METHOD FOR CONVERTING DATA BETWEEN COLOUR SPACES

Abstract

A method for converting an initial datum between a colour space of a first colorimetric system and a colour space of a second colorimetric system, the initial datum being formed of at least one element expressed in a colorimetric reference system, the method includes: converting the initial datum into a projected datum, by expressing the at least one element in the colour space of the first colorimetric system; adapting the projected datum into an adapted datum, by expressing the at least one element in the colour space of the second colorimetric system. The colour space of the first colorimetric system and of the second colorimetric system are each a hyperbolic space defined by a hyperbolic metric projective reference system.

Claims

1-23. (canceled)

24. A computer-implemented method for converting at least one piece of data, referred to as initial piece of data, between a colour space of at least one colourimetric system, referred to as first colourimetric system, and a colour space of at least one colourimetric system, referred to as second colourimetric system, the at least one initial piece of data consisting of at least one element expressed in a colourimetric reference frame, referred to as initial reference frame, said method comprising the following steps of: converting the at least one initial piece of data into at least one piece of data, referred to as projected piece of data, by expressing the at least one element in the colour space of the at least one first colourimetric system or of the at least one second colourimetric system, adapting the at least one projected piece of data into at least one piece of data, referred to as adapted piece of data, by expressing the at least one element in the colour space of the at least one first colourimetric system or of the at least one second colourimetric system using a transfer function relating the colour spaces of the at least one first colourimetric system and of the at least one second colourimetric system, said colour space of the at least one adapted piece of data being different from the colour space of the at least one projected piece of data, wherein the colour space of the at least one first colourimetric system and of the at least one second colourimetric system are each a hyperbolic space defined by a hyperbolic metric projective reference frame.

25. The method according to claim 24, wherein the conversion step comprises a step of changing reference frame from the initial reference frame to a hyperbolic metric projective reference frame using at least one mathematical operator to express the at least one element of the at least one initial piece of data in the hyperbolic colour space of the at least one first colourimetric system or of the at least one second colourimetric system.

26. The method according to claim 25, wherein the at least one mathematical operator comprises at least one projection operator comprising: a decorrelation matrix ?, and/or a Euclidean rotation matrix P.

27. The method according to claim 24, wherein the hyperbolic metric projective reference frame of the at least one first colourimetric system and of the at least one second colourimetric system comprise a common projective axis.

28. The method according to claim 27, wherein the hyperbolic colour space comprises a convex cone oriented along an axis of the hyperbolic metric projective reference frame, preferably along the common projective axis, and with an aperture 2.sup.0.5.

29. The method according to claim 24, wherein the hyperbolic metric projective reference frame of the at least one first colourimetric system and/or of the at least one second colourimetric system is constructed in an R.sup.4 base.

30. The method according to claim 24, wherein each hyperbolic metric projective reference frame is defined by: a black point defining the origin of the hyperbolic metric projective reference frame, three base vectors, preferably three orthogonal base vectors, a white point defined by the sum of the three base vectors.

31. The method according to claim 30, wherein at least one of the vectors of the hyperbolic metric projective reference frame of the at least one first colourimetric system and/or of the at least one second colourimetric system is a unit vector.

32. The method according to claim 24, wherein each hyperbolic colour space comprises a unit hyperboloid, the projected piece of data and/or the adapted piece of data comprise at least one component expressed in the unit hyperboloid.

33. The method according to claim 24, wherein the transfer function used in the adaptation step comprises an identity matrix.

34. The method according to claim 24, wherein the projection step and/or the adaptation step comprises a step of correcting the hyperbolic colour space of the at least one first colourimetric system and/or of the at least one second colourimetric system by using a hyperbolic rotation matrix ?.

35. The method according to claim 24, wherein prior to the conversion step, a step of designing the hyperbolic colour space of the at least one first colourimetric system from a spectral function of the at least one first colourimetric system, and/or a step of designing the hyperbolic colour space of the at least one second colourimetric system from a spectral function of the at least one second colourimetric system.

36. The method according to claim 35, wherein the step of designing the hyperbolic colour space of the at least one first colourimetric system and/or of the at least one second colourimetric system comprises the following steps of: projecting the spectral function of the at least one first colourimetric system and/or the at least one second colourimetric system into an orthonormal reference frame, and projecting said spectral function of the at least one first colourimetric system and/or the at least one second colourimetric system expressed in the orthonormal reference frame into a hyperbolic metric projective reference frame.

37. The method according to claim 24, wherein when the at least one first colourimetric system and/or the at least one second colourimetric system comprises at least one acquisition means, then said method comprises a calibration phase, referred to as first calibration phase, for defining the hyperbolic metric projective reference frame of the at least one acquisition means, said first calibration phase comprising a step of measuring a spectral function of the at least one acquisition means by using a spectrophotometer and/or a monochromator.

38. The method according to claim 24, wherein when the at least one first colourimetric system and/or the at least one second colourimetric system comprises at least one display means, then said method comprises a calibration phase, referred to as second calibration phase, for defining the hyperbolic metric projective reference frame of the at least one display means, said second calibration phase comprising a step of measuring a spectral function of the at least one display means using a spectrophotometer.

39. The method according to claim 24, wherein the at least one initial piece of data is an image and that the at least one element is a pixel of the initial image.

40. The method according to claim 24, wherein the initial piece of data comes from the at least one first colourimetric system or from the at least one second colourimetric system or is of any origin.

41. The method according to claim 24, wherein the at least one projected piece of data is an image.

42. The method according to claim 24, wherein the at least one projected piece of data comprises three components: an intensity component k a saturability component s, and a hue component ?.

43. The method according to claim 24, wherein the at least one adapted piece of data comprises three components: an intensity component k, a saturability component s, and a hue component ?.

44. A computer program comprising instructions executable by a computing device, which when executed, implement all the steps of the method according to claim 24.

45. A computing device comprising means configured to implement all the steps of the method according to claim 24.

46. An equipment for converting at least one piece of data between at least one acquisition means and at least one display means, comprising: a computing device comprising means configured to implement all the steps of the method according to claim 24, at least one acquisition means arranged to acquire at least one piece of data, referred to as acquired piece of data, and/or at least one display means for displaying at least one piece of data, referred to as displayed piece of data.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0120] Further advantages and features of the invention will become apparent upon reading the detailed description of implementations and embodiments, which are by no means limiting, and the following appended drawings.

[0121] FIG. 1A is a schematic representation of one example of spectral functions according to CIE1931 XYZ;

[0122] FIG. 1B is a schematic representation of the colour space associated with the spectral functions of FIG. 1A;

[0123] FIG. 2 is a schematic representation of a first non-limiting exemplary embodiment of a method according to the invention;

[0124] FIG. 3 is a schematic representation of a second non-limiting exemplary embodiment of a method according to the invention;

[0125] FIG. 4 is a schematic representation of a non-limiting exemplary embodiment of a step according to the invention of designing a hyperbolic colour space of a colourimetric system;

[0126] FIG. 5 is a schematic representation of a first non-limiting exemplary embodiment of a conversion step of the method according to the invention;

[0127] FIG. 6A is a schematic representation of a second non-limiting exemplary embodiment of a conversion step of the method according to the invention;

[0128] FIG. 6B is a representation of all the elements making up the initial piece of data in FIG. 6A, represented in a hyperbolic colour space.

[0129] FIG. 7 is a schematic representation of a third non-limiting exemplary embodiment of a method according to the invention;

[0130] FIG. 8 is a schematic representation of a third example of a step of designing the hyperbolic colour space according to the invention of a first colourimetric system on the basis of a spectral function of the first colourimetric system and a step of designing the hyperbolic colour space according to the invention of a second colourimetric system on the basis of a spectral function of the second colourimetric system;

[0131] FIG. 9 is a schematic representation of a fourth non-limiting exemplary embodiment of a method according to the invention;

[0132] FIG. 10 is a schematic representation of a fifth non-limiting exemplary embodiment of a method according to the invention;

[0133] FIG. 11 is a schematic representation of one example of several iterations of a method according to the invention;

[0134] FIG. 12 is a schematic representation of a first example of a device according to the invention;

[0135] FIG. 13 is a schematic representation of a second example of a device according to the invention;

[0136] FIG. 14 is a schematic representation of a first example of equipment according to the invention;

[0137] FIG. 15 is a schematic representation of a second example of equipment according to the invention.

DETAILED DESCRIPTION

[0138] It is understood that embodiments described below are by no means limitative. It is especially possible to envisage alternatives to the invention comprising only a selection of the characteristics described hereinafter in isolation from the other characteristics described, if this selection of characteristics is sufficient to confer a technical advantage or to differentiate the invention from prior art. This selection includes at least one characteristic which is preferably functional without structural details, or with only part of the structural details if this part alone is sufficient to confer a technical advantage or to differentiate the invention from prior art.

[0139] In particular, all the alternatives and all the embodiments described can be combined with each other if there is nothing technically opposite to such a combination.

[0140] In the figures, elements common to several figures retain the same reference.

[0141] FIG. 1A illustrates three spectral functions, noted 102, 104 and 106 respectively, in a colour space defined by the CIE1931 XYZ.

[0142] These spectral functions 102, 104, 106 are called colourimetric functions of the reference CIE observer. These spectral functions 102, 104, 106 represent a chromatic response of a normalised human eye. This means that these spectral functions 102, 104, 106 are normalised and are not related to characteristics in colourimetric systems other than the human eye.

[0143] FIG. 1B illustrates a colour space 108 defined from the spectral functions 102, 104, 106 of the FIG. 1A part. The colour space 108 is not hyperbolic. A chromaticity diagram 110, known as the CIE chromaticity diagram, can be drawn from the colour space 108. The chromaticity diagram 110 is two-dimensional. Each dimension of the chromaticity diagram depends on a spectral function 102, 104, 106 defined in FIG. 1A.

[0144] FIG. 2 is a schematic representation of a non-limiting exemplary embodiment of a method 200 according to the invention.

[0145] The method 200 illustrated in FIG. 2 is a computer-implemented method.

[0146] In this example, the method 200 relates to the conversion of at least one piece of data between a colour space 204 of a first colourimetric system and a colour space 206 of a second colourimetric system.

[0147] The at least one initial piece of data 202 consists of at least one element expressed in a colourimetric reference frame, called the initial reference frame.

[0148] The method 200 comprises the following steps of: [0149] converting 208 the at least one initial piece of data 202 into at least one piece of data, referred to as projected piece of data 210, by expressing the at least one element in the colour space 204 of the first colourimetric system, [0150] adapting 212 the at least one projected piece of data 210 into at least one piece of data, referred to as adapted piece of data 214, by expressing the at least one element in the colour space 206 of the second colourimetric system using a transfer function relating the colour spaces 204, 206 of the first colourimetric system and of the second colourimetric system, said colour space of the at least one adapted piece of data 214 being different from the colour space of the at least one projected piece of data 210.

[0151] The colour space 204, 206 of the first colourimetric system and of the second colourimetric system are each a hyperbolic space defined by a hyperbolic metric projective reference frame.

[0152] By way of non-limiting example, the initial piece of data 202 is an image 202 in R, G, B format. The element of the initial piece of data 202 is, in this example, a pixel comprising coordinates expressed in the initial reference frame which is an R, G, B reference frame.

[0153] Of course, in other alternatives to the method 200, said initial piece of data 202 may comprise several pixels (i.e. elements). In this case, the conversion and adaptation steps are applied to all the pixels of the initial piece of data 202.

[0154] Preferably, the conversion step 208 corresponds to a reference frame change step to switch from the initial R, G, B type reference frame to a hyperbolic metric projective reference frame. In the case of FIG. 2, this corresponds to a change of reference frame to the hyperbolic metric projective reference frame of the first colourimetric system. For this, at least one mathematical operator is used in the conversion step 208 to express the element of the initial piece of data 202 in the hyperbolic colour space of the first colourimetric system.

[0155] Preferably the mathematical operator is a projection operator. The projection operator may comprise: [0156] a decorrelation matrix noted r, and/or [0157] a Euclidean rotation matrix noted P.

[0158] The conversion step 208 provides the projected piece of data 210.

[0159] The transfer function may comprise an identity matrix.

[0160] In the case of FIG. 2, the projected piece of data 210 is an image and comprises as many elements (i.e. pixels) as the initial piece of data 202. Thus, no information is lost after the conversion step 208.

[0161] By way of non-limiting example, the projected piece of data 210 comprises three components: [0162] an intensity component, noted k, [0163] a saturability component, noted s, and [0164] a hue component, noted ?.

[0165] The adaptation step 212 provides the adapted piece of data 214.

[0166] The adapted piece of data 214 is an image and comprises as many elements (i.e. pixels) as the initial piece of data 202. Thus no information is lost after the adaptation step 210.

[0167] By way of non-limiting example, the adapted piece of data 214 comprises three components: [0168] an intensity component, noted k, [0169] a saturability component, noted s, and [0170] a hue component, noted ?.

[0171] By way of non-limiting example, the first colourimetric system is a camera and the second colourimetric system is a screen. According to this example, the initial reference frame can be the R, G, B reference frame of the camera.

[0172] In another alternative, the first colourimetric system is a first screen and the second colourimetric system is a second screen. In this example, the initial reference frame can be the R, G, B reference frame of the first screen.

[0173] Thus, according to the method 200, the first colourimetric system may be a display means or an acquisition means. The second colourimetric system may be a display means or an acquisition means.

[0174] FIG. 3 is a schematic representation of a non-limiting exemplary embodiment of a method 300 according to the invention.

[0175] The method illustrated in FIG. 3 comprises all the steps of the method 200 illustrated in FIG. 2.

[0176] Prior to the conversion step 208, the method 300 comprises a step 302 of designing the hyperbolic colour space 204 of the at least one first colourimetric system from a spectral function of the at least one first colourimetric system.

[0177] Prior to the conversion step 208, the method 300 comprises a step 304 of designing the hyperbolic colour space 206 of the at least one second colourimetric system from a spectral function of the at least one second colourimetric system.

[0178] FIG. 4 is one example of a representation of the step 302, 304 of designing the hyperbolic colour space of a colourimetric system that can be implemented by the method 300 when the spectral function of the colourimetric system is known or can be measured. According to this example, this may be the step 302 of designing the hyperbolic colour space of the first colourimetric system and/or the step 304 of designing the hyperbolic colour space of the second colourimetric system.

[0179] According to the method 300, the spectral function 401 of the at least one first colourimetric system and/or of the at least one second colourimetric system may be known, for example if these colourimetric systems have already been used or because the spectral functions of each colourimetric system have been given by the manufacturer.

[0180] Thus, according to this example, each design step 302, 304 may comprise the following steps of: [0181] projecting 402 the spectral function of the first colourimetric system and of the second colourimetric system into an orthonormal reference frame, and [0182] projecting 404 said spectral function of the first colourimetric system and/or of the second colourimetric system expressed in the orthonormal reference frame into a hyperbolic metric projective reference frame.

[0183] By way of non-limiting example, the spectral function 401 is that of an acquisition means, such as a camera capable of recording light comprising wavelengths in the visible range. The spectral function 401 comprises positive values.

[0184] According to this example, the spectral function 401, defined by three measurement vectors ?.sub.1, ?.sub.2 and ?.sub.3, is projected into the orthonormal reference frame defined by three vectors ?.sub.1, ?.sub.2, ?.sub.3. The three vectors of the orthonormal reference frame define a matrix noted |?>. The three vectors of the measurement reference frame define a matrix denoted |?>.

[0185] In this example, the spectral function 401 projected into the orthonormal reference frame can be obtained using the following formula:

[00001]$\begin{array}{cc}.Math.?.Math.=?.Math.?.Math.& \left[\mathrm{Math}1\right]\end{array}$ [0186] With ? corresponding to a decorrelation matrix, and [0187] <?| corresponding to the vector matrix of the orthonormal reference frame and [0188] <?| corresponding to the vector matrix of the measurement reference frame.

[0189] In a first alternative, the decorrelation matrix ? may be known. In this case it is sufficient to apply the formula Math 1 to switch from one reference frame to another.

[0190] In a second alternative, the decorrelation matrix ? may be unknown. In this case, the decorrelation matrix can be calculated from the spectral function (in the measurement reference frame) of the colourimetric system considered by decorrelating the spectral function of said system considered.

[0191] Then, according to the method 300, the spectral function expressed in the orthonormal reference frame <?| is again projected into a hyperbolic metric projective reference frame comprising three vectors ?.sub.1, ?.sub.2, ?.sub.3. The three vectors of the hyperbolic metric projective reference frame define a matrix denoted |?>.

[0192] In this example, the spectral function 401 projected into the hyperbolic metric projective reference frame can be obtained using the following formula:

[00002]$\begin{array}{cc}.Math.?.Math.=P.Math.?.Math.& \left[\mathrm{Math}2\right]\end{array}$ [0193] With P corresponding to the Euclidean rotation matrix, and [0194] <?| corresponding to the vector matrix of the hyperbolic metric projective reference frame, and <?| corresponding to the vector matrix of the orthonormal reference frame.

[0195] The Euclidean rotation matrix P is preferably known.

[0196] Preferably, the Euclidean rotation matrix is written as

[00003]$\begin{array}{cc}P=\left[\begin{array}{ccc}-1/\sqrt{6}& 2/\sqrt{6}& -1/\sqrt{6}\\ 1/\sqrt{2}& 0& -1/\sqrt{2}\\ 1/\sqrt{3}& 1/\sqrt{3}& 1/\sqrt{3}\end{array}\right]& \left[\mathrm{Math}3\right]\end{array}$

[0197] Thus, it is sufficient to apply the formula Math 2 to switch from the orthonormal reference frame to the hyperbolic metric projective reference frame. The last projection step 404 provides, at the output of the design step 302, 304, the hyperbolic colour space 204, 206 of the colourimetric system considered by defining the cone and the unit hyperboloid which are symmetrical relative to the axis ?.sub.3.

[0198] The unit hyperboloid and the cone can be related by a common metric defined preferably by a 4?4 matrix, preferably by a diagonal matrix comprising the diagonal values (??, ??, 1, 1). The height of the cone along the axis 43 can be adapted so that the first colourimetric system corresponds with the second colourimetric system.

[0199] According to this example, the hyperbolic colour space 204, 206 of the colourimetric system is expressed in the hyperbolic metric projective reference frame. The hyperbolic metric projective reference frame is defined by a black point 406 defining the origin of the reference frame, three base vectors noted ?.sub.1, ?.sub.2, ?.sub.3, and a white point defined by an affix to the sum vector of the three base vectors noted ??.

[0200] Preferably, the three base vectors ?.sub.1, ?.sub.2, ?.sub.3 are orthogonal to each other. Preferably the affix is 1. The hyperbolic metric projective reference frame can consist of an orthogonal reference frame defined by vectors ?.sub.1, ?.sub.2, ?.sub.3 and a direction of projection oriented along ?3.

[0201] Thus, the hyperbolic metric projective reference frame is a reference frame of the affine space of dimension 4 constructed on R.sup.4 and can be written using the following formulation (O, ?.sub.1, ?.sub.2, ?.sub.3, ??) where O corresponds to the origin 406 of the reference frame and ?? corresponds to the white point.

[0202] The hyperbolic colour space comprises a convex cone 405, also noted C in the following. The cone 405 is oriented along the white point ?? of the hyperbolic metric projective reference frame. In FIG. 4, the cone 405 is oriented along the axis carried by the vector ?.sub.3 of the hyperbolic metric projective reference frame. The cone 405 preferably has an aperture of 2.sup.0.5.

[0203] The vector ?.sub.3 of the hyperbolic metric projective reference frame is preferably a unit vector.

[0204] The cone 405 can be defined according to the theory of Huseyin Yilmaz in the documents On Color Perception, Applied Research Laboratory, Sylvania Electronic Systems, Walham; and Color Vision and New approach to General Perception, Applied Research Laboratory, Sylvan Electronic Systems, A division of Sylvania Electric Products, Inc. Waltham, Massachusetts. The cone 405 may comprise an envelope. The envelope of the cone 405 is formed from Dirac distributions representing visible monochromatic colours. The envelope of the cone 405 is the locus of the colours of maximum saturation. Each positive spectral function can be represented as a point inside the cone. The envelope of the cone represents the set of pure hue colours with maximum saturation.

[0205] The vector |?.sub.3> is preferably a unit vector.

[0206] The hyperbolic colour space 204, 206 of the colourimetric system of FIG. 4 also comprises a unit hyperboloid 408. The unit hyperboloid 408 may represent the constant intensity metamerism space.

[0207] FIG. 5 is one example of a schematic representation of the step 208 of converting two initial data F, G into a hyperbolic colour space 204 of a colourimetric system (for example of the first colourimetric system) defined from spectral data of said colour space.

[0208] FIG. 5 shows a representation of a spectral function 502 of a piece of data F and a representation of a spectral function 504 of a piece of data G, thus showing the three vector components ?.sub.1, ?.sub.2, ?.sub.3 of the spectral function of a colourimetric system.

[0209] Following the conversion step 208, each initial piece of data F or G is represented in the hyperbolic colour space of the colourimetric system defined on the basis of the spectral function of said colourimetric system. The hyperbolic colour space is defined on the basis of the three vectors ?.sub.1, ?.sub.2, ?.sub.3 defining the matrix |?> in the hyperbolic metric projective reference frame. The vector ?.sub.3 is a unit vector.

[0210] In this example, the data F and G are polychromatic lights.

[0211] The spectral functions of the initial data F and G can be expressed in the hyperbolic metric projective reference frame through a linear application, denoted oe. For example, for the initial piece of data F, the linear application is defined as:

[00004]$\begin{array}{cc}\mathrm{oe}:?.fwdarw.{?}^3& \left[\mathrm{Math}4\right]\end{array}$$\begin{array}{cc}.Math.F.Math.?x=\mathrm{oe}(.Math.F.Math.)=.Math.?.Math.F.Math.=\left[\begin{array}{c}{F}_1\\ F_2\\ F_3\end{array}\right]& \left[\mathrm{Math}5\right]\end{array}$

[0212] With x corresponding to a point in hyperbolic colour space and F a spectral function (depending on wavelength) representing a light, and F1, F2, F3 corresponding to the components of the initial piece of data F expressed in the hyperbolic metric projective reference frame of the colourimetric system considered.

[0213] Each light, denoted F(?)=|F, is thus represented by a linear combination of three base functions, denoted

[00005]$\begin{array}{cc}.Math.F.Math.=F_1.Math.{?}_1.Math.+F_2.Math.{?}_2.Math.+F_3.Math.{?}_3.Math.& \left[\mathrm{Math}6\right]\end{array}$

[0214] The hyperbolic colour space 204, 206 comprises the cone 405 with an aperture 2.sup.0.5. Further, in this example, the hyperbolic colour space 204, 206 comprises several hyperboloids.

[0215] In particular, the hyperbolic colour space 204, 206 of FIG. 5 comprises the unit hyperboloid 408, also noted H.sub.1, thus a non-unit hyperboloid 505, of any intensity factor k, noted H.sub.k. The unit hyperboloid H1 has an intensity factor k equal to 1.

[0216] The equation of the envelope of the cone 405, denoted C, in the hyperbolic metric projective reference frame (0, ?.sub.1, ?.sub.2, ?.sub.3, ??) is given by:

[00006]$\begin{array}{cc}C=\left\{x={\left[x_1,x_2,x_3\right]}^t.Math.x^t\mathrm{Jx}=0\right\}& \left[\mathrm{Math}7\right]\end{array}$

With x corresponding to any point with coordinates x.sub.1, x.sub.2, x.sub.3 in the hyperbolic metric projective reference frame defined by vectors ?.sub.1, ?.sub.2, ?.sub.3 of the canonical projective reference frame also called hyperbolic metric projective reference frame, and with the matrix J defined by:

[00007]$\begin{array}{cc}J=\left[\begin{array}{ccc}-1/2& 0& 0\\ 0& -1/2& 0\\ 0& 0& 1\end{array}\right].& \left[\mathrm{Math}8\right]\end{array}$

This is again a cone 405 with matrix C(k, ?) defined by:

[00008]$\begin{array}{cc}C\left(k,?\right)=k\left[\begin{array}{c}\sqrt{2}\cos 2\mathrm{??}\\ \sqrt{2}\sin 2\mathrm{??}\\ 1\end{array}\right].& \left[\mathrm{Math}9\right]\end{array}$

[0217] The cone 405 defines a hyperbolic metric represented by the non-unit hyperboloid 505 denoted H.sub.k. The hyperbolic metric H.sub.k is defined by the formula:

[00009]$\begin{array}{cc}{H}_k=\left\{X={\left[x_1,x_2,x_3\right]}^t.Math.X^t\mathrm{JX}=k^2\right\}& \left[\mathrm{Math}10\right]\end{array}$

Where X corresponds to any point on the non-unit hyperboloid 505 with coordinates x.sub.1, x.sub.2, x.sub.3 in the projective hyperbolic metric defined by vectors ?.sub.1, ?.sub.2, ?.sub.3. In this example, any point X corresponds to any colour.

[0218] The hyperboloid H.sub.k is written according to the following formula:

[00010]$\begin{array}{cc}{H}_k\left(s,?\right)=k\left[\begin{array}{c}\sqrt{2}\sinh s\cos 2\mathrm{??}\\ \sqrt{2}\sinh s\sin 2\mathrm{??}\\ \cosh s\end{array}\right]& \left[\mathrm{Math}11\right]\end{array}$

With k corresponding to the intensity component, s the saturability component and ? the hue component of any colour X.

[0219] Following this example, any point X (i.e. colour) inside the cone 405 belongs to a hyperboloid with an intensity factor k given by the formula:

[00011]$\begin{array}{cc}k=\sqrt{X^t\mathrm{JX}}& \left[\mathrm{Math}12\right]\end{array}$

[0220] This point X can be projected into the unit hyperboloid 408 in a point x. Thus, any element expressed in any hyperboloid of factor k can be projected into a unit hyperboloid H.sub.1. By way of example, the point F belonging to the non-unit hyperboloid 505 H.sub.k is projected onto the unit hyperboloid 408 H.sub.1 at a point f. A straight line 508 connects the origin of the hyperbolic metric projective reference frame to the point F on the non-unit hyperboloid H.sub.k 505. This straight line 508 is a projective straight line 508.

[0221] In this example, the data F and G are positioned on the same projective straight line 508. Lights F and G are therefore metameric. These lights are therefore perceived in an equivalent way by the colourimetric systems.

[0222] Since lights F and G are metameric and with the same intensity, the following relationship is verified:

[00012]$\begin{array}{cc}.Math.F.Math.?.Math.G.Math.?\mathrm{oe}(.Math.F.Math.)=k.\mathrm{oe}(.Math.G.Math.)& \left[\mathrm{Math}13\right]\end{array}$

with k equal to 1 because F and G are also of the same intensity.

[0223] As the lights are positive spectral functions, they are inscribed inside the cone 405.

[0224] In this example, the point f of light F is a pure colour. The spectral function of light F in the projective hyperbolic metric is expressed in terms of the spectral function 510. The spectral function of the light F in the hyperbolic metric projective reference frame 510 is defined according to the formula f(?)=|f as the projected point of any point F of the metamerism space corresponding to a spectral light F(?). It is defined as the projection onto the unit hyperboloid H.sub.1, defined by the equation:

[00013]$\begin{array}{cc}f=\frac{F}{\sqrt{F^T\mathrm{JF}}}=\frac{F}{k}& \left[\mathrm{Math}14\right]\end{array}$

[0225] Thus a proportionality factor relates data expressed in the unit hyperboloid H.sub.1 to a non-unit hyperboloid H.sub.K.

[0226] So with any light |F, is associated its representation in the unit hyperboloid 408 as the vector F=oe(|F), and its representation in multiplicative luminance k and chrominance (s,?) as:

[00014]$\begin{array}{cc}F=\left[\begin{array}{c}{F}_1\\ F_2\\ F_3\end{array}\right]=k\left[\begin{array}{c}\sqrt{2}\sinh s\cos 2\mathrm{??}\\ \sqrt{2}\sinh s\sin 2\mathrm{??}\\ \cosh s\end{array}\right]& \left[\mathrm{Math}15\right]\end{array}$

With k corresponding to the intensity component, s the saturability component and ? the hue component of the colour F.
The intensity component k can be defined by:

[00015]$\begin{array}{cc}k=\sqrt{F^T\mathrm{JF}}& \left[\mathrm{Math}16\right]\end{array}$

The saturability component s can be defined by:

[00016]$\begin{array}{cc}s={\sinh }^{-1}\frac{\sqrt{F_1^2+F_2^2}}{\sqrt{2}k}& \left[\mathrm{Math}17\right]\end{array}$

The hue component ? can be defined by:

[00017]$\begin{array}{cc}?=\frac{1}{2?}{\tan }^{-1}\frac{F_2}{F_1}& \left[\mathrm{Math}18\right]\end{array}$

[0227] The saturability s can define the aperture of the colour in the projective hyperbolic colour space.

[0228] Expressing the projected piece of data in the unit hyperboloid H1 allows chrominance information of said projected piece of data to be encoded.

[0229] FIG. 6A is one example of a representation of the step 208 of the method 300 of converting an initial piece of data 202 in a hyperbolic colour space of a colourimetric system.

[0230] According to this example, the spectral function of the colourimetric system from which the initial piece of data 202 comes is unknown and cannot be measured. Thus, only the initial piece of data 202 is known.

[0231] By way of non-limiting example, the initial piece of data 202 is an image comprising pixels 602 expressed in R, G, B coordinates.

[0232] According to this example, each pixel 602 of the image 202 comprises three coordinates expressed according to the formula:

[00018]$\begin{array}{cc}{p}_{?}=\left[\begin{array}{c}r\\ g\\ b\end{array}\right]& \left[\mathrm{Math}19\right]\end{array}$

with p.sub.? corresponding to a pixel 602 of image 202 and

[00019]$\left[\begin{array}{c}r\\ g\\ b\end{array}\right]$

corresponding to the coordinates of pixel 602 in R, G, B space (i.e. initial reference frame).

[0233] The spectral origin of each pixel 602 is unknown.

[0234] According to this example, to perform the conversion step 208, the coordinates of the pixels 602 in R, G, B space are the same as the coordinates of the pixels 602 in the orthonormal reference frame defined by the matrix of vectors |?>. Thus, the coordinates of each pixel 602 in the orthonormal reference frame can be written according to the formula

[00020]$\begin{array}{cc}.Math.p_{?}.Math.=r.Math.{?}_1.Math.+g.Math.{?}_2.Math.+b.Math.{?}_3.Math.=.Math.?.Math.p_{?}& \left[\mathrm{Math}20\right]\end{array}$

With r, g, b corresponding to the pixel coordinates in R,G,B space, |?.sub.1>, |?.sub.2>, |?.sub.3> corresponding to the vectors of the orthonormal reference frame.

[0235] The representation of the initial piece of data 202 (image R, G, B) in the hyperbolic colour space of the colourimetric system is performed by the conversion step 208. The conversion step 208 is performed for each pixel 602 of the initial piece of data 202 according to the following formula:

[00021]$\begin{array}{cc}p={\mathrm{Pp}}_{?}& \left[\mathrm{Math}21\right]\end{array}$

with P corresponding to the Euclidean rotation matrix and p corresponding to the coordinates of a pixel 602 in the projective hyperbolic metric reference frame, p.sub.? corresponding to the coordinates of the pixel in the orthonormal reference frame.

[0236] Each pixel 602 of the initial piece of data 202 comprises coordinates in the hyperbolic colour space.

[0237] The conversion step is performed on all the pixels 602 (i.e. elements 602) of the initial piece of data 202.

[0238] FIG. 6B is a representation of the pixels 602 of the initial piece of data 202 illustrated in FIG. 6A in a hyperbolic colour space 204 defined from the initial piece of data 202 of unknown origin.

[0239] The intensity component k of the initial piece of data 202 corresponds to points on a projective straight line. The projective straight line can be defined by a line which passes through the origin 406 of the hyperbolic metric projective reference frame and which intersects a hyperboloid. The saturability s and hue ? components of the initial piece of data 202 correspond to coordinates in the unit hyperboloid 408. Each pixel 602 is expressed as a point in the hyperbolic metric projective reference frame with coordinates for a saturability component, a hue component and an intensity factor k.

[0240] Thus, it is possible to construct a hyperbolic metric colour space 204 even if the spectral components of the colourimetric system from which the initial piece of data 202 is derived are unknown.

[0241] FIG. 7 is a schematic representation of a non-limiting exemplary embodiment of a method 700 according to the invention.

[0242] The method illustrated in FIG. 7 includes all of the steps of the method 300 illustrated in FIG. 3 and FIG. 4. Only the differences will be described.

[0243] In the case of FIG. 7, the spectral function of the at least one first colourimetric system and the at least one second colourimetric system are unknown. However, these spectral functions may be determined by measurements.

[0244] In this case, the method 700 comprises, prior to the step 302 of designing the hyperbolic colour space 204 of the first colourimetric system and prior to the step 304 of designing the hyperbolic colour space 206 of the second colourimetric system: [0245] a step 702 of measuring the spectral function of the first colourimetric system, and [0246] a step 704 of measuring the spectral function of the second colourimetric system.

[0247] The step 702 of measuring and the step 302 of designing the hyperbolic colour space 204 of the first colourimetric system are included in a calibration phase 706 for defining the hyperbolic metric projective reference frame of the first colourimetric system.

[0248] The step 704 of measuring and the step 304 of designing the hyperbolic colour space 206 of the first colourimetric system are included in a calibration phase 708 for defining the hyperbolic metric projective reference frame 206 of the second colourimetric system.

[0249] In a non-limiting example, the first colourimetric system and/or the second colourimetric system may comprise an acquisition means. For example, the first colourimetric system and the second colourimetric system may be an acquisition means, such as a photographic camera or a video camera or a photon sensor. If the first colourimetric system and the second colourimetric system comprise an acquisition means, then the step of measuring 702, 704 the spectral function of the first colourimetric system and the second colourimetric system can preferably be performed by a spectrophotometer accompanied with a monochromator.

[0250] In this example, each step 702, 704 of measuring the spectral function of the means for acquiring the first colourimetric system and the second colourimetric system may comprise the following steps of: [0251] emitting spectral light, referred to as reference light, by a monochromator, towards the means for acquiring the first colourimetric system or the second colourimetric system, [0252] comparing spectral responses recorded by the spectrophotometer and the means for acquiring the first colourimetric system or second colourimetric system.

[0253] By way of non-limiting example, in the case of acquisition means, a monochromator emits spectral light equivalent to a Dirac in the visible range. This light is then measured by a spectrophotometer and simultaneously sent into a lens of an acquisition device, for example a camera. The R, G, B values delivered by the acquisition means for each light (Dirac) sent are used to calculate spectral function of the acquisition means.

[0254] In another non-limiting example, the first colourimetric system and/or the second colourimetric system may comprise a display means. For example, the first colourimetric system and the second colourimetric system may be a display means, such as a screen. If the first colourimetric system and/or the second colourimetric system comprise a display means, then the step of measuring 702, 704 the spectral function of the first colourimetric system and the second colourimetric system can preferably be performed by a spectrophotometer.

[0255] By way of example, in the case of a display, digital values (DV) are sent to a video card to generate light on a screen. This light is then measured. The measurement of the spectral function of a screen can be carried out according to the disclosure of application WO 2020/048701 A1.

[0256] In this example, the step 702 of measuring the spectral function in the measurement reference frame (noted |?.sup.1> in this example) of the first colourimetric system is provided at the input of the step 302 of designing the first hyperbolic colour space 204 of the first colourimetric system. Similarly, the step 704 of measuring the spectral function (noted |?.sup.2> in this example) in the measurement reference frame of the second colourimetric system is provided at the input of the step 304 of designing the second hyperbolic colour space 206 of the second colourimetric system.

[0257] FIG. 8 is one exemplary embodiment of a step of designing the hyperbolic colour space 302 of a first colourimetric system from a spectral function of the first colourimetric system and a step of designing the hyperbolic colour space 304 of a second colourimetric system from a spectral function of the second colourimetric system.

[0258] FIG. 8 comprises a graph 801 comprising the spectral function 802 of the first colourimetric system expressed in the measurement reference frame and the spectral function 804 of the first colourimetric system expressed in the orthonormal reference frame.

[0259] The spectral function 802 of the first colourimetric system expressed in the measurement reference frame comprises three colour components noted 802.sub.1, 802.sub.2 and 802.sub.3 respectively. The spectral function 804 of the first colourimetric system expressed in the orthonormal reference frame comprises three colour components noted 804.sub.1, 804.sub.2 and 804.sub.3 respectively.

[0260] FIG. 8 includes a graph 805 comprising the spectral function 806 of the second colourimetric system expressed in the measurement reference frame and the spectral function 808 of the second colourimetric system expressed in the orthonormal reference frame.

[0261] The spectral function 806 of the second colourimetric system expressed in the measurement reference frame (i.e. matrix |?>) comprises three colour components noted 806.sub.1, 806.sub.2 and 806.sub.3 respectively. The spectral function 804 of the first colourimetric system expressed in the orthonormal reference frame (i.e. matrix |?>) comprises three colour components noted 808.sub.1, 808.sub.2 and 808.sub.3 respectively.

[0262] By way of non-limiting example, the first colourimetric system can be an acquisition means while the second colourimetric system can be a display means.

[0263] For the first colourimetric system, the projection step 404 makes it possible to obtain the hyperbolic colour space 204 of the first colourimetric system, and for the second colourimetric system, the projection step 404 makes it possible to obtain the hyperbolic colour space 206 of the second colourimetric system.

[0264] Thus the hyperbolic metric projective reference frame associated with the first colourimetric system is defined in the same way as the hyperbolic metric projective reference frame of the second colourimetric system.

[0265] The hyperbolic colour space 204, 206 of the first colourimetric system and of the second colourimetric system each comprise a unit hyperboloid 408 and a convex cone 405.

[0266] The hyperbolic metric projective reference frame of the first colourimetric system and of the second colourimetric system comprise a common projective axis. The common projective axis corresponds to the axis defined by the unit vector ?.sub.3. Each cone 405 is centred on the common projective axis.

[0267] By way of example, a matrix |?.sup.1> is considered to be the spectral function of the first colourimetric system in the measurement reference frame and a matrix |?.sup.2> is considered to be the spectral function of the second colourimetric system in the measurement reference frame. To express data from one space to another, the hyperbolic colour space of the first colourimetric system should be able to switch over with the colour space of the second colourimetric system.

[0268] To achieve this, it is sufficient to find the spectral functions ?.sup.1, ?.sup.2, expressed in the hyperbolic metric projective reference frame of each colourimetric system to be able to perform the adaptation step 212 between the first colourimetric system and the second colourimetric system. In this example, this is possible when the hyperbolic metric projective reference frame of the first colourimetric system and the hyperbolic metric projective reference frame of the second colourimetric system comprise a common projective axis, for example the axes of the hyperbolic metric projective reference frames are similar or collinear between both representations. These functions are given by:

[00022]$\begin{array}{cc}.Math.{?}^1.Math.=P.Math.{?}^1.Math.=P{?}^1.Math.{?}^1.Math.& \left[\mathrm{Math}22\right]\end{array}$

With ?.sup.1 corresponding to the spectral function of the first colourimetric system in the hyperbolic metric projective reference frame, ?.sup.1 corresponding to the spectral function of the first colourimetric system in the orthonormal reference frame and ?.sup.1 corresponding to the spectral function of the first colourimetric system in the measurement reference frame P corresponding to the Euclidean rotation matrix and ? corresponding to the decorrelation matrix.

[00023]$\begin{array}{cc}.Math.{?}^2.Math.=P.Math.{?}^2.Math.=P{?}^2.Math.{?}^2.Math.& \left[\mathrm{Math}23\right]\end{array}$

With ?.sup.2 corresponding to the spectral function of the second colourimetric system in the hyperbolic metric projective reference frame, ?.sup.2 corresponding to the spectral function of the second colourimetric system in the orthonormal reference frame and ?.sup.2 corresponding to the spectral function of the second colourimetric system in the measurement reference frame, P corresponding to the Euclidean rotation matrix and ? corresponding to the decorrelation matrix.

[00024]$\begin{array}{cc}{?}^i,i=\left\{1,2\right\}& \left[\mathrm{Math}24\right]\end{array}$

With index 1 corresponding to the first colourimetric system and index 2 corresponding to the second colourimetric system, ?.sup.i calculated as:

[00025]$\begin{array}{cc}{?}^{i^{}}={\left(.Math.{?}^1.Math.{?}^1.Math.\right)}^{1/2}P& \left[\mathrm{Math}25\right]\end{array}$$\begin{array}{cc}v={?}^{i^{}}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]/.Math.{?}^{i^{}}\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right].Math.& \left[\mathrm{Math}26\right]\end{array}$$\begin{array}{cc}V=\left[v_1=\frac{{?}^{i^{}}\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]?v}{.Math.{?}^{i^{}}\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]?v.Math.}{v}_2=v_1?vv\right]& \left[\mathrm{Math}27\right]\end{array}$$\begin{array}{cc}{?}^i={\left(V^t{?}^{i^{}}\right)}^{-1}& \left[\mathrm{Math}28\right]\end{array}$

[0269] The axis of the hyperbolic metric projective reference frames ?.sup.i associated with each apparatus is collinear with a sum of the vectors ?.sub.1, ?.sub.2, ?.sub.3.

[0270] FIG. 9 is a schematic representation of one exemplary embodiment of a method 900 according to the invention. The method 900 illustrated in FIG. 9 comprises all the steps of method 200 or 300 or 700 illustrated in FIG. 2, 3, or 7.

[0271] In this example, the initial piece of data is of known origin. Consequently, the spectral function of the colourimetric system from which the initial piece of data originates is known.

[0272] In this example, at least one of the colourimetric systems, for example the first colourimetric system, comprises a deformed white point. For example, when the straight line between the black point and the white point (coordinate 1 along ?.sub.3) is not collinear with a direction of projection. This means that the hyperbolic colour space of at least one of the colourimetric systems involved in the method (here, for example, the first colourimetric system), is not aligned with the white of the model of the ideal observer based on the canonical reference frame for which the spectral function ?3 (?)=1. In this case, the method according to the invention can correct this error by performing correction. The correction is carried out by a step of correcting the defective hyperbolic colour space by using a hyperbolic rotation matrix noted Q.

[0273] By way of non-limiting example, the white point of the hyperbolic projective reference frame of the first colourimetric system is defective. The conversion step 208 then comprises a step 902 of correcting the hyperbolic colour space 204 of the first colourimetric system. In this example, the correction step 902 is performed before the adaptation step 212. The correction step 902 provides the hyperbolic rotation matrix.

[0274] Let W.sup.i=?|?.sub.3.sup.i, be the colour of the white of system i in hyperbolic colour space. The vector W.sup.i has the coordinate [W.sub.1.sup.i W.sub.2.sup.i W.sub.3.sup.i] in the other hyperbolic colour space. Thus, the hyperbolic rotation matrix ?, also known as the white balance matrix, can be defined by:

[00026]$\begin{array}{cc}?=R^T\mathrm{SR}& \left[\mathrm{Math}29\right]\end{array}$$\begin{array}{cc}R=\left[\begin{array}{ccc}\cos \left(2\mathrm{???}\right)& -\sin \left(2\mathrm{???}\right)& 0\\ \sin \left(2\mathrm{???}\right)& \cos \left(2\mathrm{???}\right)& 0\\ 0& 0& 1\end{array}\right]& \left[\mathrm{Math}30\right]\end{array}$$\begin{array}{cc}S=\left[\begin{array}{ccc}\cosh \left(?s\right)& 0& \sqrt{2}\sinh \left(?s\right)\\ 0& 1& 0\\ \frac{1}{\sqrt{2}}\sinh \left(?s\right)& 0& \cosh \left(?s\right)\end{array}\right]& \left[\mathrm{Math}31\right]\end{array}$$\begin{array}{cc}\mathrm{??}=-\frac{1}{2?}{\tan }^{-1}\frac{W_2^i}{W_1^i}& \left[\mathrm{Math}32\right]\end{array}$$\begin{array}{cc}?s=-{\sinh }^{-1}\frac{{\left({\left(W_1^i\right)}^2+{\left(W_2^i\right)}^2\right)}^{\frac{1}{2}}}{\sqrt{2}}& \left[\mathrm{Math}33\right]\end{array}$

With the exponent i corresponding to the colourimetric system considered, and the index 1 or 2 corresponding to the coordinate of the vector carried by |?.sub.3> in the hyperbolic colour space of the other colourimetric system (i.e. different from the system i considered), for example here in the second hyperbolic colour space.

[0275] In one alternative not illustrated, the white point of the second colourimetric system may be defective. In this case, the adaptation step 212 may comprise a step of correcting the hyperbolic colour space 206 of the second colourimetric system.

[0276] Thus, it is possible to correct the hyperbolic colour spaces of the colourimetric systems when the white point is deformed.

[0277] FIG. 10 is a schematic representation of one exemplary embodiment of a method 1000 according to the invention. The method 1000 illustrated in FIG. 10 comprises all the steps of the method 200 or 300 or 700 illustrated in FIG. 2, 3, or 7.

[0278] In this example, the initial piece of data 202 is of unknown origin. Consequently, the spectral function of the colourimetric system from which the initial piece of data originates is unknown. Furthermore, at least one of the colourimetric systems comprises a deformed white point. The coordinates of the white point are unknown.

[0279] The method 1000 illustrated in FIG. 10 may comprise a preliminary phase comprising a step of measuring a white point in the initial piece of data 202 or determining a white point of the first colourimetric system and/or of the second colourimetric system. The preliminary phase may be carried out before the adaptation step 212 and/or after the adaptation step 212.

[0280] If the first colourimetric system and/or the second colourimetric system comprises an acquisition means, then the white point may be determined by presenting a diffuse white in front of the first colourimetric system and/or the second colourimetric system.

[0281] In one alternative, the white point of the white point measurement step can be determined directly from the initial piece of data, for example by locating a white object on the initial piece of data. The pixel corresponding to the white object selected will correspond to the white point.

[0282] By way of example, the coordinates of the white point in R, G, B coordinates obtained by one of the methods described above and converted into the hyperbolic colour space of the second colourimetric system and/or the first colourimetric system, are noted:

[00027]$\begin{array}{cc}{W}_{?}=\left[\begin{array}{c}r\\ g\\ b\end{array}\right]& \left[\mathrm{Math}34\right]\end{array}$

with the index a referring to the measurement reference frame, [r g b].sup.T corresponding to the values R, G, B of the white point in the measurement reference frame of the colourimetric system considered, W corresponding to the coordinates R, G, B of the white point measured in the measurement reference frame of the colourimetric system considered.

[0283] From the coordinates of the white point in the measurement reference frame of the colourimetric system considered, the coordinates of the white point in a hyperbolic metric projective reference frame are given by the following relationship:

[00028]$\begin{array}{cc}{W}^i={\mathrm{PW}}_{?}& \left[\mathrm{Math}35\right]\end{array}$

Where the exponent i corresponds to the colourimetric system considered, P is the Euclidean rotation matrix used to express the coordinates of the white point in the hyperbolic metric projective reference frame of the system considered.

[0284] In this example and in a non-limiting manner, the second colourimetric system may comprise a deformed white point. The method 1000 may thus comprise a preliminary phase 1002 comprising a step 1004 of measuring a white point from the second colourimetric system. This step may be performed before the adaptation step 212. The preliminary phase 1002 can thus provide the second colour space 206 as well as the coordinates of the white point W.sup.i in the hyperbolic metric projective reference frame of the second colourimetric system. In this example, the adaptation step comprises the correction step 902 as defined in FIG. 9. The coordinates of the white point W.sup.i in the hyperbolic colour space of the second colourimetric system are used to calculate the hyperbolic rotation matrix ? according to the formula Math 29. In this example, the hyperbolic rotation matrix ? is used in the transfer function of the adaptation step 212. Thus, in this example, the transfer function used in the adaptation step 212 comprises a hyperbolic rotation matrix Q.

[0285] By way of example, for a hyperbolic rotation matrix between a camera and a screen, correspondence between both systems can be seen from the point of view of the ideal observer and its associated hyperbolic colourimetric model. The correspondence can be calculated as a change of reference frame from one of the systems to a hyperbolic model of the ideal observer, followed by a change of reference frame to the other system.

[0286] FIG. 11 is a schematic representation of several iterations of the method 200, or 300 or 700.

[0287] Only the differences relative to the methods illustrated in FIGS. 2, 3 and 7 will be described.

[0288] In this example, several initial data 202a, 202b, 202c are illustrated. The initial data may be encoded identically or differently. In this example, all the initial data 202a, 202b, 202c are images in R, G, B format.

[0289] The method 200, or 300, or 700 is iterated for each initial piece of data 202. There are as many iterations of the method 200, or 300, or 700 as there are initial data 202.

[0290] In this example, three initial data 202 are illustrated. In a non-limiting way, the method 200, or 300, or 700 is iterated three times, noted n.sub.a, n.sub.c and n.sub.c. By way of non-limiting example, the initial data are comprised of several elements 602 (i.e. several pixels). Consequently, in each iteration of the method 200, or 300, or 700, the conversion 208 and adaptation 212 steps are iterated for each element 602 of the initial piece of data 202.

[0291] In a non-limiting way, the projected piece of data 210 of the initial piece of data 202 is sent to several colourimetric systems called second colourimetric systems.

[0292] At each iteration n.sub.a, n.sub.b and n.sub.c of the method 200, 300 or 700, the initial piece of data 202 is projected into a projected piece of data 210. The projected piece of data 210 is then transformed into several adapted data 214. In this example, the projected piece of data 210 is transformed into three adapted data, 214.sub.1, 214.sub.2 and 214.sub.3. There are as many adapted data 214 as there are second colourimetric systems. Thus, for each iteration of the method 200, or 300, or 700, the method provides three adapted data 214. Adapted piece of data numbered 214.sub.1 corresponds to adapted piece of data 214 sent to a second colourimetric system comprising a hyperbolic colour space noted 206.sub.1. Adapted data numbered 214.sub.2 corresponds to adapted piece of data 214 sent to a second colourimetric system comprising a hyperbolic colour space noted 206.sub.2. Adapted piece of data numbered 214.sub.3 corresponds to adapted piece of data 214 sent to a second colourimetric system comprising a hyperbolic colour space noted 206.sub.3.

[0293] By way of non-limiting example, the second colourimetric systems are screens. Thus, method 1100 illustrates sending multiple images encoded in R, G, B space to several screens comprising a hyperbolic colour space.

[0294] FIG. 12 is a schematic representation of a first example of a device 1200 according to the invention.

[0295] The device 1200 is, for example, a calculator unit 1200. The device 1200 may be included in a computer.

[0296] The device 1200 arranged to implement the method 200 or 900 comprises: [0297] a conversion module 1202 configured to convert the initial piece of data 202 into a projected piece of data 210 by expressing all the elements 602 of the initial piece of data 202 in the colour space of the first colourimetric system, and [0298] an adaptation module 1204 configured to adapt the projected piece of data 210 into the adapted piece of data 214 by expressing all the elements 602 in the hyperbolic colour space of the second colourimetric system by using the transfer function relating the colour spaces of the first colourimetric system and of the second colourimetric system.

[0299] The device 1200 is arranged to implement one or more iterations of the method 200.

[0300] The conversion module 1202 may comprise a reference frame change module 1206 for implementing the reference frame change step of the conversion step 208.

[0301] The device 1200 may optionally comprise a correction module 1208 configured to correct the hyperbolic colour space of the first colourimetric system and/or the second colourimetric system by using the hyperbolic rotation matrix Q. The correction module is configured and/or programmed to implement the correction step 902.

[0302] FIG. 13 is a schematic representation of a second example of a device 1300 according to the invention. The device 1300 comprises all the elements of the device 1200.

[0303] The device 1300 is, for example, a calculator unit 1300. The device 1300 may be included in a computer.

[0304] The device 1300 is arranged to implement the method 200 or 300 or 700 or 900 or 1000 and further comprises a design module 1302 configured to design the hyperbolic colour space 204 of the first colourimetric system from the spectral function |?.sup.1> of the first colourimetric system, a design module 1304 configured to design the hyperbolic colour space 206 of the second colourimetric system from the spectral function |?.sup.2> of the second colourimetric system.

[0305] In one alternative not illustrated, a single design module is used to design the hyperbolic colour spaces of all the colourimetric systems involved in the method according to the invention. In another alternative not illustrated, the device 1300 may comprise as many design modules as there are colourimetric systems involved in the method according to the invention. Consequently, each design module may be associated with a colourimetric system.

[0306] By way of non-limiting example, each design module may be included in a calibration module configured to implement the calibration steps 706, 708.

[0307] FIG. 14 is a schematic representation of one example of equipment 1400 according to the invention. The equipment 1400 comprises the device 1200 or 1300 illustrated in FIG. 12 or 13.

[0308] The equipment 1400 comprises, by way of non-limiting example, a first colourimetric system 1402. The first colourimetric system 1402 is an acquisition means 1402 arranged to acquire at least one image. In this example, the at least one image acquired by the acquisition means 1402 is associated with the at least one initial piece of data 202. The acquisition means comprises a hyperbolic colour space, referred to as first hyperbolic colour space noted 204.

[0309] The equipment 1400 comprises, in this example, a second colourimetric system 1404. The second colourimetric system 1404 is a display means 1404, arranged to display the image acquired by the acquisition means. The image displayed by the display means is associated with the adapted piece of data 214. The display means comprises a hyperbolic colour space, referred to as second hyperbolic colour space noted 206.

[0310] The first colour space 204 and the second colour space 206 may be known or designed and/or measured as described in FIGS. 3, 4, 5, 7, 8, 9, 10.

[0311] FIG. 15 is a schematic representation of one example of equipment 1500 according to the invention. The equipment 1500 comprises the device 1200 or 1300 illustrated in FIG. 12 or 13.

[0312] Only the differences with the equipment 1400 will be described. In this example, the equipment 1500 comprises several second colourimetric systems noted 1404.sub.1, 1404.sub.2, 1404.sub.3. By way of non-limiting example, the second colourimetric systems 1404 are display means 1404. Each second colourimetric system 1404 comprises its own hyperbolic colour space 206. Each second colour space 206 may be known or designed and/or measured as described in FIGS. 3, 4, 5, 7, 8, 9, 10. The projected piece of data 210 is adapted to the hyperbolic colour spaces of each second colourimetric system 1404.sub.1, 1404.sub.2, 1404.sub.3. Thus, the device 1200 or 1300 provides an adapted piece of data 214 for each second colourimetric system 1404. In the present example, the adapted piece of data 214.sub.1 is provided to the second colourimetric system 1404.sub.1. Adapted data 214.sub.2 is provided to the second colourimetric system 1404.sub.2. Adapted data 214.sub.3 is provided to the second colourimetric system 1404.sub.3. Each adapted piece of data 214 depends on the spectral characteristics of the second colourimetric system on which it will be displayed.

[0313] In this example, each display means is arranged to display the adapted image 214 associated therewith.

[0314] Of course, the invention is not limited to the examples just described. Numerous modifications can be made to these examples without departing from the scope of the invention as described.