WO2024069529A1

WO2024069529A1 - Method for reconstructing a digital image based on digital fragments of the digital image

Info

Publication number: WO2024069529A1
Application number: PCT/IB2023/059708
Authority: WO
Inventors: Simone RUSSO
Original assignee: Whtexch Solutions S.R.L.
Priority date: 2022-09-30
Filing date: 2023-09-28
Publication date: 2024-04-04
Also published as: IT202200020115A1

Abstract

A method for reconstructing a digital image based on digital fragments of the digital image, in which the aforesaid digital fragments derive from the fragmentation of a digital image, is described. Each digital fragment corresponds to a respective micro-fraction of digital image. Each digital fragment is fungible and represents a minute portion of digital image which is substantially equivalent to every other fragment of the same digital image. The method comprises the step of assigning, to different users, respective groups of digital fragments which are disjoint from one another, i.e., they do not contain duplicate digital fragments, such that the sum of all the groups of digital fragments allows exactly reconstructing the whole original digital image. Each of such groups of digital fragments comprises a limited number of digital fragments assigned based on a random and scattered allocation of the digital fragments of the whole original digital image. The method then includes reconstructing a digital representation of the original digital image based on the aforesaid group of digital fragments, by means of at least one algorithm for digital image processing and/or reconstruction.

Description

“Method for reconstructing a digital image based on digital fragments of the digital image”

DESCRIPTION

TECHNOLOGICAL BACKGROUND OF THE INVENTION

Field of application.

The present invention relates to a method for reconstructing a digital image based on digital fragments of the digital image.

Such digital fragments may be, for example, authenticated exchangeable and fungible digital objects deriving from the fragmentation of a digital image.

Description of the prior art.

The phenomenon of fractional NFTs (Non-Fungible Tokens) has recently emerged in the growing field of Non-Fungible Tokens (NFTs).

The market and the strong growth of NFTs are of recent origin and are associated with the diffusion of blockchain technology (also known as DLT, Distributed Ledger Technology).

As is well known, an NFT is a special type of token which, among the various possibilities, can represent the title deed and written certificate of authenticity on blockchains of a unique asset of digital type.

NFTs are used in different specific applications which require unique digital objects.

Among the various applications, NFTs have allowed the circulation in unregulated markets of so-called “tokenized” images which are accessible and verifiable through DLT, thus giving value to certain digitalized or digital works.

More recently, there has also been the possibility of fractioning a single NFT (by means of the aforesaid “Fractional NFT” technology) in order to allow access by several users to a series of rights or portions of the same NFT (which are variable according to the specific NFT), thus creating a “democratization” of the access to the same asset/product.

The fungibility of the single fractions following the fragmentation process associated with, for example, mechanisms at times applied to Fractional NFTs and variants thereof, is not however a guaranteed result, especially if the latter represent fragments of the original image and given that, by definition, the starting NFTs are “not fungible” by nature.

On the other hand, the fungibility of the single fractions appears increasingly to be a desirable property for different reasons. The tangibility of the fractions increases the economic value thereof, thus ensuring increased exchangeability.

Fungibility is in fact an attribute of an asset which has significant economic value because it facilitates the exchange, diffusion and liquidity thereof without, for example, each time having to reverify the value or wonder what is involved, thus in fact slowing down the possibility of being exchanged. With reference to the importance of fungibility, think, for example, of one Euro coins with respect to the possibility of having coins all mutually different, which would make the possibility of an actual use thereof very slow and would slow down the circulation thereof.

Moreover, also from a jurisprudential viewpoint, the European legislator places large importance on fungibility, up to make explicit reference thereto in Directive MIFID II (Directive 2014/65/EU and the relative delegated regulations, including Delegated Regulation 565 of 2017) which legislates Markets in Financial Instruments for all instruments which can circulate during regulated negotiations. For example, MIFID II (Art. 8(f) of Delegated Regulation 565) says that “any other asset or right of a fungible nature” can be the underlying of financial instruments or derivatives.

Fungibility is an essential precondition for creating financial instruments and accessing Regulated Markets. On a global level, all instruments in listed financial markets are fungible by nature, just think of two or more stocks of the same company or two bonds of the same issuer with the same maturity date, and the same also applies for derivatives (those who trade these products within the same type always and in any case trade fungible products).

A further need emerging in this field is that of grouping the digital fragments into groups which in turn are fungible and which have the same fundamental properties as the single fragments so that also fractions of digital images consisting of a group of suitably arranged digital fragments are in turn exchangeable and/or sellable.

Indeed, a market of Fractional NFTs (and variants thereof) on digital images referring to the same work requires that the micro-fractions (whether they consist of single fragments or groups of digital fragments) be distributed to the subjects who buy them so as to avoid a privileged allocation (for example, reproducing the center of the work) and ensure that the allocation mechanism is equitable for the users ex ante and ex post. In fact, only in the absence of a privileged allocation, which would allow specific parts of the work itself to be recreated, it is possible to avoid certain members from having an advantage over others while purchasing the same quantity of micro-fractions.

On the other hand, the need can arise for a purchaser of a single group of digital fragments to want to reconstruct the digital image, at least for the purposes of a private enjoyment in an at least approximate manner, but from which the contents of the original image can be recognized. Two variants exist:

1 ) in a first variant, a purchaser of a sub-group of fragments is allowed to use the fragments and display the image which corresponds exactly to the fragments available by positioning them in the original position thereof prior to the fractioning;

2) a second variant, starting from the sub-group of fragments, allows reconstructing an image which is improved with respect to that obtained starting only from the sum of the available fragments.

In other words, if from an economical viewpoint and for the purposes of commercial exchanges, the value of the group of digital fragments depends on the percentage of fragments contained therein, and the digital groups are deliberately constructed so as not to allow the authenticated and perfect reconstruction of the original digital image (and, moreover, the digital fragments of each group are specially selected so as not to allow the exact reproduction of the original image or a portion thereof), from a private fruition viewpoint the need emerges to be able to reconstruct the digital image in an at least approximate manner, and from which the contents of the original image can be recognized.

Such a technical problem is currently not solved in a satisfactory manner.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a method for reconstructing a digital image based on digital fragments of the digital image, which allows at least partially obviating the drawbacks mentioned above with reference to the prior art, and responding to the aforementioned needs particularly felt in the considered technical field. Such an object is achieved by a method according to claim 1 .

Further embodiments of such a method are defined in claims 2-8.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the method according to the invention will become apparent from the following description of preferred embodiments, given by way of non-limiting indication, with reference to the accompanying drawings, in which:

- Figure 1 shows a simplified view of an allocation of digital fragments of a digital image in groups of digital fragments, according to an embodiment of the method according to the invention;

- Figure 2 shows a fractioning of a digital image into fragments, according to an embodiment of the method according to the invention; - Figure 3A shows an example of digital image to which the method of the present invention is applicable;

- Figures 3B and 3C show respective reconstructions of the digital image in Figure 3A, according to an embodiment of the method of the present invention, based on two respective different generated groups of digital fragments, each comprising 10% of the total digital fragments of the original digital image;

- Figure 3D shows a reconstruction of the digital image in Figure 3A, according to an embodiment of the method of the present invention, in Figure 3A, based on a group of digital fragments comprising the sum of the two groups of digital fragments which have given rise to the images in Figures 3B and 3C, therefore comprising 20% of the total digital fragments of the original digital image;

- Figure 3E shows an improved reconstruction of the digital image in Figure 3D, obtained based on the same group of digital fragments comprising 20% of the total digital fragments, and by applying an embodiment of the method of the present invention.

DETAILED DESCRIPTION

A method for reconstructing a digital image based on digital fragments of the digital image, in which the aforesaid digital fragments derive from the fragmentation of a digital image, is described.

Each digital fragment corresponds to a respective micro-fraction of digital image.

Each digital fragment is fungible and represents a minute portion of digital image which is substantially equivalent to every other fragment of the same digital image.

The method comprises the step of assigning, to different users, respective groups of digital fragments which are disjoint from one another, i.e., they do not contain duplicate digital fragments, such that the sum of all the groups of digital fragments allows exactly reconstructing the whole original digital image. Each of such groups of digital fragments comprises a limited number of digital fragments assigned based on a random and scattered allocation of the digital fragments of the whole original digital image.

The method then includes reconstructing a digital representation of the original digital image based on the aforesaid group of digital fragments, by means of at least one algorithm for digital image processing and/or reconstruction.

According to an embodiment of the method, the aforesaid group of digital fragments comprises a number of digital fragments equal to a fraction of the total number of digital fragments of the digital image, in which such a fraction is less than a predefined maximum fraction.

According to an embodiment of the method, given a group of assigned fragments, the aforesaid step of reconstructing a digital representation of the original image comprises simply obtaining a digital image by repositioning the digital fragments in their position prior to the fractioning. Such a methodology allows exactly reconstructing the original digital image as more digital fragments are purchased and added.

According to an embodiment of the method, given a group of assigned fragments, the aforesaid step of reconstructing a digital representation of the original image comprises improving the digital image through a combined algorithm application of linear regression and neural networks.

According to an implementation option, the aforesaid step of reconstructing a digital representation of the original image comprises the following steps:

- obtaining a first reconstruction of the digital image to be reconstructed by positioning the available digital fragments (i.e., for example, the digital fragments of a group assigned to a user) in the original position thereof;

- obtaining a second improved reconstructed digital image by applying a gradient variation algorithm to reconstruct pixels not belonging to the available digital fragments, comprised between two known pixels belonging to available digital fragments and having two respective color coordinates, with colors gradually varying between the color coordinates of said two known pixels; the aforesaid gradient, representative of color coordinate variation speeds, is a vector containing the partial derivatives with respect to the color coordinates.

According to an implementation option, the aforesaid step of reconstructing a digital representation of the original image further comprises obtaining a third improved reconstructed digital image by applying, to the second improved reconstructed digital image, a linear regression algorithm with gradient descent, which puts in relation the gradients of close points to find a reconstruction pattern also between the points the color coordinates of which are not known.

Further details on the aforesaid linear regression algorithms with gradient descent are provided below by way of explanation.

Imagine, for example, tracing a line between two pixels which color is known (i.e., which color coordinates, for example, RGB, are known) and suppose (as reasonable) that as the distance between such two points decreases, basically the color difference, i.e., gradient, also decreases between the two. The gradient is defined here as the vector containing the partial derivatives with respect to the three color coordinates/dimensions, for example, RGB (note that there are not four coordinates since the alpha channel in our case simply indicates whether the pixel is owned or not). Hence, the gradient indicates the speed with which a variable between two specific points varies.

According to an implementation option, the linear regression technique is used jointly with the gradient. The linear regression technique does not use only the single point the gradient of which is assessed (that, being a vector and not a function, relates to the point), rather allows relating close points to find a pattern.

In other words, if the gradient deals with discrete portions (single pixels) starting from known pixels, the linear regression allows finding a pattern between unknown points and thus improving the gradient.

According to different embodiments included in the method of the invention, all the aforesaid techniques are employed within the context of a larger neural network comprising also other very important information.

For example, according to an embodiment, the aforesaid step of reconstructing a digital representation of the original image comprises employing a multi-layer neural network, in which the various layers perform operations such as reconstructing unknown pixels based on known adjacent pixels, and/or reconstructing pixel patterns based on known and reconstructed pixels, and/or reconstructing macro-patterns associated with macro-aspects of the digital image based on the aforesaid pixel patterns.

For example: if the original digital image were a lake surrounded by land and, for simplicity of exemplary illustration, only two colors were available, for example, blue and brown, how could the points of the shore at the border between lake and land be processed? In this case, it is useful to provide some kind of pattern on known and reconstructed pixels, in which such a pixel pattern is determined through a first layer of a neural network.

Again, using the example of the lake, a further step is that of taking advantage of both known pixels and reconstructed pixels to determine a further “lakeshore” macropattern. Unless there are unforeseeable objects (for example, a boat drawn in the unknown pixels), a “shore” macro-pattern can be reconstructed.

Using a neural network with feedback, any unknown pixels reconstructed with incorrect color can be corrected and the color thereof can be modified should there be part of a pattern (boat, shore, person).

The aforesaid operations are performed in this example by a second layer of the neural network.

According to the example disclosed herein, a third layer performs a lighting correction to verify and improve previously identified patterns, only using in this sense different color spaces (conventionally HSB).

According to an embodiment, the aforesaid digital fragments are authenticated and fungible digital fragments.

According to an embodiment, the aforesaid groups of digital fragments are authenticated and fungible groups.

In order to show some results and advantages obtainable by the method disclosed above, refer to Figure 3. In particular, Figure 3A shows an example of original digital image to which the present method is applicable.

Suppose that a first group of digital fragments of such an image, equal to 10% of the total, is generated and assigned by means of the present method, to a first user, who purchases such a first digital group; Figure 3B shows a reconstruction of the original digital image carried out based on such a first group of digital fragments.

Also suppose that a second group of digital fragments of the aforesaid image, equal to 10% of the total (therefore with a number of fragments equal to the number of fragments of the aforesaid first group, but comprising different fragments with respect to the first group), is generated and assigned, by means of the present method, to a second user, who purchases such a second digital group; Figure 3C shows a reconstruction of the original digital image carried out based on such a second group of digital fragments.

Suppose now that the second user also purchases, from the first user, the first group of digital fragments and combines them with the second group of digital fragments, thus having available a group of digital fragments comprising 20% of the digital fragments of the original digital image. By applying image reconstruction algorithms of the present method, the second user can obtain a reconstruction of the original digital image, as depicted in Figure 3D, representing 20% of the fragments repositioned in the original position thereof.

Finally, by applying the image improvement algorithms provided in the method of the present invention, a further improvement of the reconstructed digital image is obtained, as shown in Figure 3E.

In other words, the reconstructions depicted in Figures 3D and 3E are based on the same group of digital fragments comprising a number of digital fragments equal to 20% of the number of digital fragments of the whole original digital image; however, in the reconstruction shown in Figure 3E, the method for reconstructing a digital image also comprising the image improvement algorithms was employed. The comparison between the improved quality reconstruction shown in Figure 3E and the reconstruction shown in Figure 3D shows an improvement and advantage obtainable by virtue of the present method.

In order to better disclose the groups of digital fragments on which the method for reconstructing digital images of the present invention can operate, further details on how such groups can be generated starting from digital fragments are provided by way of example.

According to an implementation option, the digital fragments from a given portion of digital image which are allocated to one group of digital fragments alone are randomly selected within a portion of digital image into which the digital image is divided.

Note that in this description, the concepts of “image portion” into which the digital image is divided and “group of digital fragments” into which the same digital image is divided play very different roles; the “portions of images” are adjacent and recognizable areas of image, while “groups of digital fragments” are sets of digital fragments selected in a random and scattered manner.

Actually, it is desirable for the “portions of image” and the “groups of digital fragments” to be as disjointed and different as possible so that no group of digital fragments allows the reconstruction of an image portion or contains fragments privileging one or the other portion.

The circumstance described above is also shown in a simplified manner (and obviously with a very limited number of fragments, portions and groups, with respect to more realistic cases) in Figure 1 , where there is shown how digital fragments (represented by black and grey dots) originating from different portions P1 -PK-PN of the digital image can be allocated in groups G1 -Gn, and where there is shown how the composition, in terms of digital fragments, of the portions P1 -PK-PN and of the groups G1 -Gn, must be as uncoupled as possible.

In other words, the allocation of the digital fragments of each portion of digital image must be distributed randomly and in a scattered manner in the groups of digital fragments.

In particular, according to an implementation option, the allocation of the digital fragments in the groups of digital fragments is carried out so as not to allow the reconstruction of the digital image or a portion thereof starting from the digital fragments included in one group alone.

According to different possible embodiments, the method applies to digital fragments in which each digital fragment comprises one or more pixels or one or more fractions of pixels of the original digital image.

According to an implementation option, each fraction of pixel corresponds to one or more bits forming the pixel according to the digital image coding by which the digital image is coded.

For example, the digital image coding by which the digital image is coded is PNG or JPG or BMP coding.

According to an embodiment of the method, the group of digital fragments is generated by reaggregating a plurality of digital fragments into a group of digital fragments, which in turn is fungible.

According to an implementation option, the fungible reaggregated groups of digital fragments are such that a complete reaggregation results in the original digital image.

According to an embodiment of the method, all the groups of digital fragments generated comprise an equal number of digital fragments, and therefore represent the same fraction and/or percentage of the digital image.

According to another embodiment of the method, the groups of digital fragments generated comprise a different number of digital fragments, and therefore represent a different fraction and/or percentage of the digital image.

In order to better disclose the digital fragments forming the groups of digital fragments, a method for generating such fragments, i.e., for fragmenting digital images intended to give rise to exchangeable and fungible authenticated digital objects, is described below.

The method for generating digital fragments comprises the step of fragmenting the digital image into a plurality of fragments, in which each fragment corresponds to a respective micro-fraction of digital image, in which each digital image fragment (i.e., micro-fraction) is fungible.

The fact that each digital image fragment is fungible implies that each of such fragments represents an extremely minute portion of digital image which is substantially indistinguishable and equivalent to every other fragment of the same digital image.

The fractioning into micro-fractions is carried out so that the sum of all the digital image fragments deriving from the aforesaid digital image allows reconstructing the whole original digital image.

Each fragment of the aforesaid plurality of micro-fractions of digital image is then authenticated so as to generate a respective plurality of fractioned fungible and authenticated digital objects, each corresponding to an authenticated fragment.

The aforesaid fragmentation step comprises:

- defining a number N of fragments into which the digital image is to be fractioned;

- dividing the digital image into pixels and/or fractions of pixels;

- generating each fragment of the aforesaid plurality of digital image fragments so that all the fragments have the same dimension and/or resolution, corresponding to a group of pixels or to one pixel, or to a group of fractions of pixels, or to a single fraction of pixel, or to a combination of one or more pixels and one or more sub-pixels, based on the aforesaid predefined number N of fragments.

“Resolution” (defined at times in this description also as “dimension”) means in this description the (integer or fractional) number of pixels forming a digital image or a fragment thereof, for example, divided into number of pixels for each two-dimensional axis.

According to an embodiment of the method, given the predefined number of fragments and the original resolution of the digital image, in pixels, the aforesaid fragmenting step further comprises calculating the resolution of each micro-fraction as the integer or decimal number given by the division of the original dimension of the image in pixels by the predefined number N of fragments.

In particular, according to an implementation option, given the predefined number of fragments and the original resolution of the digital image in pixels, the aforesaid fragmentation step comprises the initial division of the digital image into n rows and m columns such that the number of rows n by the number of columns m is equal to the total number N of fragments. The width and the height of the initial image are then divided by the number of columns m and the number of rows n, respectively, thus obtaining a pair of values a and b which form the resolution of each fragment. Therefore, in this case, there is a number of (whole and/or fractions) of pixels in each fragment equal to a x b = A.

For example, Figure 2 shows a digital image divided into N fragments, according to a matrix of n rows and m columns (naturally, for purposes of illustration, the number of rows and columns is very small; in real cases, the numbers m and n are much larger).

Each fragment has a resolution of a pixels in width and b pixels in height, i.e., it comprises a total number of pixels (resolution) equal to A = a x b. The total number of pixels (resolution) R of the digital image is thus less than or equal to A x N, and is hence increased by the value obtained by multiplying the resolutions of the single fragments, i.e., (a x n) x (b x m). The increase occurs if there are pixels shared by overlapping fragments.

For example, single overlapping fragments means that if, in the original digital image, there were 7 pixels (px) in width corresponding to two fragments of 4 px each, each fragment would be the result of 3.5 pixels and 0.5 empty pixels. Thus, adding the areas of two fragments of 4 px obtains a dimension of 8 which is a majorant of 7.

According to another implementation technique aiming to obtain the information contained originally, the information contained in the single fragments is added after positioning them in a matrix having a dimension equal to the original resolution.

The example shown in Figure 2 relates to an integer number of pixels per fragment but (as also described hereinbelow in greater detail) the numbers involved can also be decimals and/or fractions.

To give an idea of the orders of magnitude involved, by mere way of example, an example is provided here of a fragmentation method implemented on a digital image representing the painting “Mona Lisa” where R (image resolution) is equal to 3000 x 4471 pixels (for a total of 13,413,000 pixels); N (number of fragments) is equal to 6,000,000; A is equal to R/N = 2.2355 (in this case, decimal).

According to an implementation option, each fragment is constructed as a grouping of equal whole pixels and fractions of pixels, with a number of whole pixels equal to the integer part of the aforesaid fragment resolution, and with a number of fractions of pixels, belonging to other contiguous pixels, corresponding to the decimal part of the aforesaid fragment resolution.

In particular, according to an implementation example, each fragment is constructed by grouping together a number of whole and/or fractions of pixels equal to A. In each fragment, the number of whole pixels is equal to the number of whole pixels within the resolution a x b of the fragment itself. Similarly, the number of fractions of pixels is equal to the number of fragments of pixels (contiguous to the whole pixels of that fragment) present in the resolution a x b of that fragment.

According to another implementation option, each fragment is constructed as a grouping of fractions of pixels belonging to adjacent pixels so as to achieve the total number A of pixels.

According to another implementation option, if the number of pixels of the digital image is a multiple of the number of fragments to be generated, the aforesaid number of pixels of each fragment is selected equal to one pixel or to a group of pixels, in which each group comprises a number of pixels equal to the division between the number of pixels of the digital image and the number of fragments to be generated.

According to an implementation option, the number of pixels of each fragment is equal to one.

According to an embodiment of the method, each fraction of pixel corresponds to one or more bits forming the pixel according to the digital image coding with which the digital image is coded.

In this case, the minimum unit of division corresponds to a single bit of the aforesaid bits in which the pixel is coded.

According to an implementation option, if the predefined number of fragments is not a multiple of the aforesaid minimum unit of division, the method comprises determining a corrected number of fragments as similar as possible to the predefined number of fragments, such that the corrected number of fragments is a multiple of the aforesaid minimum unit of division.

According to an implementation option, each fragment consists of a plurality of the aforesaid minimum units of division belonging to the same pixel or to adjacent pixels.

According to different possible implementation options, the coding is possible on different file formats, including PNG, JPG, and BMP.

According to a particular implementation option, each pixel is divided into multiples of 8 bits starting from the third multiple (24, 32, etc.).

According to an embodiment of the method, each fragment (i.e., micro-fraction) consists of one or more whole pixels and/or one or more partial pixels, and/or a combination of one or more whole pixels and one or more partial pixels.

In this case, each whole pixel consists of a vector containing the bits by which the respective pixel is coded, and each partial pixel consists of a vector containing the information bits by which the selected fraction of the original whole pixel is coded, in the respective positions, and a 0 value in the other positions.

According to different possible implementation options, the step of authenticating each fragment of the aforesaid plurality of digital image fragments so as to generate a respective plurality of fractioned fungible and authenticated digital objects, each corresponding to an authenticated fragment, is performed according to technologies known per se, based on Distributed Ledger Technology, DLT, and/or Blockchain technology.

As can be noted, the object of the present invention is fully achieved by the method disclosed above by virtue of the functional features thereof.

Indeed, the method disclosed above meets the need to allow a reconstruction of an approximate digital representation of the original digital image, at least for the purposes of a private enjoyment/display from which the contents of the original image can be recognized, even starting from a group of digital fragments consisting of digital fragments which are specially selected in a random and distributed manner from the original digital image.

In order to meet contingent needs, those skilled in the art may make changes and adaptations to the embodiments of the method described above or can replace elements with others which are functionally equivalent, without departing from the scope of the following claims. Each of the features described above as belonging to a possible embodiment can be implemented irrespective of the other embodiments described.

Claims

1 . A method for reconstructing a digital image based on digital fragments of the digital image, wherein said digital fragments derive from the fragmentation of a digital image, wherein each digital fragment corresponds to a respective micro-fraction of digital image, wherein each digital fragment is fungible and represents a minute portion of digital image and is substantially equivalent to every other fragment of the same digital image, wherein the method comprises:

- assigning, to different users, respective groups of digital fragments which are disjoint from one another, that is they do not contain duplicate digital fragments, such that the sum of all the groups of digital fragments allows exactly reconstructing the whole original digital image, wherein each group of digital fragments comprises a limited number of digital fragments assigned based on a random and scattered allocation of the digital fragments of the whole original digital image;

- reconstructing a digital representation of the original digital image based on said group of digital fragments, by means of at least one algorithm for digital image processing and/or reconstruction.

2. A method according to claim 1 , wherein said group of digital fragments comprises a number of digital fragments equal to a fraction of the total number of digital fragments of the digital image, wherein said fraction is less than a predefined maximum fraction.

3. A method according to claim 1 or claim 2, wherein given a group of assigned fragments, said step of reconstructing a digital representation of the original image comprises obtaining a digital image by repositioning the digital fragments in their position prior to the fractioning.

4. A method according to claim 1 or claim 2, wherein given a group of assigned fragments, said step of reconstructing a digital representation of the original image comprises improving the digital image through a combined algorithm application of linear regression and neural networks.

5. A method according to claim 1 or claim 2, wherein given a group of assigned fragments, said step of reconstructing a digital representation of the original image comprises the following steps:

- obtaining a first reconstruction of the digital image to be reconstructed by positioning the available digital fragments in the original position thereof;

- obtaining a second improved reconstructed digital image by applying a gradient variation algorithm to reconstruct pixels not belonging to the available digital fragments, comprised between two known pixels belonging to available digital fragments and having two respective color coordinates, with colors gradually varying between the color coordinates of said two known pixels, wherein said gradient, representative of color coordinate variation speed, is a vector containing the partial derivatives with respect to the color coordinates.

6. A method according to claim 5, wherein said step of reconstructing a digital representation of the original image further comprises obtaining a third improved reconstructed digital image by applying, to the second improved reconstructed digital image, a linear regression algorithm with gradient descent, which puts in relationship the gradients of close points to find a reconstruction pattern also between points of which the color coordinates are not known.

7. A method according to any one of the preceding claims, wherein said step of reconstructing a digital representation of the original image comprises employing a multilayer neural network, wherein the various layers perform operations such as reconstructing unknown pixels based on known adjacent pixels, and/or reconstructing pixel patterns based on known and reconstructed pixels, and/or reconstructing macropatterns associated with macro-aspects of the digital image based on the aforesaid pixel patterns, and/or performing a lighting correction to verify and improve previously identified patterns.

8. A method according to any one of the preceding claims, wherein said digital fragments are authenticated and fungible digital fragments and/or wherein said groups of digital fragments are authenticated and fungible groups.