EP3994890A1

EP3994890A1 - Method and device for coding a digital hologram sequence

Info

Publication number: EP3994890A1
Application number: EP20733836.9A
Authority: EP
Inventors: Patrick Gioia; Antonin GILLES
Original assignee: Fondation B Com
Current assignee: Fondation B Com
Priority date: 2019-07-05
Filing date: 2020-06-24
Publication date: 2022-05-11
Also published as: FR3098367B1; US20220272380A1; FR3098367A1; US12132933B2; WO2021004797A1

Abstract

The present invention concerns a method and a device for coding a sequence comprising at least a first digital hologram (H₁) representing a first scene and a second digital hologram (H₂) representing a second scene, the first digital hologram (H₁) and the second digital hologram (H₂) being represented by means of a set of wavelets each defined by a multiplet of coordinates in a multidimensional space. The first hologram (H₁) is represented by a set of first coefficients (c₁(k,s,X)) respectively associated with at least some of the wavelets of the set of wavelets, and the second hologram (H₂) is represented by a set of second coefficients (C₂(k',s',X')) respectively associated with at least some of the wavelets of the set of wavelets. The coding method comprises the following steps: - for each of a plurality of seconds coefficients (C₂(k',s',X')), determining a remainder (l_k',s',X') by a difference between the second coefficient concerned (C₂(k',s',X')), associated with a first wavelet defined by a given multiplet ((k',s',X')), and the first coefficient (c1(k,s,X)) associated with a second wavelet defined by a multiplet ((k,s,X)) having as its image the multiplet ((k',s',X')) given by transform (G_i) in the multidimensional space; - coding the determined remainders (l_k',s',X'). The transform (G_i) is determined by analysis of variation between the first scene represented by the first digital hologram (H₁) and the second scene represented by the second digital hologram (H₂).

Description

Method and device for encoding a sequence of digital holograms

Technical field of the invention

The present invention relates to the technical field of digital holography.

It relates in particular to a method and a device for encoding a sequence of digital holograms.

State of the art

It has already been proposed, for example in the article "View-dependent compression of digital hologram based on matching pursuit", by Anas El Rhammad, Patrick Gioia, Antonin Gilles, Marco Cagnazzo and Béatrice Pesquet-Popescu in Optics, Photonics, and Digital Technologies for Imaging Applications V. International Society for Optics and Photonics, 2018, vol. 10679, p.106790L, to represent a digital hologram using a set of wavelets (e.g. Gabor wavelets).

Each wavelet is defined by several characteristic parameters of the wavelet concerned. The digital hologram is then represented by a set of coefficients associated respectively with the different wavelets.

The digital hologram can thus be easily reconstructed by summing the different wavelets, each time weighted by the associated coefficient.

Presentation of the invention

In this context, the present invention proposes a method for encoding a sequence comprising at least a first digital hologram representing a first scene and a second digital hologram representing a second scene, the first digital hologram and the second digital hologram being represented by means of a set of wavelets each defined by a multiplet of coordinates in a multidimensional space,

the first hologram being represented by a set of first coefficients respectively associated with at least some of the wavelets of said set of wavelets and the second hologram being represented by a set of second coefficients respectively associated with at least some of the wavelets of said set of wavelets,

the coding method comprising the following steps: - for each of a plurality of second coefficients, determination of a residue by the difference between the second coefficient concerned, associated with a first wavelet defined by a given byte, and the first coefficient associated with a second wavelet defined by a byte having for image the multiplet given by transformation in multidimensional space;

- coding of the determined residues,

wherein the transformation is determined by analyzing the variation between the first scene represented by the first digital hologram and the second scene represented by the second digital hologram.

The transformation makes it possible to assign at least some of the first coefficients to wavelets other than those to which these first coefficients are assigned in the first hologram.

This transformation thus makes it possible to construct (at least in part) a predicted hologram, which can be subtracted from the second hologram (coefficient by coefficient) in order to obtain residues of lesser value, the coding of which is more efficient.

On the other hand, because the transformation is determined by analyzing the variation between the first scene represented by the first digital hologram and the second scene represented by the second digital hologram, the predicted hologram will best approximate the second hologram. This variation can correspond in practice to the movement of an object between the first scene and the second scene.

It is also possible to provide, for at least one second coefficient outside of said plurality of second coefficients, a step of determining a residue by difference between this second coefficient, associated with a third wavelet defined by another given multiplet, and the first coefficient associated with a fourth wavelet defined by another multiplet having for image the other multiplet given by another transformation in multidimensional space.

Another transformation is thus used for other second coefficients, which makes it possible to refine the prediction of the second hologram using the first hologram.

This other transformation is for example determined by analyzing another variation between the first scene and the second scene. This other variation may correspond in practice to the movement of another object (different from the aforementioned object) between the first scene and the second scene.

The coding method can also comprise the following steps:

- distribution of at least part of the wavelets into different groups of wavelets respectively associated with different parts of the first scene or of the second scene;

- determination of a transformation of the multidimensional space for each group of wavelets;

- for each of the second coefficients of a given group of wavelets, determination of a residue by the difference between the second coefficient concerned, associated with a fifth wavelet defined by a given multiplet, and the first coefficient associated with a sixth wavelet defined by a multiplet having as an image this multiplet given by the transformation associated with the given wavelet group.

The above-mentioned transformation can be determined in practice as a function of a movement, between the first scene and the second scene, of a set of connected points (a set of points called "connected component" in the following description).

The transformation can be determined for example on the basis of three-dimensional representations of the first scene and of the second scene.

According to another possible embodiment, the coding method can comprise the following steps:

- construction of a first depth map using the first digital hologram;

- construction of a second depth map using the second digital hologram;

- determination of the transformation on the basis of the first depth map and the second depth map.

According to one possible embodiment, the depth being defined in a given direction (here a given direction of the three-dimensional space containing the scene represented by the first digital hologram), the step of constructing the first depth map (and / or the construction step of the second depth map) may include the following steps: - reconstruction, by means of the first digital hologram (or, as the case may be, by means of the second digital hologram), of the light field at a plurality of points;

- for each of a plurality of depths, segmenting the points associated with the relevant depth into a plurality of segments, and determining values of a sharpness metric respectively associated with said segments on the basis of the light field reconstructed on the relevant segment;

- for each element of the first (or second, as the case may be) depth map, determination of the depth for which the sharpness metric is maximum among a set of segments aligned in said given direction and respectively associated with the different depths of the plurality depths (the depth thus determined can then be associated with the element concerned of the first depth map, or of the second depth map as the case may be).

As described below, the coordinates of said multidimensional space can respectively represent a parameter representative of a first spatial coordinate in the plane of the hologram, a parameter representative of a second spatial coordinate in the plane of the hologram, a parameter of spatial frequency expansion and an orientation parameter.

The invention also proposes a device for encoding a sequence comprising at least a first digital hologram representing a first scene and a second digital hologram representing a second scene, the first digital hologram and the second digital hologram being represented by means of a set of wavelets each defined by a multiplet of coordinates in a multidimensional space, the encoding device comprising:

a unit for storing a set of first coefficients, respectively associated with at least some of the wavelets of said set of wavelets, and of a set of second coefficients, respectively associated with at least some of the wavelets of said set of wavelets, the set of first coefficients representing the first digital hologram and the set of second coefficients representing the second digital hologram;

a unit for determining, for each of a plurality of second coefficients, a residue by difference between the second coefficient concerned, associated with a first wavelet defined by a given multiplet, and the first coefficient associated with a second wavelet defined by a multiplet having for image the multiplet given by transformation in multidimensional space;

- a coding unit for the determined residues,

wherein the determining unit is adapted to determine the transformation by variation analysis between the first scene represented by the first digital hologram and the second scene represented by the second digital hologram.

The determination unit and the coding unit can for example be implemented in practice by means of a processor of the coding device, this processor being programmed (for example by means of computer program instructions stored in a memory of the coding device) to implement respectively the steps of determining the residues and the step of coding the residues.

The invention further provides, independently, a method of distributing coefficients respectively associated with wavelets into a plurality of sets of coefficients, the coefficients associated with the wavelets representing a digital hologram intended to reproduce a scene comprising a plurality of parts. , the method comprising the following steps implemented for each of a plurality of said coefficients:

- determination of a line corresponding to the light ray represented by the wavelet associated with the coefficient concerned;

- assignment of the coefficient concerned to a set associated with the part of the scene crossed by the determined straight line.

When each wavelet is defined by a coordinate byte in multidimensional space, the line can be determined using the coordinates of that byte.

For example, when these coordinates (defining the wavelet) include a first spatial coordinate in the plane of the hologram, a second spatial coordinate in the plane of the hologram, a spatial frequency dilation parameter and an orientation parameter , the orientation of the line corresponding to the light ray represented by the wavelet is determined as a function of the expansion parameter and the orientation parameter and / or the position of the straight line corresponding to the light ray represented by a roundelette is determined as a function of these first and second spatial coordinates.

The invention finally proposes, again independently, a method of constructing a depth map relating to a scene represented by a digital hologram, the depth being defined according to a given direction in space (here the three-dimensional space containing the scene), the method comprising the following steps:

- reconstruction, using the digital hologram, of the light field at a plurality of points in space;

- for each of a plurality of depths, segmentation of the points associated with the depth concerned into a plurality of segments, and determination of values of a sharpness metric respectively associated with said segments on the basis of the light field reconstructed on the segment concerned ( that is to say on the basis of the values of the reconstructed light field relating to the points of the segment concerned);

- for each element of the depth map, determination of the depth for which the sharpness metric is maximum among a set of segments aligned in said given direction and respectively associated with the different depths of the plurality of depths, and association of the depth as well determined to this element.

When the digital hologram is represented by coefficients respectively associated with wavelets, the reconstruction of the light field is carried out by means of these coefficients.

Of course, the different characteristics, variants and embodiments of the invention can be associated with each other in various combinations insofar as they are not incompatible or mutually exclusive.

Detailed description of the invention

In addition, various other characteristics of the invention emerge from the appended description given with reference to the drawings which illustrate non-limiting embodiments of the invention and in which:

FIG. 1 represents a coding device according to an exemplary implementation of the invention; FIG. 2 represents the steps of a coding method in accordance with the teachings of the invention;

- Figure 3 shows the relative positioning of a digital hologram and the scene that this digital hologram represents;

FIG. 4 schematically illustrates the calculation of the residues during coding; and

- Figure 5 shows steps in a method of constructing a depth map from a digital hologram.

The encoding device 1 of FIG. 1 comprises a processor 2 and a storage device 4 (such as a hard disk or a memory). The encoding device 1 can also include a communication circuit 6 allowing the processor 2 to exchange data with an external electronic device (not shown).

The storage device 4 stores at least two digital holograms H ₁ ,, H ₂ (each represented by a set of coefficients as explained below) forming part of a sequence of digital holograms (this sequence being intended to reproduce the evolution in the time of a given three-dimensional scene).

In the example described here, the storage device 4 furthermore stores a three-dimensional representation Si; S2 of the three-dimensional scene represented by each of the digital holograms H ₁ , H ₂ . As a variant, however, no three-dimensional representation of the scene could be present within the coding device 1. This is particularly the case when the digital holograms H ₁ , H ₂ are received by the coding device 1 via the encoding circuit. communication 6.

The digital holograms H ₁ , H ₂ can indeed in practice be constructed (prior to the coding method described below) within the coding device 1 on the basis of the three-dimensional representations Si, S2 (for example as described in 'article "View-dependent compression of digital hologram based on matching pursuit" already mentioned), or be received from an external electronic device.

The storage device 4 also stores computer program instructions designed to implement a method as described below with reference to FIG. 2 when these instructions are executed by the processor 2. For the remainder of the description, we take a context such as that shown in FIG. 3: using a reference (O, x, y, z), the digital holograms H ₁ , H ₂ are defined in the plane of equation z = 0.

The digital holograms H ₁ ,, H ₂ are represented here respectively by two sets of real coefficients c ₁ (k, s, X), C ₂ (k, s, X), each coefficient c ₁ (k, s, X) , C2 (k, s, X) being associated with a Gabor-Morlet wavelet Y _{k, s, X} defined by the parameters k, s, X, where

- k is a parameter (integer) which defines the orientation q _k of the wavelet, with q _k = 2pk / N (k varying between 0 and N-1);

- s is a parameter (integer) which defines the expansion of the spatial frequencies (s varying between 1 and a);

- X is a couple of integers which respectively define the two-dimensional spatial coordinates in the plane of the digital hologram (i.e. the plane (O, x, y) in figure 3), with X ϵ [0 , N _x [x [0, N _y [.

The values N, a, N _x and N _y are fixed for the representation considered.

In other words, each Gabor-Morlet wavelet Y _{k, s, X} is defined by a multiplet of coordinates k, s, X in a multidimensional space (here in 4 dimensions).

Hereinafter referred to as “first coefficients” the coefficients c ₁ (k, s, X) representing the digital hologram Hi and “second coefficients” the coefficients c ₂ (k, s, X) representing the digital hologram H ₂ .

We will denote respectively X _x and X _y the first and second component of X.

The digital holograms H ₁ , H ₂ could therefore be reconstructed as follows:

H ₁ = S _{k, s, X} C ₁ (k, s, X). Y _{k, s, X}

H ₂ = S _{k, s, X} C ₂ (k, s, X). Y _{k, s, X}

(the summation being performed for all the integers k included between 0 and N-1, for all the integers s between 1 and a and for all the pairs X of integers included in [0, N _x [x [0, N _y [),

with Y _{k, s, X} the function defined by Y _{k, s, X} (Y) = 1 / s .F (R _k ^-1 [(Y-hx) / (s. D _s )]) for Y ϵ

R ² ,

where hx = (X _x .D _x , X _y . D _y ), D _x and D _y and D _s denote discretization steps respectively of the first spatial component in the plane of the hologram, of the second spatial component in the plane of the hologram and the expansion of spatial frequencies, for A ϵ R ² ,

where | A | and A _x denote respectively the norm (or modulus) of A and its first component, exp is the exponential function (exp (r) = e ^r ), f a parameter (predefined for the representation concerned) and

With reference to FIG. 2, an example of a coding method in accordance with the invention is now described. This method aims at a differential coding of the digital hologram H ₂ on the basis of the digital hologram H ₁ . In this differential coding, the digital hologram H ₁ is used as the reference digital hologram.

This method begins here with a step E2 of segmentation of the coefficients into sets of coefficients E, respectively associated with parts P, of the scene (which amounts to grouping the wavelets Y _{k, s, X} into groups of wavelets respectively associated with these parts P, of the scene).

Each part P of the scene is formed by a set of points from the same region that may have a similar movement. Such a part P, of the scene is referred to below as a “connected component”. In practice, this is, for example, an object in the scene.

In the example described here, the connected components P, are for example identified on the basis of the three-dimensional representation Si of the scene (three-dimensional representation corresponding to the digital hologram H ₁ ).

As a variant, the connected components P, can be reconstructed from a digital hologram (here H ₁ ), for example by means of a depth map, as described below.

In step E2, for each coefficient c ₁ (k, s, X) of the digital hologram H ₁ ,, it is determined which part P, (or connected component) of the scene is crossed by a straight line D (representing a light ray associated with a patch Y _{k, s, X} ) passing through the point of coordinates X (in the plane of the digital hologram) and oriented according to the directing vector V _{k, s} of coordinates:

(cos [q _k ] .sin [f _s ], sin [q _k ] .sin [f _s ], cos [f _s ]), with f _s = arcsin (lf / (sD _S) ) (where l is the reference wavelength of the digital hologram).

The coefficient c ₁ (k, s, X) is then placed in the set E associated with the part P, crossed by this line D.

We thus construct a plurality of sets E _i , each set E, comprising coefficients c ₁ (k, s, X) associated with wavelets Y _{k, s, X} which model light rays having an intersection with the part P, associated with the set E, concerned. In other words, each set E, corresponds to a group of wavelets Y _{k, s, x} which model light rays having an intersection with the part P associated with the set E, concerned.

In certain embodiments (for example when the scene contains a single object, ie a single connected component P ₁ ), the segmentation step E2 could be omitted. In this case, it is considered in the following that a single set E, of coefficients (in this case the set E ₁ ) is processed.

The method of FIG. 2 continues with a step E4 at which a rigid transformation F is determined, for each connected component (or part) P, of the scene.

This rigid transformation F is for example determined by analyzing the movement of the connected component P, between the scene represented by the hologram H ₁ and the scene represented by the hologram H _2.

This motion analysis is for example performed by comparing the three-dimensional representation Si (scene represented by the digital hologram H ₁ ), and the three-dimensional representation S2 (scene represented by the digital hologram H ₂ ). We refer for example on this subject to the article "A Hierarchical Method for 3D Rigid Motion Estimation", by Srinark T., Kambhamettu C., Stone M. in Computer Vision - ACCV 2006. ACCV 2006 Lecture Notes in Computer Science, flight 3852. Springer, Berlin, Heidelberg.

As a variant, this motion analysis could be performed by comparing a first depth map derived (as explained below) from the digital hologram H ₁ and a second depth map derived (as explained below) from l digital hologram H _2. Such depth maps make it possible to come back to the above-mentioned three-dimensional case. For each connected component P ,, we classically decompose the rigid transformation F, into a translation t ⁱ = (t ⁱ x, t ⁱ y, t ⁱ z) and a rotation r ⁱ which can be written (using the angles d 'Euler) in matrix form using the following three matrices:

The method of FIG. 2 then comprises a step E6 of determining, for each set E _i of coefficients, a linear transformation T, of the space-frequency domain on the basis of the rigid transformation determined in step E4 for the component connected P, associated with the set E _i concerned.

In the example described here, the linear transformation T _i is defined as follows (on the basis of the corresponding rigid transformation F _i ):

where l is the already mentioned reference wavelength and l ₂ the identity matrix with 2 rows and 2 columns.

The method of FIG. 2 then comprises in step E8 the construction of a predicted digital hologram H _p as a function of the digital hologram H ₁ and by means of the linear transformations Ti determined in step E6.

To do this, for each coefficient c ₁ (k, s, X) associated with a wavelet Y _{k, s, X} defined by the multiplet (k, s, X) within the digital hologram H ₁ , we determine at which wavelet Y _{k, s, X} applies this coefficient c ₁ (k, s, X) within the predicted hologram H _p by means of the transformation T _i associated with the set E _i containing this coefficient c ₁ (k, s, X):

by setting x1 = f. [cos (q _k )] / (sD _s ), x2 = f. [sin (q _k )] / (sD _s ) and h = (h _x , h _y ) = (X _x . D _x , X _y. D _y we calculate

and, by setting q ‘= atan2 (x1, x2), we then have:

k '= ent (Nq' / p), where ent is the function "integer part", s '= ent (f / [SQRT (x' + x ' ₂ ² ) .Ds)]) and X' = (ent (h'x / Dx), ent (h '/ Dx),

with h '= (h' _x , h'y).

In other words, for each set E, of coefficients, one defines (as it has just been indicated), using the transformation T _i associated with this set E ,, a transformation G, in the multidimensional space (here 4-dimensional) such that a coefficient c ₁ (k, s, X) being part of the set E, and applied to a small Y _{k, s, X} in the digital hologram H ₁ is applied to the Y wavelet _Gi (k, s, X) in the digital hologram predicts H _p , as schematically represented in figure 4. (We therefore have: (k ', s', X') = G _i (k, s, X). )

This transformation G, is thus the transformation which corresponds, in the multidimensional space of the definition coordinates of the wavelets, to the rigid transformation F, of the connected component P ,. This linear transformation G, is valid for the coefficients of the set E, associated with this connected component P ,.

The predicted digital hologram H _p can therefore be written

H _p = S _{k, s, X} C ₁ (k, S, X). Y _Gi (k, s, X)

In this summation, we will not take into account the coefficients c ₁ (k, s, X) for which the image G _i (k, s, X) is outside the domain of values used in the representation concerned, it is ie here outside the following part of the multidimensional space: [0, N-1] x [1, a] x [0, N _x [x [0, N _y [. These coefficients correspond in fact to rays which go beyond the framework of the digital hologram.

The method of FIG. 2 then comprises a step E10 for determining a set of residues by difference between the digital hologram H ₂ (hologram to be encoded) and the digital hologram H _p predicted on the basis of the digital hologram Hi (digital reference hologram).

Precisely, for each coefficient C ₂ (k ', s', X') of the digital hologram H ₂ (this coefficient being relative to a wavelet Y _{k ', s', X'} defined by the multiplet (k ', s ', X')), we determine a residue l _{k ', s', '} by the difference between this coefficient C2 (k', s ', X') and the coefficient relating to the same wavelet Y _{k ', s', X '} in the digital hologram predicts H _p , or c ₁ (k, s, X), as shown in figure 4, with (k', s ', X') = Gi (k, s, X) as already indicated. We thus have:

l _{k ', s', '} = c ₂ (k', s ', X') - C ₁ (k, s, X).

Each residue is therefore determined by the difference between a coefficient c ₂ (k ', s', X '), associated (in the digital hologram H ₂ ) with a roundet Y _{k', s ', X'} defined by the multiplet (k ', s', X'), and a coefficient c ₁ (k, s, X), associated in the digital hologram H ₁ ,, to a wavelet Y _{k, s, X} defined by a multiplet (k, s, X) having for image the multiplet (k ', s', X') by the transformation G, associated with the set E, comprising the coefficient c ₁ (k, s, X).

The method of FIG. 2 finally comprises a step E12 for coding the residues

Ik ’, s’, X ’·

For example, we proceed as follows to do this:

- ordering of the residues l _{k ', s',} _' according to a predetermined order of the bytes

(k ’, s’, X ’);

- entropy coding of ordered residues using a method such as Huffman coding or arithmetic coding.

In the example which has just been described, the differential coding of the digital hologram H ₂ is carried out with reference to a single digital hologram H ₁ ,. As a variant, provision could be made to encode the digital hologram H ₂ with reference to two digital holograms located respectively before and after the digital hologram H ₂ in the sequence of digital holograms.

In this case, the value of the bidirectionally predicted coefficients may be equal to the average of the coefficients predicted from said two digital holograms.

For example, if we denote by H ₃ a digital hologram subsequent to the digital hologram H ₂ in the digital hologram sequence and c ₃ the coefficients of this digital hologram H ₃ , the residue will be defined by:

l _k-, s ' _, x = c ₂ (k', s ', X') - (c ₁ (k, s, X) + c ₃ (k ”, s”, X ”)) / 2, where as before (k ', s', X ') = Gi (k, s, X) and where (k', s ', X') = G'i (k ”, s”, X ”), with G'i a transformation defined analogously to the transformation G ,, but this time on the basis of a rigid transformation F ', determined as a function of the evolution of a connected component P, of the scene represented by the digital hologram H ₃ to the scene represented by digital hologram H ₂ .

FIG. 5 represents steps of a method of constructing a depth map from a digital hologram H (this method can be applied to the hologram Hi and / or to the hologram H ₂ as already indicated) .

Depth here is understood in direction (Oz).

We denote by M _x and M _y the desired horizontal and vertical resolutions for the depth map, and M _z the number of levels of the depth map.

Finally, we denote z _min and z _max the minimum and maximum values of the z coordinate in the scene (these values being predefined).

The method of FIG. 5 begins with a step E20 at which a variable d is initialized to the value 0.

The method then comprises a step E22 for reconstructing the light field U at the depth Z _d = d. (Z _max - z _min ) / M _z + z _min , for example using the propagation of the angular spectrum:

U = F ^-1 {F (H) .exp (2TTiz _d .SQRT [l- ² -f _x ² -f _y ² ])},

where SORT is the square root function, F and F ^-1 are the forward and reverse Fourier transforms, respectively, and f _x and f _y are the frequency coordinates of the hologram in the Fourier domain.

The method then comprises a step E24 of segmenting the reconstructed field U into M _x .M _y segments (rectangular), each segment having a horizontal resolution K _x and a vertical resolution K _y . (The field reconstructed using the hologram H at a horizontal resolution N _x and a vertical resolution N _y as already indicated and we therefore have: M _X .K _X = N _x and M _y .K _y = N _y .)

The method then comprises a step E26 of calculating a sharpness metric v for each of the segments obtained in step E24. If we refer to each segment by a horizontal index i and a vertical index j, we calculate the value v [i, j, d] of the sharpness metric for each segment of indices i, j, here by means of the normalized variance : where is the average intensity of the field on the segment concerned:

As a variant, another sharpness metric could be used, for example one of the metrics mentioned in the article "Comparative analysis of autofocus functions in digital in-line phase-shifting holographÿ ', by ESR Fonseca, PT Fiadeiro, M. Pereira , and A. Pinheiro in Appl. Opt., AO, vol. 55, no. 27, pp. 7663-7674, Sep. 2016.

(Such a calculation of a sharpness metric is carried out for all the segments, that is to say for all i included between 0 and M _x -1 and for all j included between 0 and M _y -1.)

The processing relating to the depth Z _d associated with the current variable d is then terminated.

The method then comprises a step E28 of incrementing the variable d and a step E30 of testing the equality between the current value of the variable d and the number Mz of levels of the depth map.

In the event of a tie (arrow P), all the levels have been processed and the process continues at step E32 described below.

In the absence of equality in step E30 (arrow N), the method loops to step E22 for processing the depth level Z _d corresponding to the (new) current value of the variable d.

The method can then construct in step E32 the depth map D by choosing, for each element of the map (here identified by the indices i, j), the depth (denoted here D [i, j]) for which the sharpness metric is maximum (among the different segments aligned along the Oz axis, all here with indices i, j, and associated respectively with the different depths for d varying from 0 to M _z -1). With the notations already used, we have:

D [i, j] = argmax _d v [i, j, d].

We thus obtain a depth value D [i, j] for all the elements of the depth D map, i.e. here for all i between 0 and M _x -1 and for all j between 0 and M _y -1.

The depth map D thus obtained can be used as already mentioned to determine the connected components (or parts) P of the scene, for example by means of a partitioning algorithm (or “clustering algorithm”). A k-means algorithm can be used for this, for example as described in the article "Some methods for classification and analysis of multivariate observations", by MacQueen, J. in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics, 281 --297, University of California Press, Berkeley, Calif. , 1967.

In this case, the partitioning algorithm makes it possible to group together the connected segments (here of indices i, j) having close depth values (here D [i, j]), the groups thus produced forming the connected components P _i .

Claims

1. Method for coding a sequence comprising at least a first digital hologram (H ₁ ), representing a first scene and a second digital hologram (H ₂ ) representing a second scene, the first digital hologram (H ₁ ), and the second digital hologram (H ₂ ) being represented by means of a set of wavelets each defined by a multiplet of coordinates in a multidimensional space,

the first hologram (H ₁ ), being represented by a set of first coefficients (c ₁ (k, s, X)) respectively associated with at least some of the wavelets of said set of wavelets and the second hologram (H ₂ ) being represented by a set of second coefficients (C2 (k ', s', X')) respectively associated with at least some of the wavelets of said set of wavelets,

the coding method comprising the following steps:

- for each of a plurality of second coefficients (C ₂ (k ', s', X ')), determination (E10) of a residue (l _{k', s ','} ) by difference between the second coefficient concerned (C2 (k ', s', X ')), associated with a first wavelet defined by a given multiplet ((k', s ', X')), and the first coefficient (c ₁ (k, s, X )) associated with a second wavelet defined by a multiplet ((k, s, X)) having for image the given multiplet ((k ', s', X')) by transformation (G,) in multidimensional space;

- coding (E12) of the determined residues (l _{k ', s','} ),

in which the transformation (G _i ) is determined by analysis of the variation between the first scene represented by the first digital hologram (H ₁ ), and the second scene represented by the second digital hologram (H ₂ ).

2. The method of claim 1, wherein said variation corresponds to the movement of an object between the first scene and the second scene.

3. Method according to claim 1 or 2, comprising, for at least one second coefficient outside of said plurality of second coefficients, a step of determining a residue by difference between this second coefficient, associated with a third wavelet defined by another. given multiplet, and the first coefficient associated with a fourth wavelet defined by another multiplet having for image the other multiplet given by another transformation in multidimensional space.

4. The method of claim 3, wherein the other transformation is determined by analyzing another variation between the first scene and the second scene.

5. Method according to claim 3 or 4, comprising the following steps:

- distribution of at least part of the wavelets into different groups of wavelets respectively associated with different parts (P,) of the first scene or of the second scene;

- determination of a transformation (G,) of the multidimensional space for each group of wavelets;

6. Method according to one of claims 1 to 5, wherein the transformation (G _i ) is determined as a function of a movement, between the first scene and the second scene, of a set of connected points (P _i ). .

7. Method according to one of claims 1 to 6, wherein the transformation is determined on the basis of three-dimensional representations of the first scene and the second scene.

8. Method according to one of claims 1 to 6, comprising the following steps:

- construction of a first depth map using the first digital hologram (H ₁ ),;

- construction of a second depth map using the second digital hologram (H ₂ );

9. The method of claim 8, wherein, the depth being defined in a given direction (Oz), the step of constructing the first depth map comprises the following steps:

- reconstruction (E22), by means of the first digital hologram (H ₁ ), of the light field at a plurality of points;

- for each of a plurality of depths, segmentation (E24) of the points associated with the depth concerned into a plurality of segments, and determination of values of a sharpness metric respectively associated with said segments on the basis of the light field reconstructed on the affected segment; - For each element of the first depth map, determination (CONSTR) of the depth for which the sharpness metric is maximum among a set of segments aligned in said given direction and respectively associated with the different depths of the plurality of depths.

10. Method according to one of claims 1 to 9, wherein the coordinates of said multidimensional space respectively represent a parameter representative of a first spatial coordinate in the plane of the hologram, a parameter representative of a second spatial coordinate in the hologram plane, a spatial frequency expansion parameter (s) and an orientation parameter (k).

1 1. Coding device (1) of a sequence comprising at least a first digital hologram (H ₁ ), representing a first scene and a second digital hologram (H ₂ ) representing a second scene, the first digital hologram (H ₁ ), and the second digital hologram (H ₂ ) being represented by means of a set of wavelets each defined by a byte of coordinates in a multidimensional space, the encoding device comprising:

- a storage unit (4) of a set of first coefficients (c ₁ (k, s, X)), respectively associated with at least some of the wavelets of said set of wavelets, and of a set of second coefficients ( C ₂ (k ', s', X')), respectively associated with at least some of the wavelets of said set of wavelets, the set of first coefficients (c ₁ (k, s, X)) representing the first digital hologram (H ₁ ), and the set of second coefficients (C ₂ (k ', s', X')) representing the second digital hologram (H ₂ );

- a determination unit (2), for each of a plurality of second coefficients (C ₂ (k ', s', X')), of a residue (l _{k ', s,'} ) by difference between the second concerned coefficient (C ₂ (k ', s', X ')), associated with a first wavelet defined by a given multiplet ((k', s ', X')), and the first coefficient (c ₁ (k , s, X)) associated with a second wavelet defined by a multiplet ((k, s, X)) having for image the multiplet given ((k ', s', X')) by transformation (G,) in l multidimensional space;

- a coding unit (2) of the determined residues (l _{k ', s,'} ),

wherein the determining unit (2) is adapted to determine the transformation (G,) by analysis of variation between the first scene represented by the first digital hologram (H ₁ ), and the second scene represented by the second digital hologram ( H ₂ ).

12. Device according to claim 11, wherein said variation corresponds to the movement of an object between the first scene and the second scene.