trans_from_rgb — Transform an image from the RGB color space to an arbitrary color space.
trans_from_rgb(ImageRed, ImageGreen, ImageBlue : ImageResult1, ImageResult2, ImageResult3 : ColorSpace : )
trans_from_rgb transforms an image from the RGB color
space to an arbitrary color space (ColorSpace). The
three channels of the image are passed as three separate images on
input and output.
The operator trans_from_rgb supports the image types byte, uint2,
int4, and real. In the case of real images, all values should lay within
0 and 1. If not, the results of the transformation may not be reasonable.
Certain scalings are performed accordingly to the image type:
Considering byte and uint2 images, the domain of color space values is generally mapped to the full domain of [0..255] or [0..65535], respectively. Because of this, the origin of signed values (e.g., CIELab) may not be at the center of the domain.
Hue values are represented by angles of [0..2PI[ and are coded for the particular image types differently:
byte-images map the angle domain to [0..255].
uint2/int4-images are coded in minutes of arc [0..21600[, except for the transformations 'cielchab' and 'cielchuv' for int4-images, where they are coded in seconds of arc [0..1296000[.
real-images are coded in radians [0..2PI[, except for the transformations 'cielchab' and 'cielchuv', where the standards ISO 11664-4:2008 and ISO 11664-5:2009 require the hue to be specified in degrees.
Saturation values are represented by percentages of [0..100] and are coded differently for the particular image type:
byte-images map the saturation values to [0..255].
uint2/int4-images map the saturation values to [0..10000].
real-images map the saturation values to [0..1].
Supported are the transformations listed below. Note, all domains are based on RGB values scaled to [0; 1]. To obtain the domain of a certain image type, they must be scaled accordingly with the value range. Due to different precision the values obtained using the given equations may slightly differ from the values returned by the operator.
Note, this implies that , , and are not independent of each other.
The primary colors used correspond to sRGB respectively CIE Rec. 709. D65 is used as white point.
Min := min([R, G, B]) Max := max([R, G, B]) L := (Min + Max) / 2 if (Max == Min) H := 0 S := 0 else if (L > 0.5) S := (Max - Min) / (2 - Max - Min) else S := (Max - Min) / (Max + Min) endif if (R == Max) H := ((G - B) / (Max - Min)) * rad(60) elseif (G == Max) H := (2 + (B - R) / (Max - Min)) * rad(60) elseif (B == Max) H := (4 + (R - G) / (Max - Min)) * rad(60) endif endif
Min := min([R, G, B]) Max := max([R, G, B]) V := Max if (Max == Min) S := 0 H := 0 else S := (Max - Min) / Max if (R == Max) H := ((G - B) / (Max - Min)) * rad(60) elseif (G == Max) H := (2 + (B - R) / (Max - Min)) * rad(60) elseif (B == Max) H := (4 + (R - G) / (Max - Min)) * rad(60) endif endif
Min := min([R, G, B]) Max := max([R, G, B]) I := (R + G + B) / 3 if (I == 0) H := 0 S := 1 else S := 1 - Min / I if (S == 0) H := 0 else X := (R + R - G - B) / 2 Y := (R - G) * (R - G) + (R - B) * (G - B) Z := sqrt(Y) if (Z == 0) H := 0 else H := acos(X / Z) endif if (B > G) H := rad(360) - H endif endif endif
where
Black point B: (, , ) = (0, 0, 0)
White point W (according to image type):
byte: (, , ) = (255, 255, 255)
uint2: (, , ) = (, , )
int4: (, , ) = (, , )
real: (, , ) = (1.0, 1.0, 1.0)
(Scaled to the maximum gray value in the case of byte and uint2. In the case of int4 L and a are scaled to the maximum gray value, b is scaled to the minimum gray value, such that the origin stays at 0.)
where
lies
between 0° and 90° if and are both positive,
between 90° and 180° if is negative and is positive,
between 180° and 270° if and are both negative, and
between 270° and 360° if is positive and is negative.
Black point B: (, , ) = (0, 0, 0)
White point W (according to image type):
byte: (, , ) = (255, 255, 255)
uint2: (, , ) = (, , )
int4: (, , ) = (, , )
real: (, , ) = (1.0, 1.0, 1.0)
(Scaled to the maximum gray value in the case of byte and uint2. In the case of int4, L and C are scaled to the maximum gray value, while h is given in seconds of arc.)