AUGMENTED AUTHENTICATION PROCESS OF A MATERIAL OBJECT

Abstract

The invention relates to a process for determining a relational signature between two images, which includes the following steps: - the application of a first image and a second image, - a step for calculating similarity vectors between blocks belonging to the first and second images respectively, the similarity vectors form a trace vector field, the trace vector field contains at least one disordered region in the sense of an entropic criterion, - a step for recording the image, which is a representation of the calculated trace vector field, as the relational trace. The invention also relates to a process for verifying the identity of a candidate image relative to an original image, which, according to the invention, applies the process for determining a relational signature.

Description

[0001] The present invention relates to the technical field of authentication and integrity control of physical objects, as well as the field of visual cryptography. In a preferred, but not exclusive, application, the invention relates to the field of unit authentication of physical objects.

[0002] Image matching methods are known for object recognition / localization in visual servoing or navigation in robotics, for reconstructing the same scene from different viewpoints in stereoscopy, for assembling partially overlapping views in panoramic photography, and for pattern recognition in image retrieval / indexing of image databases. Methods for tracking objects over time also exist. However, all these methods seek to determine the degree of similarity between two images without enabling authentication of the images or the subjects from which the images originate or of which the images are acquisitions. Relevant prior art includes Wan-Lei Zhao et al.: "Scale-Rotation Invariant Pattern Entropy for Keypoint-Based Near-Duplicate Detection", IEEE TRANSACTIONS ON IMAGE PROCESSING, vol. 17, no.2, February 2009 (2009-02), pages 412-423, XP011249840, ISSN: 1057-7149 and Chong-Wah Ngo et al.: "Fast tracking of near-duplicate keyframes in broadcast domain with transitivity propagation", ACM MULTIMEDIA 2006 & CO-LOCATED WORKSHOPS: OCTOBER 23 - 27, 2006, SANTA BARBARA, CALIFIRNIA, USA; MM '06; PROCEEDINGS, ACM PRESS, [NEW YORK, NY], October 23, 2006 (2006-10-23), pages 845-854, XP058233396, DOI: 10.1145 / 1180639.1180827.

[0003] Thus, the need arose for a method of relating two images that could account for the intrinsic randomness present in at least one of the two images, or even account for the intrinsic randomness present in both images and make it explicit through comparison. In other words, a method of relating two images that allows for the explicit identification and use of the unique variability, at different scales, of attributes such as texture or contours.

[0004] To achieve this objective, the invention relates to a method for determining a relational fingerprint between two images comprising: the implementation of a first image of a material subject and a reference image different from the first image, a phase of calculating similarity vectors between tiles belonging respectively to the image of the material subject and to the reference image, using a calculation method defined by a type of similarity indicator and a similarity rank to obtain a field of fingerprint vectors, formed by the similarity vectors, comprising at least one disordered region in the sense of an entropic criterion, a phase of recording as a relational fingerprint of a representation of the field of fingerprint vectors calculated in the previous step, a step of using as a relational signature of a digital representation of the relational fingerprint.

[0005] The relational fingerprint according to the invention is capable of being used in various applications for example to authenticate, identify, inspect, an image or a material subject after acquisition of an image of the latter.

[0006] The invention has the advantage of implementing, on the one hand, the unique, non-reproducible, and unpredictable properties of matter originating from a physical subject, and uses the correlation of images, particularly to determine a so-called relational fingerprint of a first image in relation to a second image, at least one of the images being an image of a physical subject. From this relational fingerprint, a relational signature can be derived via digital conditioning, intended for performing automatic authentication tasks. From this relational fingerprint, a relational stimulus can also be derived via cognitive conditioning, intended to enable authentication that appeals to at least one of the senses of a human user without prior training or specific equipment, by using the user's ability to gauge or judge the presence and quality of a phenomenon. This is what we call augmented authentication.

[0007] For the purposes of this invention, a vector field can be understood as one or more scalar fields, and more generally as one or more tensor fields, given that a zeroth-order tensor is a scalar and a first-order tensor is a vector. Thus, for the purposes of this invention, the expression "vector field" should be understood as equivalent to the expression "tensor field," the two expressions being interchangeable unless otherwise indicated. A variant of the invention implementing tensor fields, possibly of different orders, for determining the same relational footprint is conceivable, provided it is not incompatible with the various implementation characteristics of the method.

[0008] The set of similarity vectors calculated during the similarity vector calculation phase between tiles belonging to the first and second images can be considered equivalent to at least one vector field, in that it is theoretically possible to calculate one or more similarity vectors at any point in the reference image. This calculation method, defined by a similarity indicator type and a similarity rank, applies to each point and each similarity vector. It is also possible to extend a portion of the computable field by interpolation, extrapolation, or a vector function with predetermined values ​​to all other points in the reference image to approximate or reconstruct a field in the strict sense.

[0009] A footprint vector field, in the sense of the invention, is a sampled version of a vector field in the strict sense, consisting of one or more similarity vector fields, this or these fields being made up of similarity vectors calculated each at their point of application according to the same calculation method.

[0010] Thus, a footprint vector field, as defined in the invention, can be composed of a similarity vector field or a superposition of similarity vector fields. Several similarity vector fields can therefore be superimposed to form a footprint vector field.

[0011] By superposition of similarity vector fields we mean, for example at the same point of application the vector sum of their respective similarity vectors, and / or at any points of application the juxtaposition of their respective similarity vectors.

[0012] It is understood that, where applicable, the manipulations of similarity vector fields, described above, have a point-by-point impact on the constitutive similarity vectors of the footprint vector field, and on their individual method of calculation.

[0013] Furthermore, it may be useful in certain implementations of the invention to keep a history of the manipulations carried out (for each similarity vector its method of calculation of obtaining and the possible combinations with other vectors) in particular before finalizing a relational fingerprint, and classifying its constituents.

[0014] The field of imprint vectors comprises, according to the method of the invention, at least one disordered region and, where applicable, one regular region.

[0015] The representation of the footprint vector field(s) calculated according to the described method includes, to form the relational footprint, as appropriate: the set of calculated similarity vectors only part of the calculated similarity vectors all or part of the vectors resulting from a combination of the calculated similarity vectors.

[0016] In addition, the relational fingerprint can contain in particular for each similarity vector considered its calculation method and / or its disordered or unordered nature in the sense of an entropic criterion.

[0017] According to the process of the invention, the relational fingerprint is put into a form suitable for the realization of functionalities such as authentication in various configurations in different forms.

[0018] Thus, the relational fingerprint can consist of one or more classes of similarity vectors, depending on whether they are disordered or not, and / or obtained according to one calculation method or another, and / or geographically distributed in one way or another within an image, and / or independent or not of each other, and / or stable or not...

[0019] The relational fingerprint may contain only one class of similarity vectors, consisting of all or part of the similarity vectors forming the calculated fingerprint vector field.

[0020] The relational fingerprints of a set of subject images can refer to the same subject image. If so, the same subject image can be part of a second or subsequent set of subject images, each referencing a different reference image.

[0021] The relational imprint of a subject image can refer to a reference image of a different class (example of the subject image of a cellular material in reference to a reference image which is an image of a piece of paper, or even of a piece of a person's skin).

[0022] The relational fingerprint of a subject image can also refer to an image of the same class (for example, a banknote with its stub) or even to itself. In the latter case, the subject image can be transformed to generate a reference image, enabling a first-order similarity calculation of a fingerprint vector field, a region of which is disordered. Depending on a preferred method, the subject image is transformed into a negative (compatible with the dynamic range of the potential rendering device) before applying the similarity vector calculation phase.

[0023] The relational fingerprint of a subject image can also refer to an image of a given class, possibly formed and / or described at least partially by an image synthesis process such as a dynamic texture generation process. When the image synthesis process uses at least one input parameter belonging to a high-dimensional set, as in the case of a reaction-diffusion process with a (pseudo-)random input image, this or these input parameters can serve as a seed, possibly secret, to generate the corresponding reference image on demand.

[0024] A relational fingerprint can also be determined according to one or more reference images, allowing the process of the invention to be used in several environments, each using the same reference image, while maintaining a seal between the environments.

[0025] According to one feature of the invention, the method includes, prior to the recording phase, a classification step of similarity vectors into at least one class called disordered, and one class called regular, consisting of assigning each of the similarity vectors to one or the other of the classes according to a regional entropic criterion and a classification threshold.

[0026] According to one feature of the invention, when the similarity indicator is chosen to be calculated at a rank equal to one, each similarity vector is poured / added either into the disordered class or into the regular class, depending on whether or not it satisfies the entropic criterion, the zero vector being able to then be introduced / added respectively into the regular class, or into the disordered class respectively, as a complement.

[0027] The relational fingerprint can be recorded, for example, as a list of sets of similarity vectors linked to their reference points, according to their class of membership.

[0028] According to one feature of the invention, the relational signature is recorded for later use, preferably in a database or even in a graphic code.

[0029] According to one feature of the invention, the method includes a step of compressing the footprint vector field and recording the result of the compression as a relational footprint.

[0030] According to one feature of the invention, the recording of the relational fingerprint is associated with the recording of at least one of the images used.

[0031] It should be noted that, for the purposes of this invention, the term "recording" without further specification is understood in a broad sense, provided of course that it is compatible with the corresponding implementation of the invention. Thus, the term "recording" refers, for the purposes of this invention, to any recording in any suitable manner, whether in digital or analog form. Among the recording methods compatible with the invention, the following may be cited in particular: recording in any computer and / or electronic format, recording in printed form on a medium suitable for implementing the invention, photographic recording, in color or black and white, recording in holographic form, and recording in engraved form, particularly by laser, without this list being exhaustive.

[0032] For the purposes of this invention, a "block" is understood to be a portion of a scanned image containing spatial information about the structure or microstructure of a material object (for example, naturally occurring inhomogeneities), and / or information of a synthetic structural nature (for example, a synthesized pattern or pseudo-randomness), and / or local features calculated from this structural or microstructural spatial information (for example, local invariant descriptors). Within the context of this invention, the terms "texture" or "micro-texture" refer to what is visible or observable in an image, while the terms "structure" or "microstructure" refer to the material subject itself. Thus, a texture or micro-texture of the authentication region corresponds to an image of the structure or microstructure of the authentication region.

[0033] The similarity vector calculation phase includes: a step of determining a common frame of reference for the first and second images; a step of determining, in the first image, a set of reference tiles each associated with at least one reference point having coordinates in the common frame of reference; a step of searching in the second image for concordance tiles which are each paired with a reference tile with which they have a certain degree of similarity and are each associated with at least one reference point having coordinates in the common frame of reference; a step of calculating the coordinates of each similarity vector from the coordinates of the reference points of each reference tile and the associated concordance tile.

[0034] According to one feature of the invention, the similarity vectors are calculated in the plane or in a two-dimensional space.

[0035] The reference tiles may or may not cover the entire support image, may overlap, or may be disjoint, leaving part of the support image uncovered.

[0036] The reference tiles and / or their spatial distribution can be predetermined or self-adaptive. It is even possible to combine these two configurations for the same image.

[0037] We can predetermine them based on, for example: of a given grid, knowing that this grid can be made up of tiles of regular or irregular shape, size and position (distorted grid); or of a set of distinct unit tiles, of regular or irregular shape, size and position, with or without overlap;

[0038] The reference blocks and / or their spatial distribution can also be determined in a self-adaptive manner, automatically during the implementation of a local feature detection algorithm, for example.

[0039] The reference points and / or their spatial distribution can be predetermined or self-adaptive. It is even possible to combine these two configurations for the same image.

[0040] We can predetermine them based on, for example: nodes of a given grid, knowing that this grid may be regular or not (distorted grid); or of a point cloud.

[0041] Reference points and / or their spatial distribution can also be determined in a self-adaptive manner, automatically during the implementation of a characteristic point detection algorithm, for example.

[0042] The step of searching for concordance tiles may involve, for each reference tile, the calculation of a series of similarity indices between the portion of the first image corresponding to said reference tile and an inspection portion of the second image, the inspection portion being moved into the second image for each similarity index and selecting as the concordance tile associated with said reference tile, the inspection portion showing a remarkable degree of similarity with said reference tile.

[0043] The step of searching for concordance tiles may also include determining, in the second image, a set of inspection tiles, and, for each reference tile: the calculation of a series of similarity indices, each similarity index being calculated between the portion of the first image corresponding to said reference pad and the portion of the second image corresponding to an inspection pad, the inspection pad being different for each index, the selection as concordance pad associated with said reference pad, the inspection pad exhibiting a given degree of similarity with said reference pad.

[0044] The determination of the sets of reference and inspection tiles can be carried out in a self-adaptive manner by implementing a feature detection and feature description algorithm, for example from Law filters or local binary patterns (LBP) or signal level gradient(s) or on spatio-temporal distributions, for example integrated into the following methods: A-KAZE, SURF, SIFT, ORB.....

[0045] The step of searching for concordance blocks can still be done by combining the two approaches described above, sequentially and / or simultaneously.

[0046] According to the invention, the similarity between two tiles is evaluated using a calculation method, with a similarity indicator and a chosen similarity rank n (the first maximum if n=1, the second maximum if n=2, etc.). The value of this index, called the similarity index (positive or absolute), is higher the more similar the tiles are. The remarkable degree of similarity is the highest similarity index in the series of similarity indices calculated for a given reference tile and for a given calculation method.

[0047] According to one feature of the invention, the degree of similarity corresponds to the rank of the inspection pad selected as the concordance pad in the series of inspection pads ordered according to their index of similarity with the reference pad in descending order.

[0048] Standardized correlation or correlation by difference can be used as a type of similarity indicator. More generally, the inverse of a suitable distance or divergence can be used as a similarity indicator. The similarity indicator can also be applied to the matching of characteristic points of interest detected and quantified using local descriptors between tiles, for example, derived from Law filters or local binary patterns (LBPs), or from gradients calculated on signal levels or spatiotemporal distributions. Thus, the comparison means integrated into the following methods: A-KAZE, SURF, SIFT, ORB, etc., can be used as similarity indicators within the meaning of the invention.

[0049] According to one feature of the invention, during the calculation phase of similarity vectors between the first and second images, the local similarity indicator is chosen at a local rank greater than or equal to one.

[0050] According to one feature of the invention, the two implemented images are identical and a rank 2 similarity indicator is chosen to calculate the similarity vectors in determining the relational fingerprint.

[0051] According to the method of the invention, the similarity vectors are calculated up to a sufficiently high rank to obtain a field of footprint vectors comprising at least one disordered region in the sense of an entropic criterion.

[0052] In the context of the invention, the entropic criterion is intended to determine whether a candidate similarity vector is disordered or not with respect to similarity vectors located in one of its neighborhoods, the shape and size of which are predefined. This binary criterion consists, for example, of applying a predefined threshold to an unpredictability index, evaluated in the neighborhood, such that 5 is the entropy of the (normalized) histogram of the orientation of the similarity vectors, possibly weighted by their norm. The entropic criterion is then verified, and the candidate similarity vector will be classified as disordered (i.e., placed in the class of disordered vectors) when the unpredictability index has a value greater than (or equal to) the threshold value (for example, 1 BIT). Otherwise, the candidate similarity vector will be placed in the regular class.Alternatively, the ratio of the mean to the standard deviation of the magnitudes of similarity vectors in the neighborhood of a candidate similarity vector can be considered an entropic criterion. If this ratio is greater than 1, the candidate similarity vector typically joins the disordered class; otherwise, it is placed in the regular class. It goes without saying that a compromise between neighborhood size and discrimination precision must be sought. Similarly, the shape of the neighborhood can be important depending on whether one is working with rows, columns, or rectangular blocks. Other entropic criteria are applicable within the scope of this invention. For the purposes of the invention, when a region of a similarity vector field of rank n includes, in a connected region, a dense set of similarity vectors that are all disordered, in the sense of lacking an underlying rule and exhibiting a chaotic appearance, it is said to be disordered of rank n.Otherwise, it is said to be regular, in the sense of the existence of an underlying rule, for example in the sense of the regularity of the underlying vector field it represents and the continuity of the associated field lines. One can also, for example, speak of an ordered class as illustrated in [reference]. figure 7 , insofar as the angular distribution on the right is only slightly dispersed, whereas for the disordered class, the angular distribution is completely dispersed over the 360° of the unit circle. Similarly, as illustrated in figure 14 , we can speak of a regular class in 14-B insofar as the applicable rule is 'the most matches in the blank print area' whereas in 14-A there is an absence of a match on the area considered, therefore implicitly a disorder of the match.

[0053] The images used in the invention must have, at least in certain regions, locally variable spatial structures so as to allow for a meaningful evaluation of the similarity, as defined by the similarity indicator, between reference areas of the first image and portions or inspection areas of the second image. For the purposes of this invention, locally variable structures refer to the presence of image attributes such as contours and / or textures, possibly multi-scale, capable of characterizing the subject image's membership in a class of images or of characterizing the subject image within the same class of images.

[0054] According to one feature of the invention, the reference image for each material subject is the inverted image of the image of the material subject, reference image used for the method of determining the relational imprint.

[0055] According to one feature of the invention, the reference image is identical for all the material subjects considered.

[0056] According to one feature of the invention, a concatenation of several images can be used as a reference image, which amounts to calculating similarity vectors on the same starting image relative to several material subjects, for example, or material subjects and synthetic images.

[0057] The term "image" should be understood in its broadest sense and not limited to the sole meaning of an optical image resulting, in particular, from the exposure of the authentication region to visible light. Thus, authentication and verification images can be obtained by any type of exposure of the authentication region in conjunction with a suitable acquisition chain, provided that the same type or nature of exposure is used for both the authentication and verification images. Among the types of exposure or acquisition methods that can be considered are: ultrasound, far-infrared, terahertz, X-rays or gamma rays, X-ray or laser tomography, X-ray radiography, and magnetic resonance imaging, without this list being exhaustive.The term image in the sense of the invention can also be understood as a 3D representation of a material subject with an adapted micro_texture representing the stable, intrinsic, unique and non-reproducible microstructure of the material subject in question.

[0058] Optical and / or digital image enhancement preprocessing can be applied to improve the signal-to-noise ratio and / or visual perception. Examples include optical (variable focal length devices) and / or digital zoom to better select the viewing scale, image deconvolution to eliminate focus errors or camera shake, bandpass filtering to select / prioritize details in intermediate frequencies, and contrast enhancement to accentuate contrast.Thus, to facilitate the visualization of the relational fingerprint, the authentication and verification images can, prior to being displayed or even saved, undergo one or more enhancement processes such as, for example, increased contrast, increased brightness, equalization of the grayscale histogram levels, equalization of the histograms in the decomposition colors, and bandpass filtering. In this regard, it should be noted that the method according to the invention can be implemented with grayscale images and / or with color or multispectral images, or even binary images.

[0059] According to another feature of the invention, the position of the authentication region on the item to be authenticated is recorded. Such recording, although not strictly necessary, facilitates the verification phase.

[0060] According to yet another feature of the invention, the position of the authentication region on the item to be authenticated is marked on the item. This marking, although not strictly necessary, also facilitates the verification phase.

[0061] According to one feature of the invention, the calculation phase of the footprint vector field includes, prior to the calculation of the footprint vector field, a transformation step of one and / or the other of the first and second images.

[0062] According to one feature of the invention, the applied image transformation step consists of at least one geometric transformation applied locally to an image selected from among linear transformations or combinations of linear transformations. Preferably, the transformation is a transformation with at least one fixed or quasi-fixed point. By quasi-fixed point, it is understood that a point undergoing a very small displacement.

[0063] According to another characteristic, image transformation induces a reduced or small or very small amplitude modification of the modified image portion of the image of the authentication region before modification.

[0064] According to yet another feature of the invention, the relative displacement is a translation, a rotation or a combination of one or more rotations and / or translations.

[0065] According to yet another feature of the invention, the relative displacement distance is reduced or of small or very small amplitude.

[0066] According to one feature of the invention, the transformation step is a recalibration.

[0067] According to one feature of the invention, the method includes, prior to the calculation phase, a parameterization step comprising the determination of at least one of the following parameters: size, shape, position of the reference pad(s) applied to the first image, predefined spatial distribution of the reference points or algorithm used and initial data to determine them size, shape, position of the inspection pad(s) applied to the second image, similarity indicators chosen and where applicable the rank(s) to be used, where applicable as initial value(s) during an incremental search for a disordered region, order(s) of use of the first and second images, size, shape of the neighborhood for the evaluation of the entropic criterion, threshold density from which a connected region formed of disordered vectors is declared disordered size, shape, position of the reference and / or concordance pads, order of use of the first and second images, size and shape of an evaluation window for determining the existence of a disordered region.

[0068] According to one feature of the invention, the method includes a step of using as a relative or relational signature of one image with respect to another a digital representation of the relational fingerprint.

[0069] According to one feature of the invention, the method includes a sensory representation step of the relational imprint. This sensory representation is preferably visual and / or auditory and / or tactile.

[0070] According to one feature of the invention, the calculation phase of the footprint vector field comprises: a step of calculating several intermediate similarity vector fields between one of the two images and the other image having undergone a different transformation from one intermediate similarity vector to another, comparing the intermediate similarity vector fields with each other and preserving as an imprint vector field the intermediate similarity vector field exhibiting an optimum of similarity, maximum or minimum.

[0071] According to one feature of the invention, the method includes, prior to the recording phase, a step of decomposing the field of similarity vectors into at least one part called regular and one part called disordered, consisting of assigning each of the similarity vectors to one or the other of the regular and disordered parts according to a regional entropic criterion.

[0072] According to one feature of the invention, when the local optimum of similarity is chosen at an order equal to one, for a local rank considered, the relevant similarity vector is added either to the disordered component of the footprint vector field, or to the regular component of the footprint vector field, depending on whether or not it satisfies the regional entropic criterion, the zero vector then being added respectively to the regular component, or to the disordered component.

[0073] According to one feature of the invention, the method includes a relational fingerprint coding step, a digital formatting, in order to obtain a relational signature of an image with respect to a reference image, which can serve as a robust unitary authenticator of the subject image or the imaged material subject.

[0074] In this latter case, originating from the material subject and not corresponding to it as a mere identifier, the relational signature is intended to unambiguously distinguish the material subject (uniqueness and intrinsic character, hence non-reproducibility) while being regenerable at any moment from a new image acquisition, and stable over time within the framework of the material subject's normal evolution. The reference image can be a natural or synthetic image of a completely different nature from the initial image (for example, the relational signature of a piece of paper compared to a piece of sintered bronze or even a piece of leather).

[0075] The coding of the relational fingerprint then constitutes a step in obtaining the relational signature where the similarity vectors, in particular the similarity vectors of the disordered class, are subjected to quantification according to the "letters of a coding alphabet", typically but not exhaustively binary, quaternary or other.

[0076] The coding step can preserve the sequencing of the relational fingerprint's similarity vectors according to the topology of the reference image from which they originate. Within a hierarchical access system for the random fingerprint, the coding step can use a pseudo-random permutation of the obtained letters, generated using a secret seed.

[0077] According to a preferred embodiment of the invention, the encoding of the relational fingerprint's similarity vectors is performed according to their orientation, using a compass rose subdivided into equal angular sectors, typically in quaternary mode {Northeast, Northwest, Southwest, Southeast} or in binary mode {Northeast\Southwest, Northwest\Southeast}. Quantization can be followed by bit assignment according to, for example, a Gray code, and / or compression, for example entropic, range-based, or Huffman-type, or algorithmic, for example dictionary-based.

[0078] In a preferred form, the relational signature is a concatenated bit string, obtained by encoding the similarity vectors of the disordered class according to the Northeast \ Southwest and Northwest \ Southeast angular sectors in which its similarity vectors are inscribed.

[0079] A relational signature can be used to discriminate and / or identify the subject image in a set of images or the material subject object of its acquisition in a set of material subjects.

[0080] A relational signature can be obtained from a reference image which is a transform of the subject image. It then takes on a more "absolute" character.

[0081] The relational signature, as an example of practical application, allows for the stable and certain discrimination of a paper sample within a ream of paper: a set of 200 material subject elements, centimeter-sized portions of imaged paper sheets, are considered here. The relational signature exhibits a more "absolute" character insofar as the reference image is the complement to 1 of the standardized image of a material subject.The implementation parameters are: a distribution of reference points according to the nodes of a regular grid with a step size of 24x24 pixels; reference tiles, of size 64x64 pixels, centered on these reference points; for each reference tile, four inspection tiles of size 64x64 pixels partitioning an inspection portion of 128x128 pixels centered on the reference points; , the standardized centered correlation at rank 1 as the calculation method (calculation of the series of similarity indices by superimposing the current reference tile on each inspection tile considered, and choosing as the concordance tile the one with the highest similarity index) and a neighborhood size of 3x3 (i.e. the 8 similarity vectors surrounding the current vector) considered for the evaluation of the entropic criterion.The disordered class / component is thus composed of 11 x 15 = 165 vectors (Figure where every other vector is represented) whose Northeast / Southwest direction, coded "0", or Northwest / Southeast direction, coded "1", gives a 165-bit binary signature. The normalized Hamming distance measured between signatures from different subject images of distinct material subjects is on average (49.987 ± 4.659)% with a bias of less than 0.02%. The Hamming distance measured between signatures from different subject images of the same material subject, after image registration, is on average (5.454 ± 1.967)%. The two distributions are quantitatively separated by 12.452 in the sense of the absolute difference between their means normalized by the square root of the half-sum of their variances.This provides a relevant discriminatory power for the automatic use of relational signatures from the perspective of unitary authentication of material subjects in families containing several million or billion individuals.

[0082] The relational signature can be used as a seed, for example at the input of an algorithm for generating pseudo-random numbers or images.

[0083] Relational signatures can be used within cryptographic mechanisms.

[0084] When the subject image results from the acquisition of an image of a physical subject, a relational signature, which then contains true randomness, can be refined by algorithmic reprocessing. The relational signature can be subjected (without transcoding if it is binary) to a Von Neumann correction and an exclusive OR operation, or to a hash function, or even to a resilient function in order to constitute a random number generator.

[0085] As such, the relational signature can constitute an image to be shared within the framework of a visual sharing of a secret (this is referred to as visual cryptography when the relational signature satisfies the criteria of a sequence of independent random numbers). In a preferred form, the relational signature results from a relational fingerprint reduced to its disordered class / component, quantified according to the Northwest (NW or 1), Southwest (SW or 2), Southeast (SE or 3), and Northeast (NE or 4) angular sectors in which its similarity vectors are inscribed. By substituting each quaternary code with a triangular submatrix respectively upper right, upper left, lower left, and lower right, the shared image thus constructed possesses a texture of elementary triangular shapes.In a secret two-participant sharing, the second shared image can be constructed, for example, by considering the same triangle as that adopted in the first shared image at the same location if the bit of the secret message at that location is 0, by considering the opposite triangle (e.g. SE if the triangle in the first shared image was NO) if the bit of the secret message at that location is 1. When the subject image results from the acquisition of an image of a material subject, the first shared image may not be saved but reconstructed from a new acquisition of the material subject.

[0086] According to the invention, the triangular texture of the shared images can be used to introduce an anti-fraud mechanism for the shared images. An additional image, stored by the trusted third party when constructing the images to be shared, can be used during the decryption of the secret message. This additional image, the same size as the shared images, is designed to point to the triangle opposite the triangle associated with each quaternary code in the first shared image after the construction of the second shared image, by means of a sub-matrix that is zero except in the West (W), South (S), East, or North (N), respectively.The second shared image is constructed by copying the corresponding triangle from the first shared image if the message bit is 0, so that the superposition of the two shared images produces a triangle at that location. If the message bit is 1, a different but not opposite triangle is randomly or pseudo-randomly selected, so that the superposition of the two shared images produces a notch (and not a square) at that location. At this location, the additional image is constructed so that, when superimposed on the two shared images, the resulting shape is a right angle if the message bit is 0, and a square (rectangle) if the message bit is 1. To illustrate: if the code at position i of the relational signature is 1, a triangle NO is created at that position in the first shared image (within a square submatrix).If the message bit is 0, a triangle N0 is created at that same position in the second shared image, and a sub-matrix (of the same size), zero except at E (or S depending on a [pseudo-]random selection), is created in the additional image. If the message bit is 1, a triangle S0 (or NE depending on a [pseudo-]random selection) is created at that same position in the second shared image, and a sub-matrix zero except at E (respectively S) is created in the additional image. In this way, the fraudulent substitution of one triangle for another in a shared image results in the following: when the two shared images are superimposed, a square appears on average half the time at the message location instead of a notch; when the two shared images and the additional image are superimposed, a notch appears on average half the time at the background location (the area complementary to the message) instead of a right angle.

[0087] The relational signature can also be used to authenticate the subject image according to a knowledge-free protocol. Because it does not reveal the structures of the subject and reference images, the relational signature can be advantageously used as a response to a challenge consisting of a model synthesis of a class of reference images. A shared secret seed, or one derived from the relational signature, can be used upon receiving the challenge to generate the reference image according to the model (which can be defined down to the seed level by an equation, typically in the case of a reaction-diffusion algorithm). The relational fingerprint between the subject image and the generated reference image is then determined, hence the associated relational signature.When the subject image results from the acquisition (under predefined conditions) of an image of a material subject not clonable at the acquisition scale, the material subject in question can be used as a physical unclonable function (of the type "Physical Unclonable Functions") intended for its authentication through the previous challenge / response pairs.

[0088] According to one feature of the invention, the same reference image is used as the first and second image systematically for a set of images, allowing the calculation of a set of relational signatures according to the same reference.

[0089] According to one feature of the invention, the method for determining a relational fingerprint is implemented with at least one image of a material subject exhibiting an area with intrinsic and random microtexture. In certain embodiments, this area with intrinsic random microtexture can be referred to as an authentication area. In this regard, the inventors have demonstrated that the relational fingerprint within the meaning of the invention can be determined from images of areas with intrinsic and random microtexture without requiring these areas to have shapes, contours, or patterns with a dimension significantly larger than that of the intrinsic random microtexture.

[0090] In the context of the invention, the microtexture is intrinsic and random in that it results from the very nature of the authentication zone. In a preferred embodiment of the invention, each subject to be authenticated belongs to families of subjects comprising at least one authentication region with an essentially random intrinsic structure that is not easily reproducible, i.e., whose reproduction is difficult or even impossible because it results from a process that is not predictable at the observational scale. Such an authentication region with an essentially random, not easily reproducible intrinsic continuous medium structure corresponds to Physical Unclonable Functions (PUFs), as defined in particular by the English publication Encyclopedia of Cryptography and Security, 01 / 2011 edition, pages 929 to 934, in the article by Jorge Guajardo.Preferably, the authentication region of a material subject conforming to the invention corresponds to an intrinsic non-clonal physical function designated in English by "Intrinsic PUFs" in the aforementioned article.

[0091] The inventors take advantage of the fact that the random nature of the authentication region's microstructure is inherent or intrinsic to the very nature of the subject, resulting from its process of creation, development, or growth. Therefore, it is unnecessary to add any particular structure to the authentication region, such as an impression or engraving. However, this does not preclude the use of natural or introduced singularities to facilitate registration and / or relative scaling, for example, or any other transformation of one image relative to another.

[0092] The inventors further demonstrated that a regular similarity vector field is visually apparent only when the images of random structures are identical up to minor modifications, and not apparent when the images are not identical up to a transformation or small deformations, or when they do not result from the acquisition of the same authentication region from a subject. It should be noted that visually, the similarity vectors of a regular similarity vector field appear to be carried by underlying field lines.

[0093] The invention can thus ensure unitary visual authentication via relational fingerprinting and sensory conditioning while allowing, as previously discussed, automatic unitary authentication via relational signature.

[0094] The visualization of a sufficiently dense similarity vector field, whether regular or not, also allows, within the framework of the invention, for the operator to be reassured or confident in their decision-making process regarding the authenticity of the item to be authenticated. In this respect, it should be emphasized that the invention eliminates doubt as to the authenticity of the item to be authenticated insofar as a regular similarity vector field is observed. Authenticity is then certain (provided the implementation conditions are properly met). Conversely, if a regular vector field is not observed, it is possible to conclude with certainty that the item is not authentic, provided that strict implementation parameters have been respected and that the physical item has not undergone excessively damaging alterations between its recording and its verification.

[0095] Furthermore, the inventors have demonstrated that, provided the physical subject exhibits sufficient stability over time, images taken at different times, even if separated by several days, months, or years, can, according to the invention, generate such regular similarity vector fields. Moreover, according to the invention, the subject to be authenticated can undergo modifications after the authentication image is recorded while remaining authenticable, insofar as a portion of the authentication region has not been significantly affected by these modifications, whether intentional or not.

[0096] According to one feature of the invention, a candidate relational signature is automatically compared with a previously recorded authentic relational signature, in a database for example, according to a statistical similarity criterion allowing the candidate relational signature to be considered as similar to the recorded relational signature if a decision threshold is reached.

[0097] According to one feature of the invention, for each implemented relational signature, at least one image used to generate a relational signature is an acquisition from a reference area of ​​a physical subject, said reference area having an intrinsic and random microstructure, also called a non-clonable physical structure (PUF). In this context, validation based on reaching the decision threshold also implies that a candidate physical subject is similar to, or even identical to, the reference physical subject. The relational signature for the candidate subject is then established from at least one image of an authentication area or region of the candidate subject having an intrinsic and random microstructure.Similarly, the relational signature relating to the reference or authentic subject is established from at least one image of an authentication zone or region of the authentic subject having an intrinsic and random microstructure. There will be identity or similarity of the relational signatures if the authentication zones are identical or similar. For the purposes of the invention, the image is said to be of the zone with an intrinsic and random microstructure in that the image includes at least said zone but is not necessarily composed solely of that zone.

[0098] According to one feature of the invention, the authentication and / or verification images undergo at least one descreening and / or filtering (bandpass, for example) before being implemented as described in the invention. This feature makes it possible to eliminate any periodic patterns that could interfere with or hinder the proper execution of the various steps involved in determining a viable relational fingerprint or relational signature in the case of an authentic subject.

[0099] The process of analyzing the characteristic relationship between two images through a relational fingerprint also allows the use of cognitive representations of this fingerprint to determine, at a glance, the total or partial degree of similarity between the two images. This involves conditioning, a cognitive shaping of the relational fingerprint so that it can be perceived and interpreted by a human, or even a humanoid, in a sensory authentication process. This conditioning complements conditioning in the form of a relational signature: the former is primarily designed to enable intuitive decision-making at the user level, while the latter is primarily designed to enable automated decision-making by a machine.These conditions can converge when relational signatures are implemented according to our process for the purpose of visual cryptography, and it is the user who must judge the result obtained (intelligible, possible attack, aesthetic aspect,...) or more generally when a relational signature is used to produce an effect perceptible to a user.

[0100] In this document, we refer to the conditioning of the relational imprint as a relational stimulus, a signal capable of being perceived by the sensory system of an average user and allowing them to interpret it. Perception is understood to include visual, auditory, olfactory, tactile, and gustatory perceptions, as well as temporal and spatial perceptions, whether experienced in whole or in part, separately or simultaneously. We will speak of sensory authentication in general, and of visual, tactile, auditory, etc., authentication respectively, depending on whether it utilizes the user's visual, tactile, auditory, or other abilities.

[0101] During the relational stimulus shaping stage, a preferred mode is to rely on the user's visual (SVH) and / or auditory and / or tactile and / or audiovisual and / or spatio-temporal perception abilities.

[0102] As an example of a relational stimulus, from a given relational imprint can be a representation of it in the form of a colored or uncolored image, with one or more distinct 1D, 2D or even 3D regions, which will appeal to the user's visual perception abilities.

[0103] Possibility of representing with different colours depending on the class(es) constituting the relational footprint.

[0104] An embodiment of the invention as a method for visually authenticating a candidate image against an authentic image is characterized in that it comprises the following steps: implementation of the process of determining a relational fingerprint with the authentic image as the first image and the candidate image as the second image, or vice versa, visual, graphic presentation of one or more classes of similarity vectors constituting the relational fingerprint, on one of the two images implemented, conclusion of at least partial or regional authenticity of the candidate image relative to the authentic image, in case of observation of at least one regular region in the visualization resulting from the determined relational fingerprint.

[0105] The visual verification phase may include, prior to the presentation stage, a step to search for an authentic image to compare with the candidate image. This step may involve determining the relational signature of the candidate image, followed by sending the determined relational signature to a server. In response to this transmission, and based on the relational signature, the server automatically sends one or more authentication images to the electronic verification device for use in the presentation stage. The server will then contain a database of authentication images indexed based on a relational signature and, optionally, an identifier for the subjects to be authenticated.The verification can then consist of quantitatively comparing the signature extracted from the candidate subject either to the signature pointed to as a reference in the database (one-to-one authentication), or to a subset of n signatures identified in the database (n small, typically on the order of 1 to 10) as the closest signatures and / or the most probable authentic subjects (1-to-n identification), the corresponding authentication images can then be submitted to the operator's visual recognition or transmitted as such for execution by the operator of the process that is the subject of the invention.

[0106] An extension of the use described above consists of the following: the support image on which the visualization of one or more classes of similarity vectors constituting the relational fingerprint is applied, is made up of the fusion (blending according to alpha channel) of the candidate and authentic images, the images are implemented in such a way that they can show a Glass type effect if they are at least partially.

[0107] This provides a user with additional assistance that is particularly valuable when the Glass-type phenomenon is not obvious enough or when the user is not sufficiently aware of its detection.

[0108] Another method of using the invention's process as a method for authenticating a candidate image against an authentic image involves a relational stimulus other than a visual one and includes the following steps: a- RECORDING: determination of a relational imprint between the authentic image and a chosen reference image, determination of a relational stimulus, from the relational imprint, addressing at least one chosen type of perception, between the authentic image and a chosen reference image, implementation of a support content compatible with the chosen type of perception, recognizable or intelligible by the user, modulation of the support content with all or part of the relational stimulus, the result of the modulation being generally little or not recognizable or intelligible by the user, recording of the result of the modulation of the support content and where appropriate indexing with the authentic image and / or the chosen reference image, accompanied where appropriate by the chosen type of perception.b- CONTROL: determination of a relational imprint between the candidate image and the chosen reference image, determination of a relational stimulus, from the relational imprint, addressing the same type of perception as that used with the authentic image during its recording, between the candidate image and a chosen reference image, implementation of the result of the modulation corresponding to the authentic image, attempt to de-modulate the result of the modulation with all or part of the relational stimulus determined from the candidate image, conclusion of the authenticity of the candidate image in relation to the authentic image in case of clear or intelligible perception by the user of at least part of the support content demodulated by the candidate image.

[0109] The invention also relates to a method for the individual authentication of each physical item in a set of physical items, characterized in that it consists, for each item in the set, of: implement the method of determining a relational fingerprint as described above between an authentic image of the material subject and a reference image, and record the relational fingerprint, calculated in association with an authentic image of said material subject, when authenticating a material subject; implement the authentication method according to the invention.

[0110] It is entirely possible to use a relational signature which is implemented in place of a relational fingerprint.

[0111] Authentication can be achieved through a relational stimulus and can appeal to human cognitive functions, in particular by implementing one of the user's memories.

[0112] It can also be anticipated that the steps described above can be implemented repeatedly or successively by a user who interacts primarily through touch, speech, and / or vision with a device in a temporal and / or spatial manner. This allows for the creation of real-time, engaging effects that refine decision-making and / or establish a link between two images, two products, or a user and a product, all under the guise of an action that, at first glance, appears unrelated.

[0113] The use of a smartphone, tablet, or laptop-type terminal seems particularly relevant for this interaction, via a dedicated application / computer program, which would allow the user to benefit from this application and its publisher to gain knowledge about this user, their network, etc., via data captured or present in the terminal.

[0114] The invention also relates to an electronic device that can be used for either implementation of the authentication method according to the invention, particularly for the verification phase. Preferably, but not strictly necessary, the electronic device includes a touchscreen display and is adapted to allow the magnification of the authentication image and / or the verification image to be changed by moving two contact points on the touchscreen. The touchscreen can also be used to control the relative movement of the displayed images.

[0115] Numerous implementation schemes for the present invention are possible, particularly in the security and marketing environment, and can also integrate product family recognition, 1D or 2D barcodes or other, be coupled with NFC or RFID chips.

[0116] The invention is likely to find applications in various fields, such as in a supply chain traceability process where the different stakeholders—producer, distributor, retailer, and consumer—are all interested in verifying authenticity, each with different financial and technical means at their disposal to ensure this verification. A producer holding intellectual property rights may be interested in knowing if a product being inspected is in the correct place in the supply chain (monitoring parallel markets), while a consumer is primarily concerned with whether the product in question is genuine or whether they can benefit from advice or advantages associated with an authentic product.All of this can be implemented as previously indicated with joint use of an automatic unit authentication means (relational signature and / or identifier) ​​and a sensory authentication means as described in this invention.

[0117] The invention can be implemented in various authentication, identification, integrity control, and visual cryptography applications. In this regard, it should be considered that, within the context of the invention, the terms "authentication," "identification," and "integrity control" may be considered equivalent depending on the intended application.

[0118] An important application of relational fingerprinting is when, according to the method of the invention, a relational fingerprint of an image of a material subject is calculated relative to a reference image, and all or part of this relational fingerprint is used to register the image of the material subject relative to the reference image. This is generally done prior to determining a relational signature or a relational stimulus.

[0119] This preferred mode can be implemented for a set of images from a set of physical subjects, and the registration is thus performed automatically according to the same reference image. The use of similarity indicators such as detectors / descriptors like SIFT, SURF, ORB, or A-KAZE can be particularly useful for this purpose.

[0120] It is also possible to use distinct classes of similarity vectors present in a relational fingerprint, to on the one hand re-register images from a material subject, but also to calculate one or more relational signatures and / or one or more relational stimuli.

[0121] The present invention also enables integrity checks to be performed, in particular by using visual authentication between a candidate image and an authentic image supposedly originating from the same material subject or from a material subject belonging to the same family. If the compared regions are intact, then a regularity will appear in at least one similarity vector field corresponding to these regions, without major discontinuities; whereas if part of these regions has undergone a modification, then dissimilarities must appear at that location, reflected by the presence of a local irregularity in the field.

[0122] Among the material subjects comprising an authentication region suitable for implementing the authentication process according to the invention, it is possible to mention in particular: paper and cardboard packaging; fibrous materials; sintered metallic, plastic, ceramic or other materials; alveolar or cellular materials; leathers including shagreen; wood; metals in particular machined, stamped, molded, injected or rolled; plastics; rubber; woven or non-woven textiles (with possible unweaving); certain pelts or feathers; images of natural scenes such as landscape images, images of buildings, images of walls or roads; biometric prints, skin and fingerprints, the iris of an eye; works of art; powdered products or materials without this list being either limiting or exhaustive.

[0123] Of course, the different characteristics, variants and forms of implementation of the process according to the invention can be associated with each other in various combinations insofar as they are not incompatible or exclusive of each other.

[0124] Various aspects of the invention will emerge from the description below, made with reference to the attached figures which illustrate non-limiting examples of implementation of the invention. There figure 1 Explicit methods for calculating similarity vectors at a given rank, The figure 2 shows an example of a similarity vector field obtained in the context of an implementation of the process according to the invention, The figure 3 shows another example of a similarity vector field obtained in the context of an implementation of the process according to the invention, The figure 4 represents a field of fingerprint vectors resulting from the superposition of similarity vector fields, The figure 5 represents another field of imprint or similarity vectors resulting from the implementation of so many subject images formed by a sheet of paper, The figure 6 illustrates a representation of the relational imprint illustrated at the figure 5 There figure 7 illustrates the angular distribution of a disordered class and a regular class of similarity vectors of the footprint vector field of the figure 5 , There figure 8 illustrates a binary or quaternary coding method for a similarity vector of a relational fingerprint, The figure 9 illustrates statistical results obtained by binary coding of relational fingerprints, thus forming relational signatures. figure 10 illustrates a quaternary coding according to the compass rose of a relational imprint according to the invention, The figure 11 explicitly describes a visual cryptography-type scheme constructed from a relational signature according to the invention, The figure 12 illustrates another visual cryptography-type scheme with an image integrity verification by a trusted third party based on a quaternary relational signature, The figure 13 illustrates two cases of relational stimulus (here visual) resulting from the cognitive conditioning of a relational imprint according to the invention, The figure 14 illustrates another type of relational stimulus in the graphic form of colored segments, The figure 15 illustrates an application of integrity control for a printed pattern, The figure 16 illustrates a biometric authentication method through the visual presentation of the relational fingerprint between two different skin imprint acquisitions.

[0125] According to the invention, the similarity between a first image and a second image, or between parts of these images, is evaluated using a similarity indicator that gives a positive value that is all the greater the more similar the first and second images, or their respective parts, are. The standardized correlation coefficient method (in the statistical sense) is a preferred similarity indicator for the invention. Correlation indicator methods in general, such as the difference correlation indicator, are examples of other similarity indicators. The inverse of a distance or divergence (in the mathematical sense) between the images or their parts constitutes yet another family of possible similarity indicators.

[0126] Thus, different calculation methods can be implemented. For illustrative purposes only and not as an exhaustive list, the figure 1 This demonstrates a first example of calculating a similarity vector based on the standard central correlation coefficient (as a similarity indicator) at rank 2, using as the first image 1-A the image, with dimensions of 1637x1601, of a leather bag. In this context, the leather bag is the material subject.

[0127] According to this first example, the second image, 1-B, with dimensions of 768x825, is an image of a portion of semi-rigid foam packaging. A similarity index is calculated between a reference pad from the first image, 1-A, and inspection pads 1, 2, and 3, with dimensions of 128x128, from the second image, 1-B. The values ​​of the standardized correlation coefficient obtained (as similarity indices) are, respectively, -0.029 (pad 1), -0.050 (pad 2), and 0.032 (pad 3). By ordering the absolute values ​​of these similarity indices in ascending order, rank 1 corresponds to tile 2, rank 2 to tile 3 and rank 3 to tile 2. The similarity vector at rank 2 applied to the reference point, center of the reference tile a, then points towards the center of the concordance tile at rank 2, here the center of tile 3, it being considered that the coordinates of these two centers are determined in the same orthonormal coordinate system and the norm of the similarity vector is normalized to 1.

[0128] The figure 1 This also shows a second example of calculating a similarity vector using the standardized centered correlation coefficient (as a similarity indicator) by implementing the same image 1-A as the first image and a 1142x1162 ceramic image as the second image 2-C. The reference tile b is then successively compared to each of a series of inspection tiles corresponding to the 128x128 tile / translated one pixel at a time. The resulting standardized centered correlation coefficient values ​​(as similarity indices) constitute a 255x255 correlation figure with local extrema of different ranks, represented as a 1-D grayscale image or a 1-E grayscale surface.The similarity vector at rank 2 applied to the reference point, center of the reference block b, then points towards the center of the concordance block offering the local maximum of rank 2 among the values ​​of the calculated correlation coefficient (similarity indices).

[0129] According to a third example of implementation of the invention illustrated figure 2 The similarity vectors are calculated using the standardized centered correlation coefficient (as a similarity indicator) on the subject image of a leather bag element 2-A and the reference image of a semi-rigid foam packaging element 2-B after filtering the images using a bandpass filter (here the real part of a Gabor wavelet) 2-C between the 128x128 reference area and the 128x128 inspection area shown in solid lines, respectively in dashed lines, extracted from the filtered images 2-D and 2-E. The similarity vectors at rank 2 (respectively at rank 1) associated with the secondary (respectively primary) local maxima of the correlation figures are indicated in white (respectively in black) in the corresponding correlation figures 2-F in solid lines and 2-G in dashed lines.

[0130] According to a fourth example of implementation of the invention illustrated figure 3 The first image, 3-A, is used as a ground glass subject image, 384x384 pixels, acquired by reflection under diffuse lighting. The second image, or reference image, 3-B, of the same size, synthesized by reaction-diffusion from a seed, is used as a second image or reference image. Image 3-C shows a first-order similarity vector field calculated using standardized first-order correlation as a similarity indicator and comparing 32x32 reference tiles from image 3-A, each centered on a node of a regular 32x32 grid, to 32x32 inspection tiles from image 3-B. Each similarity vector is then applied to the center of a reference tile and directed towards the center of the inspection tile with the highest similarity coefficient to that reference tile.The norm of each similarity vector corresponds to the value of said similarity coefficient, given that the coordinates of these two centers are determined in the same orthonormal coordinate system.

[0131] There figure 4 This shows a footprint vector field (bottom) formed by the superposition of a similarity vector field calculated according to a regular grid by a first method at rank k (top) and a similarity vector field calculated according to points of interest by another method at rank I (middle). Each of the similarity vectors is plotted at its point of application in the footprint vector field and vectorially summed, where applicable, with the similarity vectors that apply at that same point.

[0132] There figure 5 This illustrates the graphical representation, forming a footprint vector field, of a first-order similarity vector field obtained by comparing a first image, whose subject is a first printed pattern document, with a second image, or reference image, whose subject is a second document with the same printed pattern but distinct from the first. The similarity vector field is calculated by correlating reference tiles and inspection portions, centered on the nodes of a 64x64 reference grid, with interpolation of the correlation peak in the vicinity of the maxima maximorum.

[0133] There figure 6 illustrates a representation of the relational imprint extracted from the figure 5 where its listed ( Fig. 6-A ) in pixels the u and v coordinates of each of the similarity vectors whose application (reference) points are distributed according to a regular grid ( Fig. 6-B ) of step 64x64 and starting at x=0 and y=175 to end at x=1856 and y=1455, according to three classes of similarity vectors after using an entropic criterion (see the figure 7 ): the disordered class that occupies most of the figure 5 , then two regular classes corresponding to the printed pattern areas, respectively in the upper left and lower right. The graph ( Fig. 6C ) corresponding to the calculation of the points (x+u, y+v), without applying a scale factor for visualization as used for vectors figure 5 This also allows you to quickly see the three classes mentioned above. Note that the grid spacing (x,y) can be saved in an associated parameters file, or alternatively, within the relational footprint itself.

[0134] There figure 7 This illustrates the angular distribution of the disordered class and a regular class, as previously mentioned, obtained using an entropic criterion of the histogram type for the angular distribution of similarity vectors in a 1x5 neighborhood around each similarity vector (here, the two aligned similarity vectors on either side of the considered similarity vector, excluding edge effects). The unit circle is divided into eight angular sectors of 45 degrees each, and the distribution is analyzed according to whether the angles of the similarity vectors in the neighborhood belong to a given angular sector. As a threshold, we consider that if at least three of the eight available sectors are activated for the same neighborhood, then the central vector must belong to the disordered class; otherwise, it will belong to the ordered similarity vector class.

[0135] There figure 8 This illustrates a binary or quaternary encoding method for a relational fingerprint similarity vector. Depending on the orientation of the similarity vector, it can be assigned the value of the Northwest, Southwest, Northeast, or Southeast compass rose in quaternary encoding. In binary encoding, a vector oriented either Northwest or Southeast will take the value "1", and if it is oriented either Northeast or Southwest, it will take the value "0", or vice versa.

[0136] There figure 9 illustrates statistical results obtained by binary coding of relational fingerprints thus forming relational signatures.

[0137] To establish these results, the relational fingerprints of 200 sheets of paper from the same ream were imaged on an element on the order of 1 cm². Each relational fingerprint is formed from a first-order similarity vector field calculated by correlation between successive reference tiles and 64x64 pixel inspection portions on a regular grid of 24x24 pixel nodes, between a subject image centered by its standard deviation and the one's complement image as the reference image (inversion of the subject image in the image analysis sense). For each relational fingerprint, the 11 x 15 similarity vectors are binary-encoded as described previously, and the resulting 165 bits are concatenated to form the relational signature.

[0138] Figure 9-A shows the Hamming distance calculated on 200 pairs of relational signatures (165 bits each) derived from acquisitions of the same paper elements (dashed line), and the Hamming distance calculated on 200 pairs of relational signatures (165 bits each) derived from acquisitions of different paper elements (solid line). Figure 9-B shows the histogram of Hamming distances between relational signatures derived from acquisitions of different paper elements. The average distance is (49.99 ± 4.66)%. These statistics demonstrate the potential for good discrimination between different and identical paper elements using the proposed method.

[0139] Figure 9-C represents the histogram of Hamming distances between relational signatures deduced from acquisitions of the same paper elements. The average distance is (45 + / - 1.97)%.

[0140] There figure 10 illustrates a quaternary coding according to the compass rose of a relational imprint of a subject image relative to a reference image, by bijectively associating oriented isosceles triangles with the directions SW,SE,NE,NO of the compass rose.

[0141] There figure 11 explicitly describes a visual cryptography-type scheme constructed from a quaternary relational signature. Construction of a shared image 211-B of the visual cryptography type of a message image (binary) from the relational signature of the previous figure 11-A assimilated to a shared image 1, as follows: if the value of the current bit of the message (binary) is 1 (resp. 0), the corresponding triangle in image 2 is chosen so as to form a square (resp. a triangle) by union with the current triangle of the shared image 1.

[0142] The image resulting from the superposition / stacking of the two previous shared images reveals the message 11-C.

[0143] There figure 12 illustrates another visual cryptography type scheme with image integrity verification by a trusted third party from a quaternary relational signature.

[0144] Thumbnail 12-A illustrates the relational signature serving as shared image 1. Thumbnail 12-B represents shared image 2. Thumbnail 12-C is the integrity verification image (held by a trusted third party). Thumbnail 12-D corresponds to the image after superimposition of shared images 1 and 2, thumbnail 12-E to the image after superimposition of the verification image and shared images 1 and 2. Thumbnail 12-F shows the image after superimposition of the verification image and shared image 2. Thumbnail 12-G represents the result in case of fraudulent manipulation of shared image 2 (change of a "0" to an "8"... in place of...). Thumbnail 12-H represents the image after superimposition of the verification image and the attacked shared images 1 and 2, 12-I image after superimposition of the verification image and the attacked shared image 2: anomalies are visible at the point of attack.Thumbnail 12-J is the image after superimposing the verification image and the unattacked shared image 1: no anomaly is seen on the whole image.

[0145] There figure 13 illustrates two cases of relational stimulus (here visual) resulting from the cognitive conditioning of relational imprinting.

[0146] Figure 13-A shows a visual relational stimulus in the form of arrows representing the disordered and regular classes of the relational fingerprint of a patterned paper document relative to a different patterned paper document (the relational fingerprint of a fingerprint vector field calculated using first-order cross-correlation as the similarity indicator, with the reference points being the nodes of a regular grid). This shows us a disordered region, i.e., a region where the similarity vectors are disordered. This region corresponds to the area where only the paper microstructure is visible in both samples. Two regular regions, comprising regular similarity vectors, appear in the printed areas in the upper left and lower right of the image.If one of the two samples is authentic, then the imprinted pattern on the second sample is authenticated (subject to variations in material), but not the microstructures of the second sample. Therefore, it is a different candidate from the authentic sample in terms of its constituent material. The supporting image in this case is one of the two samples used in the process.

[0147] Image 13-B also shows a visual relational stimulus in graphic form, but between two images of the same printed paper document. This reveals regular similarity vectors between two identical images (apart from distortions induced by manual measurement in this case) of the same paper sample. If one of the two samples is authentic, then we authenticate not only the printed pattern on the second sample, but also the microstructures of the second; therefore, it is authentic from a material standpoint.

[0148] The figure 14 This illustrates another type of relational stimulus in graphical form, using colored or grayscale segments. Figure 14-A shows a representation of the relational fingerprint vectors of the image of a printed paper document relative to the image of a different printed paper document with the same printed pattern (the relational fingerprint of a fingerprint vector field calculated using the A-KAZE detector / descriptor as a similarity indicator, after bandpass filtering the images). Each segment of the cognitive conditioning connects a characteristic reference point detected in the subject image to its counterpart in the reference image on the image obtained by concatenating the two previous images.This shows us that, in this alternative form of representation, two different samples produce similar point relationships only in the printed areas at the top left and bottom right of the image, and conversely, nothing in the areas where only the paper's microstructure is visible on both samples. The underlying image in this case is a juxtaposition of the samples.

[0149] Image 14-B shows a similar representation, but between two acquisitions of the same printed paper document. This demonstrates that two identical samples produce similar point relationships distributed across all samples (printed portion and portion derived from the microstructure) and in a much larger number compared to the previous case (on the order of 10 to 20 times more). The figure 15 This illustrates an application of integrity control for a printed pattern. In this control, the visual representation of the relational fingerprint indicates areas of non-similarity, reflected by the predominant local appearance of disordered similarity vectors. The relational fingerprint was obtained using cross-correlation and rank 1 as similarity indicators, with reference points drawn from a regular grid. The supporting image in this case is the original image implemented in the process. According to this application, thumbnail 15-A corresponds to the original image, thumbnail 15-B represents the modified image, while thumbnail 15-C is a visual representation of the relational fingerprint resulting from the comparison of these two images.

[0150] There figure 16 This illustrates a biometric authentication method using the visual presentation of the relational fingerprint between two different skin print acquisitions and an authentic reference acquisition. The latter was obtained using cross-correlation and rank 1 as similarity indicators, with reference points derived from a regular grid. Registration of the candidate images with respect to the original image was performed using a detector / descriptor method before calculating the similarity vectors.

[0151] This shows us that two different fingerprints produce a largely disordered similarity vector field (left: candidate image 2 vs. original image), whereas regular, small-dimensional similarity vector fields appear (right: candidate image 1 vs. original image) when two fingerprints share a common authentication region. Note that the boundary between the gray and black areas of the rejected images also appears on these similarity vectors, as described in the integrity check application. The supporting image in this case is the original image used in the process.

[0152] It should be noted that the "rejected" image could be a relevant visual representation within the meaning of the invention in that it is no longer comparable to a skin-type image in case 2, whereas the characteristic micro-texture of a fingerprint is still recognizable in acquisition 1. At the figure 16 , thumbnail 16-A shows the authentic original Image, thumbnail 16-B represents the raw candidate image 1, thumbnail 16-C illustrates rejected candidate image 2, thumbnail 16-D corresponds to rejected candidate image 1, thumbnail 16-E is a visual presentation of image 2 compared to the original image while thumbnail 16-F is a visual presentation of image 1 compared to the original image.

[0153] There figure 17This section presents examples of relative transformations applied to one of two acquisitions of the same physical subject, showing largely regular similarity vector field patterns and illustrating the possibilities for real-time implementation if a user interacts with a touchscreen simultaneously with the calculations and visual representations. The thumbnails respectively show: 17-A an Expansion of 5% 17-B a Recalibration (almost zero transformation) - 17-C a Rotation of 5° combined with a translation 17-D a simple Translation.

Claims

1. Method for determining a relational imprint between two images comprising the following steps: - the implementation of a first image and of a material subject and of a reference image different from the first image, - a phase of calculating vectors of similarity between tiles belonging respectively to the image of the material subject and to the reference image, by using a calculating method defined by a type of similarity indicator and a similarity row to obtain a field of imprint vectors, formed by the similarity vectors, comprising at least one haphazard region disordered in the sense of an entropy criterion, - a phase of recording in the guise of relational imprint of a representation of the calculated field of imprint vectors, - a step of using, in the guide of a relational signature, a digital representation of the relational imprint.

2. Method according to the preceding claim, characterized in that it comprises a step of compressing the field of imprint vectors and recording in the guise of a relationship imprint of the result of the compression.

3. Method according to any one of the preceding claims, characterized in that the recording of the relational imprint is associated with the recording of at least one of the images used.

4. Method according to any one of the preceding claims, characterized in that the reference image is identical for a set of material subjects considered.

5. Method according to any one of the preceding claims, characterized in that the reference image is a concatenation of several images.

6. Method according to any one of the preceding claims, characterized in that the phase of calculating the field of imprint vectors comprises, prior to the calculation of the field of imprint vectors, a step of transforming one and / or the other of the two images.

7. Method according to the preceding claim, characterized in that the transformation step is a recalibration.

8. Method according to the preceding claim, characterized in that it comprises a calculation of a relational imprint of the image of the material subject in relation to the reference image, a recalibration of the image of the material subject with respect to the reference image, based on the calculated relational imprint and calculation of another relational imprint of the recalibrated image of the material subject in relation to the reference image, this other relational imprint being used to determine the relational signature.

9. Method according to any one of the preceding claims, characterized in that the phase of calculating similarity vectors comprises: - a step of determining a system which is common to the image of the material subject and to the reference image, - a step of determining, in one of the two images, a set of reference tiles, each associated with at least one reference point having coordinates in the common system, - a step of searching in the other of the two images of concordance tiles, which are each matched with a reference tile, with which they have a certain degree of similarity, and are each associated with at least one reference point having coordinates in the common system, - calculating the coordinates of each similarity vector from the coordinates of the reference points of each reference tile and of the associated concordance tile.

10. Method according to claim 9, characterized in that the reference tiles are determined self-adaptively by means of a local characteristic detection algorithm.

11. Method according to any one of claims 9 or 10, characterized in that the concordance tile search step comprises: - the determination, in the other image, of a set of inspection tiles, - for each reference tile: - the calculation of a series of similarity indices, each similarity index being calculated between the portion of one of the two images corresponding to said reference tile and the portion of the other image corresponding to an inspection tile, the inspection tile being different for each similarity index calculation, - the selection as a concordance tile associated with said reference tile, the inspection tile having a given degree of similarity with said reference tile.

12. Method according to any one of the preceding claims, characterized in that it comprises, prior to the recording phase, a step of breaking down the field of similarity vectors into at least one so-called regular part and one so-called haphazard, disordered part, consisting of allocating each of the similarity vectors to one or the other of the regular and haphazard, disordered parts, according to a regional entropy criterion.

13. Method according to the preceding claim, characterized in that when the local optimum of similarity is chosen at an order equal to one, for a local row considered, the similarity vector in question is added, either in the haphazard, disordered component of the field of imprint vectors, or in the regular component of the field of imprint vectors, according to which it verifies or not the regional entropy criterion, the zero vector thus being added respectively in the regular component, or in the haphazard, disordered component.

14. Method for authenticating a candidate image with respect to an authentic image, characterized in that it implements the method for determining a relational imprint according to any one of claims 1 to 13.

15. Authentication method according to the preceding claim, characterized in that a relational signature of the candidate image and a relational signature of the authentic image are determined by means of the method according to any one of claims 1 to 13, and are compared with one another, according to a statistical similarity criterion, making it possible to consider the candidate relational signature as similar to the recorded relational signature, if a decision threshold is reached.