last elements LV(k) of the LV vector may not be modified by the introduction of the watermark WMi into the LV vector.

[0117] So, if the size of the submatrix EA is PxQ, the maximum number of elements that can be extracted is given by the number PxQ which must be greater than the size K of the vector LV. So:

[0118] P x Q > K

[0119] The remaining Li elements LV(k) of the LV vector are impacted by the introduction of the WMV watermark of length Li. They come from a 1083 combination with the WMi(j) elements of the WMi watermark.

[0120] Preferably, the elements LV(k) of the vector LV are modified as follows: to obtain 1084 a WMV vector of WMV(k) elements which remain to be introduced 1085 into the FT_lm matrix.

[0121] The value of the so-called weighting coefficient a can be chosen according to a compromise between the visibility of the WMi watermark and the reliability of detection 20 of the WMi watermark. If a is large the watermark is visible, this will be the case for example in figures 10B and 11 B which were obtained with a coefficient a equal to 2.0. If a is too small the detection of the WMi watermark may not be reliable. For example, the coefficient a of the order of 0.1 will be chosen to have a reasonable compromise between visibility and reliability of detection 20. Figures 10A and 11A were obtained with a coefficient a equal to 0.1. We note by comparing two by two figures 10A and 11 A and figures 10B and 11 B, as well as by comparing figures 12A and 212B with each other, that the watermark WMi actually has an increased visual impact on the watermarked WMlm image, as well as on its representation FT_WMIm in the frequency space, when the coefficient a equals 2.0.However, as we will see below, with reference to figures 13A and 13B, the watermark WMi introduced with a coefficient a equal to 0.1 remains entirely detectable 10 by implementing the detection method according to the second aspect of the invention.

[0122] Once the WMV vector of elements WMV(k) has been generated 1084, it can be introduced 1085 into the matrix FT_lm in place of the integration zone EA, which can here be called the integration or introduction zone. The introduction of the WMV vector of elements WMV(k) into the integration zone EA of the matrix FT_lm must be done by traversing the integration zone EA according to a so-called insertion scheme identical to the extraction scheme used to generate 1082 the vector LV. In this way, a matrix FT_WMIm is generated which represents, in the frequency domain, the image Im combined with the watermark WMi. The integration of the WMi watermark into the Im image is adaptive because the values ​​WMV(kStart) to WMV(kEnd) of the WMV vector depend on the standard deviation DLV of the elements EA(ij) of the extraction area EA in which the WMi watermark is integrated 108.

[0123] More specifically, the FT_WMIm matrix, which represents the Im image combined with the WMi watermark, is obtained as follows. First, a copy of the FT_lm matrix is ​​made into FT_WMIm:

[0124] FT_WMIm(i,f) = FT_Im(i,j);

[0125] For i = 1 , ... , M ; And j = 1 , ... , N

[0126] Then, the WMV vector is introduced 1084 into the matrix FT_WMIm, and more particularly into the insertion zone EA according to an integration scheme 31 identical to the extraction scheme 30 used to generate 1082 the LV vector, i.e. in a zigzag fashion according to the preferred embodiment. This introduction 1084 can be expressed in the form of the following equations: a. FT_WMIm(ni,mi) = WMVÇF) b. FT_WMIm(ni, mi + 1) = WMV(2) c. FT_WMIm (ni + l,mi) = WMV(3) d. FT_WMIm(ni + 2, mi) = WMV(4) e. FT_WMIm (ni + l,mi + l) = WMV(5) f. FT_WMIm (ni,mi + 2) = WMV(6) g....

[0127] With reference to Figure 4B, the WMlm image watermarked with the WMi watermark is then simply obtained by applying 109 a frequency transformation IT, inverse to the frequency transformation FT, on the matrix FT_WMIm.

[0128] As mentioned above, the coefficients of the frequency transform FT of the Im image, like that of the WMlm image, decrease when the indices i and j increase. The elements of the LV vector which are in fact the frequency components of the WMlm image in the EA area also decrease when k increases. For this reason, it is preferable to adapt the WMi watermark to the LV vector before integrating it into the FT_lm matrix. This is the role of the filtering and / or the multiplication by the weighting function F(j) used for the generation of the WMi watermark. In addition, since compression techniques attenuate high frequencies in the WMlm image, it is preferable to filter the high frequencies of the WMi watermark before integrating it into the FT_lm matrix. This makes the WMi watermark more resistant to compression.

[0129] Multiple tattoos

[0130] As already mentioned above, different watermarks WM1 , WM2, ... can be introduced at different locations of the matrix FT_WMIm. Each corresponding integration area EA1 , EA2, ... can be defined by its first element (m1 , n1), (m2, n2), ..., and the different integration areas EA1 , EA2, ... can overlap as illustrated in Figure 5. The different integration areas EA1 , EA2 ... can have dimensions P1xQ1 , P2xQ2 ... which are different from each other.

[0131] Thus, each WMi watermark, with i = 1 , ... , O, is defined by the parameters: a. The code Wi (sequence of numbers or text), b. The length of the random sequence Li c. The position (ni, mi) in the matrix FT_lm of the first element of the insertion zone EAi. This quadruplet of parameters grouping the code Wi and the 3 numbers Li, ni and mi can be considered as an identity ID of the WMi watermark:

[0132] ID_WMi = (Wi,Li,ni,mi)

[0133] The number kStart determining the start of the WMi watermark integration area is preferably a constant of the order of 100. The number Li of elements of the WMi watermark can be fixed for all watermarks or variable. It is preferably greater than 1000 for reliable detection of the WMi watermark.

[0134] Detecting the presence of a tattoo

[0135] As already mentioned, the detector 20 illustrated in Figure 1 has the objective of determining whether a particular watermark WMi defined by the set (Wi, Li, ni, mi) is present or not in an image. The detection 20 according to the preferred embodiment of the invention is based on the principle of the correlation receiver or the optimal receiver with matched filter. An example of such a receiver is described in the article by R. Pickholtz, D. Schilling and L. Milstein, entitled "Theory of Spread-Spectrum Communications - A Tutorial, published in "IEEE Transactions on Communications", vol. 30, no. 5, pp. 855-884, in May 1982.

[0136] The preferred embodiment of the detection method 20 according to the second aspect of the invention is described below with reference to Figures 6A, 6B, 13A and 13B.

[0137] This type of detection 20 requires knowledge of the WMi vector that corresponds to the watermark sought, as well as the type of algorithm used to generate the sequence of random numbers.

[0138] This vector is generated by the detector 20 from the identity (Wi, Li, ni, mi) of the watermark WMi to be searched for using the principle illustrated in the diagram of figure 2.

[0139] More particularly, depending on the size Li of the watermark WMi and the provided user code Wi, the (pseudo)random number generator is implemented 205 by initializing it 204 with the user code Wi, to generate 206 a sequence of (pseudo)random numbers AWMi(j) having the size Li. Then, from the sequence of (pseudo)random numbers AWMi(j), the watermark WMi is generated 206, the latter having the size Li of the sequence of (pseudo)random numbers AWMi(j). The same filtering 2061 and / or the same multiplication 2062 as the filtering 1061 and the multiplication 1062 can be implemented, to obtain 207 the watermark WMi again, as illustrated in Figure 7.

[0140] The detector 20 uses the same random number generation algorithm as the generator 105. It can be said that the detector 20 must know the encryption algorithm and the private code Wi used to generate 107 the watermark WMi before its integration 108 into the matrix FT_lm.

[0141] The operation of the detector 20 is illustrated in Figure 6B.

[0142] Referring to Figure 6A, after providing 201 the image WMlm, we apply 202 to it the same FT transform as that applied 102 to the image Im which was to be watermarked. Thus, we generate 203 the matrix of coefficients of the transform FT_WMIm.

[0143] In the case where a Fourier transformation is used, each element of the FT_WMIm matrix is ​​composed of a complex number that represents the modulus (amplitude) of the frequency component and the phase (angle) of the frequency component. The modulus of each frequency component corresponds to the intensity of the image. The detection of the presence of the watermark is done using only the modulus of the frequency components of the FT_WMIm matrix.

[0144] With reference to Figure 6B, from the zone EA whose position is defined by the coordinates mi and ni of its first element, we extract 207 the vector LVm.

[0145] This extraction is carried out in a similar manner to that of the LV vector described above in relation to the first aspect of the invention.

[0146] More particularly, this extraction consists of: a. assigning, to a first element LVm(1) of the vector LVm, the value of the element FT_WMIm(ni, mi) of the matrix FT_WMIm, then b. assigning respectively, to each of the following elements of the vector LVm, the value of each of the elements FT_WMIm(i,j) following the determined element FT_WMIm(ni, mi) of the matrix FT_WMIm by browsing it according to an extraction scheme identical to that followed during the extraction 1082 of the vector LV.

[0147] Then, we calculate the values ​​Cxy(k) of a cross-correlation function Cxy between the generated WMi watermark 205 and the extracted LVm vector 207. The cross-correlation function can for example take the following form:

[0148] Figure 6B illustrates the process of calculating 208 the Cxy(k) values ​​for k = 1 and k = 2.

[0149] According to the correlation receiver theory, if the WMi watermark is present in the extracted LVm vector 207, for a displacement k=kStart, the value of the Cxy(kStart) function is maximum.

[0150] In practice, to increase the reliability of the detection 20, we search for the maximum of the cross-correlation function Cxy in an area of ​​1 to 4 points around kStart, for example, for an area of ​​1 point (d=1), between kStart-1 and kStart+1. Then, the maximum of the cross-correlation function Cxy must be in the area Cxy(kStart-l), Cxy(kStart), Cxy(kStart+1). If this is the case, the watermark WMi is judged to be present in the vector LVm and the watermark defined by (Wi, Li, ni, mi) is detected. If the maximum of Cxy is not in the specified area, the watermark WMi is judged not to exist in the image.

[0151] When the watermark exists in the image, the maximum of the Cxy signal is located at a specific location (around kStart) and the Cxy signal has a particular shape (see Fig. 13A and 13B). When the watermark does not exist in the image, the cross-correlation between the watermark and the image is representative of noise; it therefore does not a priori present the aforementioned particular shape. It is possible that the maximum of this noise is located at the location of the expected maximum (kStart = 100, in the case of Figures 13A and 13B). In this case, a "False Positive" is detected. However, the maximum of the noise that then represents the cross-correlation between the watermark and the image can be located anywhere on the Cxy signal with the same probability. Therefore, the probability of detecting a False Positive is given by: PFP = 1 / Li, where Li is the size of the WMi watermark. Thus, the longer the WMi watermark signal, the lower the probability of detecting a False Positive. For Li = 1000, PFP = 0.001.In practice, we typically work with Li = 10000, therefore with PFP = 0.0001 (1 in 10000).

[0152] In general, the probability of detecting a False Positive (FPP) is related to the probability of detecting a False Negative (FNN). When one increases, the other decreases. The optimal case is observed when these two probabilities are of the same order of magnitude (or equal to each other). The probability of detecting a False Negative (FNP) depends on the image and the coefficient a and cannot be directly calculated. Experimentally, for a of the order of 0.1, and for an image in which there are not too many contrast differences, the probability of detecting a False Positive (FNP) is of the same order of magnitude as the probability of detecting a False Negative (FNP).

[0153] If multiple watermarks have been applied to the image Im, the detection procedure 20 is repeated for each watermark WMi of the set, depending on the parameters (Wi, Li, ni, mi) that identify it. As already mentioned below, the graphs of Figures 13A and 13B illustrate, continuously, the values ​​of the cross-correlation function Cxy calculated on the one hand for a weighting coefficient a equal to 0.1 (Cf. Figure 13A), on the other hand for a weighting coefficient a equal to 2.0 (Cf. Figure 13B). It is observed that, despite a much lower amplitude of variation with a weighting coefficient a equal to 0.1 than with a weighting coefficient a equal to 2.0, the detection 20 remains robust with a weighting coefficient a equal to 0.1.

[0154] Figures 12A and 12B illustrate the difference between the initial Im image and the watermarked WMlm image with a weighting coefficient a equal to 0.1 (see Figure 12A) and a weighting coefficient a equal to 2.0 (see Figure 12B), respectively. These illustrations clearly show that the visibility of the WMi watermark in the watermarked WMlm image is much higher when the weighting coefficient a is higher.

[0155] As announced above, different use cases are now described.

[0156] Marking of digital lithographs

[0157] In conventional lithography, an image is printed in several copies that form a limited edition series. Each print (copy) has three identifiers: the signature of the author (Author), the print number (Num) and the total number of lithographs (Nmax) in the series. A digital lithograph is represented by the image file. The image can be purely digital (synthetic) or a conventional digitized image. The series is composed of Nmax identical copies of this file. In each image (file), it is possible to introduce, by successive implementations of the digital watermarking method according to the first aspect of the invention, three different watermarks that correspond to “Author”, “Num” and “Nmax”. Thus, each digital image is uniquely identified even though it is part of the same series.

[0158] Strong authentication

[0159] A watermark can authenticate an image, the author, or the owner of the image. Strong authentication of a user or digital content requires that several authentication techniques be used in parallel. The digital watermarking method according to the first aspect of the invention lends itself well to this type of use. An image can be marked with different watermarks located at different locations in the frequency space. This increases the robustness of the authentication performed.

[0160] Authentication and certification of the integrity of a document

[0161] The digital watermarking method according to the first aspect of the invention can be applied for the authentication of documents or images. A document scanned in an electronic format (bmp, png, jpeg, tif, gif, psd, pdf, ...) can be considered as a digital image. This image can be watermarked 20 with the algorithm proposed by a specific watermark. The watermark makes it possible to authenticate the author or owner of the document. In addition, a hashing algorithm (SHA1, MD5, SHA-256, SHA-3 ...) can be applied to the watermarked digital file, which generates a code (HAi). This "hash code" is a unique number which depends on the digital data to which the algorithm has been applied, that is to say the digital data constituting the watermarked WMlm image. If the data is changed / modified, the "hash code" of the new data will be different from that from the original data.In this way, the "hash code" is an indicator of the integrity and originality of the digital data constituting the file.

[0162] The set of numbers in the watermark identity (the quadruplet ID_WMi) and the hash code (HAi) are the unique identifier of the document's owner, as well as its integrity.

[0163] To authenticate the integrity of a document (data file), simply calculate its "hash code" with the algorithm used for protection. If the two numbers are the same, the file has not been changed / modified and its integrity is confirmed. Authentication of the document owner is performed by detecting the WMi watermark introduced in the protection phase.

[0164] Identification of the owner and author of a document through joint use with NFT technology

[0165] The digital watermarking method according to the first aspect of the invention can be applied for the identification of the owner and author of a document by further using NFT technology. A non-fungible token or NFT (for "Non-Fungible Token" according to English terminology) is a block of data that represents a digital object (document, image, video, music) in a unique way. The NFT is permanently and indelibly recorded in a register called Blockchain. It makes it possible to prove and certify the ownership of the digital object that it represents as an asset. More specifically, it is a unique identifier that can group together all the characteristics of the asset as well as the rights and privileges of the owner of the asset and the NFT in a metadata field or structure called Metadata. In practice, it is a data structure that includes a pointer (address) to the location (memory) where the asset (document, image) is located.The asset itself is not necessarily registered in the Blockchain and may be located in a memory outside of it, for example in a data storage (or "data storage" in English terminology). The owner of the NFT has a digital wallet (or "Wallet" in English terminology) in which the address of the NFT in the Blockchain is registered.

[0166] A digital asset (image, document, etc.) has an author and an owner. The owner of the asset can change, while its author is unique. An NFT has an owner who may be different from the author.

[0167] A watermark can identify the author of the image. Using an NFT and a watermark together separates the author from the owner. As in the previous use case described, the asset can be marked with a WMi watermark and the hash code (HAi) can be calculated. Both parameters, WMi and HAi, can be written into the NFT's metadata. The hash code is thus an indicator of the asset's integrity. The asset is stored in an external memory and the NFT includes a pointer to this memory.

[0168] It should also be noted that the NFT may also include a block called a "smart contract." This is a computer code that simplifies the execution of certain operations (contractual agreements) by eliminating the need for an intermediary. The smart contract executes what is written in its code as long as certain conditions are met. This makes transactions transparent, fast, irreversible, and eliminates the possibility of fraud.

[0169] The invention is not limited to the embodiments previously described, nor to the use cases presented above, and extends to all embodiments covered by the invention.

[0170] Notably, many types of digital images include or are accompanied by metadata, and it is contemplated that some of the various parameters indicated above may be reflected in such metadata.

Claims

CLAIMS 1. Method for digitally tattooing (10) an image (1) with a watermark (2), the method implemented by a dedicated computing system or a computer comprising the following steps: • provide (101) the image Im to be watermarked, the image Im having a size NxM, • apply (102), to the image Im, a frequency transformation FT to obtain (103) a matrix FT_lm of elements FT_lm (i,j) and of the same size as the image Im provided, • provide (104) a Wi user code, • implement (105) a (pseudo)random number generator based on a deterministic algorithm by initializing it with the user code Wi, so as to generate (106) a sequence of (pseudo)random numbers AWMi(j) with j = 1, ..., Li, where the size Li of the sequence is strictly less than the size NxM of the image Im, • from the sequence of (pseudo)random numbers AWMi(j), generate (107) the watermark WMi to be tattooed on the image Im, the watermark WMi having the size Li of the sequence of (pseudo)random numbers AWMi(j), • integrating (108) the watermark WMi into the matrix FT_lm: i. by defining (1081), in the matrix FT_lm, an integration zone EA of elements EA(ij) and of size PxQ smaller than the size NxM of the matrix FT_lm and from a determined element FT_lm(ni, mi) of the matrix FT_lm such that (P-mi+1) < M and (Q-ni+1) < N, then ii. by converting (1082) the integration zone EA into a vector LV of length K equal to or smaller than the size PxQ of the integration zone EA, the conversion consisting of:

1. assign, to a first element LV(1)= EA(1,1) of the vector LV, the value of the element FT_lm(ni, mi) determined from the matrix FT_lm, then 2. assigning respectively, to each of the following elements of the vector LV, the value of each of the elements FT_lm(i,j) following the element FT_lm(ni, mi) determined from the matrix FT_lm by traversing the integration zone EA according to a so-called predetermined extraction scheme, iii. by combining (1083), with the watermark WMi, a part of the vector LV which is between a starting element LV(kStart) and an arrival element LV(kEnd), with kStart>1, kEnd <k-1 , kend-kstart="L-1" et avec k>L+2(kStart-1), so as to generate (1084) a WMV vector of size K composed of the first kStart-1 elements of the vector LV, of elements WMV(kStart) to WMV(kEnd) resulting from the combination of the elements of LV(kStart) to LV(kEnd) with the elements of WMi(1) to WMi(Li) of the watermark WMi and of the last K-kEnd elements of the vector LV, then iv. by introducing (1085) the vector WMV into the matrix FT_lm in place of the integration zone EA, by traversing the integration zone EA according to a so-called insertion scheme identical to said extraction scheme predetermined, to generate (1086) a matrix FT_WMIm which represents, in the frequency domain, the image Im combined with the watermark WMi, • apply (109), to the matrix FT_WMIm, an inverse transformation IT to the frequency transformation FT, to obtain a watermarked image WMlm.

2. Digital tattooing method (10) according to the preceding claim, in which: • the image Im being a black and white image, the frequency transformation FT is applied to the image Im, or • the image Im being a color image, the frequency transformation FT is applied: i. either to a luminance Y of the image Im in a luminance-chrominance representation (Y, Cb, Cr), ii. or to at least one of the three red, green and blue components of the image Im in a red-green-blue color representation.

3. Digital watermarking method (10) according to any one of the preceding claims, in which the generation (106) of the watermark WMi to be watermarked on the image Im comprises a filtering (1061) of the sequence of (pseudo)random numbers AWMi(j) by a low-pass filter.

4. Digital watermarking method (10) according to any one of the preceding claims, in which the generation (106) of the watermark WMi to be watermarked on the image Im comprises a multiplication (1062) by a weighting function F(j) of each number in the sequence of (pseudo)random numbers AWMi(j).

5. Digital watermarking method (10) according to the preceding claim, in which the weighting function F(j) is given by the following equation: F(f) = (Li - j) / (Li - 1) with j=1, ..., Li, where Li is the size of the sequence of (pseudo)random numbers AWMi(j).

6. Digital watermarking method (10) according to any one of the preceding claims, in which the extraction scheme is defined by a zig-zag path (30) of the elements of the matrix FTJm included in the integration zone EA, starting from the element FT_lm(ni, mi) and ending with the element FT_lm(ni+P-1, mi+Q-1).

7. Digital watermarking method (10) according to any one of the preceding claims, wherein the integration (108) of the watermark WMi in the matrix FT_lm is such that the elements WMV(kStart) to WMV(kEnd) of the WMV vector are given by the following equation: WMV(k)=LV(k)+a*DLV*WMi(j), with j=1 , ... , Li, and k = kStart, ... kEnd, where DLV is the standard deviation of the elements of the vector LV(k), WMi(j) is the jth element of the WMi watermark, and where a is a weighting coefficient taking a predetermined value.

8. Digital watermarking method (10) according to the preceding claim, in which the value of the weighting coefficient a is chosen according to a compromise between visibility of the watermark WMi in the watermarked image Im and reliability of detection of the watermark WMi, by for example, the value of the weighting coefficient a is substantially between 0.01 and 2.5, preferably substantially between 0.05 and 0.5, and for example substantially equal to 0.

1.

9. Digital watermarking method (10) according to any one of the preceding claims, in which the index kStart is greater than 10, preferably greater than 50 and even more preferably substantially equal to 100, and / or the size Li of the sequence of (pseudo)random numbers AWMi(j) is greater than 500, preferably equal to or greater than 1000.

10. Digital watermarking method (10) according to any one of the preceding claims, wherein the same image Im is watermarked with a plurality of watermarks WMi, WMj, etc.

11. Digital watermarking method (10) according to the preceding claim, in which each watermark WMi being associated with an integration zone EAi which is specific to it, the integration zone EAi of at least one watermark WMi at least partially covers the integration zone EAj of at least one other watermark WMj.

12. Method for detecting (20) at least one watermark (2) in an image (3), the method being implemented by a dedicated computing system or a computer storing, in association with each WMi watermark to be detected, a (pseudo)random number generator based on a deterministic algorithm, a so-called predetermined extraction scheme and identification data for each WMi watermark to be detected, the latter comprising, or even consisting of, a user code Wi, a size Li of the WMi watermark and coordinates (ni, mi) of an element WMIm(ni, mi) of the image WMlm from which the WMi watermark is to be searched, the method comprising the following steps: • provide (201) the WMlm image in which the WMi watermark is to be detected, the WMlm image having a size NxM strictly greater than the size Li of the WMi watermark to be detected, • apply (202), to the WMlm image, a frequency transformation FT to obtain (203) the matrix FT_WMIm of elements FT_WMIm(i,j) and of the same size as the provided WMlm image, • depending on the size Li of the watermark WMi and the user code Wi provided, implement (205) the (pseudo)random number generator by initializing it (204) with the user code Wi, to generate (206) a sequence of (pseudo)random numbers AWMi(j) having the size Li, • from the sequence of (pseudo)random numbers AWMi(j), generate (206) the watermark WMi, the latter having the size Li of the sequence of (pseudo)random numbers AWMi(j), • from the size Li of the watermark WMi, the coordinates (ni, mi) of the element WMIm(ni, mi) of the image WMlm from which the watermark WMi is to be searched and the predetermined extraction scheme, extract (207), from the matrix FT_WMIm, a vector LVm of length K=P*Q strictly greater than the size Li of the watermark WMi and strictly less than the size NxM of the image WMlm, the extraction consisting of: i. assign, to a first element LVm(1) of the vector LVm, the value of the element FT_WMIm(ni, mi) of the matrix FT_WMIm, then ii. assign respectively, to each of the following elements of the vector LVm, the value of each of the elements FT_WMIm(i,j) following the determined element FT_WMIm(ni, mi) of the matrix FT_WMIm by partially scanning it according to the so-called predetermined extraction scheme, then • as a function of the generated WMi watermark and a part of the extracted LVm vector which is between a starting element LVm(kStart) and an arrival element LVm(kEnd), where kEnd-kStart=Li-1 and K>Li+2(kStart-1), calculate (208) the values ​​Cxy(k) of a cross-correlation function Cxy between the generated WMi watermark and the extracted LVm vector, for a plurality of values ​​k of the starting index kStart between 1 and K-Li+1, and • verify (209) that the calculated values ​​Cxy(k) of the cross-correlation function Cxy include a maximum value which is representative of an effective correlation between the generated WMi watermark and the extracted LVm vector, • so as to detect, in the event of a positive verification, the WMi watermark in the WMlm image.

13. Detection method (20) according to the preceding claim, in which the values ​​Cxy(k) of the cross-correlation function Cxy are defined by the following equation:

14. Detection method (20) according to any one of claims 12 and 13, in which, the dedicated calculation system or the computer furthermore storing a value of the index kStart in association with the watermark WMi to be detected, the values ​​Cxy(k) of the cross-correlation function Cxy between the generated watermark WMi and the extracted vector LVm are calculated (208) for only the values ​​of the index k which are between kStart-d and kStart+d, where d is a predetermined integer, strictly less than kStart and between 1 and 20, preferably between 2 and 10, and even more preferably equal to 4.

15. Detection method (20) according to any one of claims 12 to 14, in which the WMlm image has been watermarked by implementing the digital watermarking method (10) according to any one of claims 1 to 11.

16. Detection method (20) according to the preceding claim, in which the WMlm image as watermarked has been modified (1020), following its watermarking, by filtering and / or adding noise and / or modifying the intensity of the pixels which compose it, before being provided (201).

17. Method for authenticating and / or identifying an Im image and / or the author, owner or authorized user of an Im image implementing the digital tattooing method (10) according to any one of claims 1 to 11 and the detection method (20) according to any one of claims 12 to 16.

18. A computer program product comprising instructions which, when implemented by a dedicated computing system or a computer, executes the steps of at least one of the digital watermarking method (10) according to any one of claims 1 to 11 and the detection method (20) according to any one of claims 12 to 16.

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