RGB, XYZ, and Lab conversions

[Ben321]

This program converts images between RGB, XYZ, and Lab formats. It's quite a large program (due to the 2 huge lookup tables for RGB/Lab conversion), so instead of posting it as an attachment, I've uploaded it to Mediafire, and have posted the download link here.

https://www.mediafire.com/?vdx3uy1z31g21as

[Tanner_H]

Hi Ben. Thanks for sharing. You weren't joking about the download file being huge!

There is a much easier way to do RGB / XYZ / Lab conversions. Code below (adopted from easyRGB.com). Note that certain assumptions have to be made when converting between RGB (which is just a color model) and an actual color space, like Lab. In these functions, sRGB and 6500k color temperature are assumed, as noted in the comments.

'This function is just a thin wrapper to RGBtoXYZ and XYZtoLAB.  There is no direct conversion from RGB to CieLAB.
Public Sub RGBtoLAB(ByVal r As Long, ByVal g As Long, ByVal b As Long, ByRef labL As Double, ByRef labA As Double, ByRef labB As Double)

    Dim x As Double, y As Double, z As Double
    RGBtoXYZ r, g, b, x, y, z
    XYZtoLab x, y, z, labL, labA, labB

End Sub

'Convert RGB to XYZ space, using an sRGB conversion and the assumption of a D65 (e.g. color temperature of 6500k) illuminant
' Formula adopted from http://www.easyrgb.com/index.php?X=MATH&H=02#text2
Public Sub RGBtoXYZ(ByVal r As Long, ByVal g As Long, ByVal b As Long, ByRef x As Double, ByRef y As Double, ByRef z As Double)

    'Normalize RGB to [0, 1]
    Dim rFloat As Double, gFloat As Double, bFloat As Double
    rFloat = r / 255
    gFloat = g / 255
    bFloat = b / 255
    
    'Convert RGB values to the sRGB color space
    If rFloat > 0.04045 Then
        rFloat = ((rFloat + 0.055) / (1.055)) ^ 2.2
    Else
        rFloat = rFloat / 12.92
    End If
    
    If gFloat > 0.04045 Then
        gFloat = ((gFloat + 0.055) / (1.055)) ^ 2.2
    Else
        gFloat = gFloat / 12.92
    End If
    
    If bFloat > 0.04045 Then
        bFloat = ((bFloat + 0.055) / (1.055)) ^ 2.2
    Else
        bFloat = bFloat / 12.92
    End If
    
    'Calculate XYZ using D65 correction
    x = rFloat * 0.4124 + gFloat * 0.3576 + bFloat * 0.1805
    y = rFloat * 0.2126 + gFloat * 0.7152 + bFloat * 0.0722
    z = rFloat * 0.0193 + gFloat * 0.1192 + bFloat * 0.9505
    
End Sub

'Convert an XYZ color to CIELab.  As with the original XYZ calculation, D65 is assumed.
' Formula adopted from http://www.easyrgb.com/index.php?X=MATH&H=07#text7, with minor changes by me (not re-applying D65 values until after
'  fXYZ has been calculated)
Public Sub XYZtoLab(ByVal x As Double, ByVal y As Double, ByVal z As Double, ByRef l As Double, ByRef a As Double, ByRef b As Double)
    l = 116 * fXYZ(y) - 16
    a = 500 * (fXYZ(x / 0.9505) - fXYZ(y))
    b = 200 * (fXYZ(y) - fXYZ(z / 1.089))
End Sub

Private Function fXYZ(ByVal t As Double) As Double
    If t > 0.008856 Then
        fXYZ = t ^ (1 / 3)
    Else
        fXYZ = (7.787 * t) + (16 / 116)
    End If
End Function

[Ben321]

Hi Ben. Thanks for sharing. You weren't joking about the download file being huge!

There is a much easier way to do RGB / XYZ / Lab conversions. Code below (adopted from easyRGB.com). Note that certain assumptions have to be made when converting between RGB (which is just a color model) and an actual color space, like Lab. In these functions, sRGB and 6500k color temperature are assumed, as noted in the comments.

'This function is just a thin wrapper to RGBtoXYZ and XYZtoLAB.  There is no direct conversion from RGB to CieLAB.
Public Sub RGBtoLAB(ByVal r As Long, ByVal g As Long, ByVal b As Long, ByRef labL As Double, ByRef labA As Double, ByRef labB As Double)

    Dim x As Double, y As Double, z As Double
    RGBtoXYZ r, g, b, x, y, z
    XYZtoLab x, y, z, labL, labA, labB

End Sub

'Convert RGB to XYZ space, using an sRGB conversion and the assumption of a D65 (e.g. color temperature of 6500k) illuminant
' Formula adopted from http://www.easyrgb.com/index.php?X=MATH&H=02#text2
Public Sub RGBtoXYZ(ByVal r As Long, ByVal g As Long, ByVal b As Long, ByRef x As Double, ByRef y As Double, ByRef z As Double)

    'Normalize RGB to [0, 1]
    Dim rFloat As Double, gFloat As Double, bFloat As Double
    rFloat = r / 255
    gFloat = g / 255
    bFloat = b / 255
    
    'Convert RGB values to the sRGB color space
    If rFloat > 0.04045 Then
        rFloat = ((rFloat + 0.055) / (1.055)) ^ 2.2
    Else
        rFloat = rFloat / 12.92
    End If
    
    If gFloat > 0.04045 Then
        gFloat = ((gFloat + 0.055) / (1.055)) ^ 2.2
    Else
        gFloat = gFloat / 12.92
    End If
    
    If bFloat > 0.04045 Then
        bFloat = ((bFloat + 0.055) / (1.055)) ^ 2.2
    Else
        bFloat = bFloat / 12.92
    End If
    
    'Calculate XYZ using D65 correction
    x = rFloat * 0.4124 + gFloat * 0.3576 + bFloat * 0.1805
    y = rFloat * 0.2126 + gFloat * 0.7152 + bFloat * 0.0722
    z = rFloat * 0.0193 + gFloat * 0.1192 + bFloat * 0.9505
    
End Sub

'Convert an XYZ color to CIELab.  As with the original XYZ calculation, D65 is assumed.
' Formula adopted from http://www.easyrgb.com/index.php?X=MATH&H=07#text7, with minor changes by me (not re-applying D65 values until after
'  fXYZ has been calculated)
Public Sub XYZtoLab(ByVal x As Double, ByVal y As Double, ByVal z As Double, ByRef l As Double, ByRef a As Double, ByRef b As Double)
    l = 116 * fXYZ(y) - 16
    a = 500 * (fXYZ(x / 0.9505) - fXYZ(y))
    b = 200 * (fXYZ(y) - fXYZ(z / 1.089))
End Sub

Private Function fXYZ(ByVal t As Double) As Double
    If t > 0.008856 Then
        fXYZ = t ^ (1 / 3)
    Else
        fXYZ = (7.787 * t) + (16 / 116)
    End If
End Function

Thanks for sharing that. I haven't tried it yet though.
By the way, you are missing the inverse transformations. Also, is this actually faster than the techniques I used in my program, when used to convert an entire image? It seems that it would be slower, since there are a lot more operations being done in your program, than in the one I wrote. Also, why do you pre-process the RGB channels before applying the RGB to XYZ transformation matrix? I'm guessing it has something to do with linearity of the RGB values when compared to actual physical brightness levels of the pixels, and compensating for a lack of linearity. However for the sake of simplifying the operation in my program when converting between RGB and XYZ, I assume that the RGB values are already representing linear brightnesses of the 3 color channels and use them as-is (no pre-processing) as inputs to the transformation matrix.

[Tanner_H]

By the way, you are missing the inverse transformations.

Yep, I don't have those on hand, though they're trivially created from the formulas at this link.

Also, is this actually faster than the techniques I used in my program, when used to convert an entire image? It seems that it would be slower, since there are a lot more operations being done in your program, than in the one I wrote.

You'd have to test, but I wouldn't underestimate the overhead of loading those massive look-up tables into RAM, let alone the cost of shipping them with your project. The formulas I shared could probably be optimized further, but as-is they're fast enough for real-time conversion on screen-sized images. (I use them to render a green screen effect in real-time, and I haven't had any speed problems on modern PCs.)

Also, why do you pre-process the RGB channels before applying the RGB to XYZ transformation matrix? I'm guessing it has something to do with linearity of the RGB values when compared to actual physical brightness levels of the pixels, and compensating for a lack of linearity. However for the sake of simplifying the operation in my program when converting between RGB and XYZ, I assume that the RGB values are already representing linear brightnesses of the 3 color channels and use them as-is (no pre-processing) as inputs to the transformation matrix.

As you probably know, RGB is just a color model, not a color space. A color like RGB(255, 0, 0) will look completely different on different devices.

Because CieLAB is an actual color space (that absolutely describes color), to get any use from it, you first have to convert your RGB data into an absolute RGB color space. Which RGB color space is up to you; sRGB is simple and straightforward, and your original RGB data was mostly likely designed against sRGB anyway. (More about sRGB here.) Adobe RGB or ProPhoto RGB are other common RGB spaces, but they're a lot more work to use.

Since the primary purpose of the CieLAB space is accurate representation of color, it's probably not a good idea to convert raw 24bpp RGB data directly through XYZ into Lab, without first performing a proper RGB color space conversion. You could save some processing time, certainly, but your Lab values wouldn't be accurate... which defeats the reason for using Lab in the first place, I think!

[reexre]

hi
I use this:

Option Explicit
'http://www.easyrgb.com/index.php?X=MATH&H=02#text2

'MULTIPLICATION IS FASTER THAN DIVISION,
'SO, SETUP SOME CONSTANTS:

Private Const INV255 As Double = 1 / 255
Private Const INV1p055 As Double = 1 / 1.055
Private Const INV12p92 As Double = 1 / 12.92
Private Const INV3 As Double = 1 / 3

Private Const kX As Double = 100 / 95.047
Private Const kY As Double = 100 / 100
Private Const kZ As Double = 100 / 108.883

Private Const INVkX As Double = 95.047 / 100
Private Const INVkY As Double = 100 / 100
Private Const INVkZ As Double = 108.883 / 100

Private Const c16d116 As Double = 16 / 116

Private Const INV7p787 As Double = 1 / 7.787

Private Const INV2p4 As Double = 1 / 2.4

Private Const INV116 As Double = 1 / 116
Private Const INV200 As Double = 1 / 200
Private Const INV500 As Double = 1 / 500

Private Const INV2p55 As Double = 1 / 2.55
Private Const INV1p275 As Double = 1 / 1.275



Public Sub RGB2lab(R As Double, G As Double, B As Double, _
                   ByRef cL As Double, ByRef cA As Double, ByRef cB As Double)

    Dim RR     As Double
    Dim GG     As Double
    Dim BB     As Double
    Dim X      As Double
    Dim Y      As Double
    Dim Z      As Double

    RR = R * INV255
    GG = G * INV255
    BB = B * INV255

    If (RR > 0.04045) Then
        RR = ((RR + 0.055) * INV1p055) ^ 2.4
    Else
        RR = RR * INV12p92
    End If

    If (GG > 0.04045) Then
        GG = ((GG + 0.055) * INV1p055) ^ 2.4
    Else
        GG = GG * INV12p92
    End If

    If (BB > 0.04045) Then
        BB = ((BB + 0.055) * INV1p055) ^ 2.4
    Else
        BB = BB * INV12p92
    End If


    'RR = RR * 100
    'GG = GG * 100
    'BB = BB * 100
    '//Observer. = 2°, Illuminant = D65
    X = RR * 0.4124 + GG * 0.3576 + BB * 0.1805
    Y = RR * 0.2126 + GG * 0.7152 + BB * 0.0722
    Z = RR * 0.0193 + GG * 0.1192 + BB * 0.9505

    '-----------------------------------------------------------
    'X = X / ref_X          '//ref_X =  95.047   Observer= 2°, Illuminant= D65
    'Y = Y / ref_Y          '//ref_Y = 100.000
    'Z = Z / ref_Z          '//ref_Z = 108.883
    X = X * kX
    Y = Y * kY
    Z = Z * kZ

    If (X > 0.008856) Then X = X ^ (INV3) Else: X = (7.787 * X) + (c16d116)
    If (Y > 0.008856) Then Y = Y ^ (INV3) Else: Y = (7.787 * Y) + (c16d116)
    If (Z > 0.008856) Then Z = Z ^ (INV3) Else: Z = (7.787 * Z) + (c16d116)

    cL = (116 * Y) - 16                '0 to 100
    cA = 500 * (X - Y)                 'Circa -100 a 100
    cB = 200 * (Y - Z)
    'Debug.Print cb


    'Transfrom output Ranges (initialy from 0 to 100  &  -100 to 100 )
    'to [from 0 to 255]

    cL = cL * 2.55
    cA = 127.5 + cA * 1.275
    cB = 127.5 + cB * 1.275
    '-----------------------


    If cL > 255 Then cL = 255
    If cL < 0 Then cL = 0
    If cA > 255 Then cA = 255
    If cB > 255 Then cB = 255

    If cB < 0 Then cB = 0
    If cA < 0 Then cA = 0


End Sub

Public Sub LAB2RGB(ByVal cL As Double, ByVal cA As Double, ByVal cB As Double, _
                   ByRef R As Double, ByRef G As Double, ByRef B As Double)

    Dim X      As Double
    Dim Y      As Double
    Dim Z      As Double
    Dim X3     As Double
    Dim Y3     As Double
    Dim Z3     As Double
    
    'Check input Range
    'If cL > 255 Then Stop: cL = 255
    'If cL < 0 Then Stop: cL = 0
    'If cA > 255 Then Stop: cA = 255
    'If cA < 0 Then Stop: cA = 0
    'If cb > 255 Then Stop: cb = 255
    'If cb < 0 Then Stop: cb = 0

    'Reset input ranges
    'from 0 to 255
    'to [from 0 to 100] & [from -100 to 100]
    cL = cL * INV2p55    '/2.55
    cA = (cA - 127.5) * INV1p275    '/ 1.275
    cB = (cB - 127.5) * INV1p275    '/ 1.275
    '-------

    Y = (cL + 16) * INV116
    X = cA * INV500 + Y
    Z = Y - cB * INV200

    X3 = X * X * X
    Y3 = Y * Y * Y
    Z3 = Z * Z * Z

    If (Y3 > 0.008856) Then Y = Y3 Else: Y = (Y - c16d116) * INV7p787
    If (X3 > 0.008856) Then X = X3 Else: X = (X - c16d116) * INV7p787
    If (Z3 > 0.008856) Then Z = Z3 Else: Z = (Z - c16d116) * INV7p787

    'X = ref_X * x     //ref_X =  95.047     Observer= 2°, Illuminant= D65
    'Y = ref_Y * y     //ref_Y = 100.000
    'Z = ref_Z * z     //ref_Z = 108.883
    X = X * INVkX
    Y = Y * INVkY
    Z = Z * INVkZ

    '--------------------------------------------------------------------------
    'x,y,z 0 to 100

    R = X * 3.2406 + Y * -1.5372 + Z * -0.4986
    G = X * -0.9689 + Y * 1.8758 + Z * 0.0415
    B = X * 0.0557 + Y * -0.204 + Z * 1.057

    If (R > 0.0031308) Then R = 1.055 * (R ^ INV2p4) - 0.055 Else: R = 12.92 * R
    If (G > 0.0031308) Then G = 1.055 * (G ^ INV2p4) - 0.055 Else: G = 12.92 * G
    If (B > 0.0031308) Then B = 1.055 * (B ^ INV2p4) - 0.055 Else: B = 12.92 * B

    R = R * 255
    G = G * 255
    B = B * 255

    If R > 255 Then R = 255
    If G > 255 Then G = 255
    If B > 255 Then B = 255
    If R < 0 Then R = 0
    If G < 0 Then G = 0
    If B < 0 Then B = 0


End Sub

this should / could be useful

[Nightwalker83]

Private Const INVkX As Double = 95.047 / 100
Private Const INVkY As Double = 100 / 100
Private Const INVkZ As Double = 108.883 / 100

Instead of that why not just?

Private Const INVkX As Double = .95047
Private Const INVkY As Double = 1
Private Const INVkZ As Double = 1.08883