Figure IV.1. Tridimensional representation of Luma (A), and chromatic signals (C1, C2).
ANNEX IV. COLOUR THEORY
O. FERRER-ROCA
University La Laguna. Tenerife.Canary Islands.Spain
The present annex tries to bring complementary information on the aspects related with colour capture and manipulation as well as possible influences that could modify it, in the aspects of visual perception, image analysis and densitometry.
IV.1. INTRODUCTION
Light can be divided into achromatic and chromatic. The only attribute of Achromatic Light is INTENSITY whose scalar measure produces the Grey Levels.
On the contrary Chromatic Light spans the electromagnetic energy spectrum from 400 nm (Blue area) to 700 nm (Red area) being the ranges over this in the infrared non-visible spectrum. The three basic qualities link to chromatic light are
RADIANCE (measured in Watts).
LUMINANCE=Y (measured in Lumens (lm)), e.g. luminance in the infrared area =0. Is defined by the Commission Internationale de lŽeclairage (CIE) as the radiant power weighted by a spectral sensitivity function that is characteristic of vision. Its magnitude is proportional to power and therefore is like intensity. Nevertheless the spectral composition is related with the brightness sensitivity of human vision.
BRIGHTNESS, a subjective descriptor not possible to measure, that embodies the achromatic notion of Intensity=I. Is defined by CIE as the attribute of a visual sensation according to which an area appears to emit more or less light, therefore is a non-linear function of Luminance. Human vision has non-linear response to brightness. This perceptual response to luminance is called by the CIE as LIGHTNESS, being roughly logarithmic for human eye.
IV.2 LIGHT COLOURS AND COLOURS OF OBJECTS
IV.2.1. LIGHT COLOURS
Due to the anatomical structure of the eye, colours are seen as combination of the three primary colours: RGB=Red, Green, Blue. According to the CIE they are located on B=435,8 nm, G=546,1nm; R=700nm. Those primary colours are mixed to produce secondary colours: Magenta (RB), Cyan (GB) and Yellow (RG).
| Combination of equal energy primary colours R(x)+G(y)+B(z)=1, gives a white light. |
IV.2.2. COLOURS OF THE OBJECTS
It is also important to clarify the differences between light colours and colours of the objects, since the property of the objects (pigments) is that substrates do absorb a primary light colour and reflect or transmit the other two. Therefore the primary pigments are MCY and the secondary pigments are RGB.
Colours of the objects are distinguished by three characteristics (IHS)-:
BRIGHTNESS; I=intensity or brightness
HUE; H=dominant wavelength perceived by the observer
SATURATION; S=indicates the amount of white light mixed with the Hue
The combination of H & S is called CHROMATICITY, therefore a colour can be simply defined with two parameters Brightness and Chroma (B-Ch). In general the latter include two signals ChA (from green to red) and ChB (from blue to yellow).
Since R(x)+G(y)+B(z)=1, only x and y are needed to determine the chroma, and z is obtained from the previous equation.
This means that colour can be reduced to LUMINANCE (Y) and Chroma (UV) also known as YIQ (Luminance, inphase and quadrature) whose conversion is as follows:
| Y=0,299 R + 0,587 G + 0,114 B U=0,596 R - 0.275 G - 0,321 B V=0,212 R - 0,523 G + 0,311 B |
IV.3 TRIDIMENSIONAL REPRESENTATION OF COLOUR
A colour Objet can be de-composed into three digital images: Luminic information (A) + 2 signals containing the differential visible spectral colour (C1; C2).
| Achromatic signal (A) | =log R + log G + log B |
| Chromatic signal (C1 & C2) | C1=3/2 (log R- log G) C2=log B- 1/2(log R+log G) |
In the tridimensional representation scheme the LUMINOSITY (A) or LUMA is the projection of a pixel (q) in the y axis.The SATURATION (S) or colour purity, depends on the amount of white contained in the pure colour and is the vector of the pixel q in the z-x plane (S=sqr (C1 2 + C2 2)). Finally the HUE (H) is a colour attribute expressed as the angle between the x axis (C1) and the S vector (H=cos (C1/S)).
Figure IV.1. Tridimensional representation of Luma (A), and chromatic signals (C1, C2).
IV.4. COLOUR SPACES
The ANSI work formed the draft IPI-CAI Common Architecture for Imaging International Standards that identifies the colour spaces. And the ISO/ANSI work provides a standardised methodology for describing the interrelationships between these standards
Table IV.1. Colour Spaces.
| Standard | Type | Colour spaces |
| YES | CIE | XYZ |
| Yxy | ||
| UVW | ||
| Yuv | ||
| L*a*b | ||
| L*u*v | ||
| Linear RGB//and Gamma RGB | CCIR-709 | |
| NTCS | ||
| EBU | ||
| SMPTE | ||
| Luminance-Chrominance | YIQ | |
| YUV | ||
| SMPTE YCrCb | ||
| CCIR-709 YCrCb | ||
| EBU YCrCb | ||
| NO | others | RGB |
| CMY | ||
| CMYK | ||
| IHS |
IV.5. RESPONSE OF THE DETECTORS.
Video systems are build in such a way that try to approximate the lightness response of human vision, that means a logarithmic response. The linear-light intensity is transformed into a non-linear video signal by gamma correction (see Chapter 2- Displays) because the vision response to intensity is effectively the inverse of a CRTs nonlinearity.
For example for a R=Linear light intensity and RŽa non-linear component such as the voltage in video systems:
RŽ=4,5 R for R< 0.018; RŽ=1.099 R 0.45 - 0.099 for 0.018 < R;
IV.5.1. VARIATIONS IN GAMMA CORRECTION
Gamma correction vary according to the outputs
1.- The video systems effectively codes into a perceptually uniform domain. A 0.45-power function is applied to the camera for gamma correction.
2.- Synthetic computer graphics calculate the interaction of light and objects. It is conventional in computer graphics to store linear-light values in the frame buffer and introduce gamma correction at the look-up table at the output of the frame buffer.
3.- Desktop computers are optimised neither for image synthesis nor for video. They have programmable gamma with either poor or no standards. Consequently image interchange among desktops produce different results. And particularly are not suitable for medical image applications if gamma correction cannot be standardised.
FIGURE IV.2. Original image on the left, transported to another platform on
the right. Image provided by Pedro Arconada with permission of IDG (http://www.idg.es/iworld)
FIGURE IV.3. Gamma correction effect produced by the different devices.
Taken from Ch.Poynton, 1998 at http://www.inforamp.net/~poynton/notes/colour_and_gamma/GammaFAQ.html
IMPORTANT NOTE |
|
Specifically, if an image originates in a Linear-light form, Gamma correction needs to be applied exactly once. Some of the problems that may appear if we do not take into account the previous premise are:
a) If we do not apply Gamma correction and the image data is applied to a CRT (display), then the midtones will be too dark.
b) If Gamma correction is applied twice the midtones will be too light.
Furthermore in JPEG and MPEG standards there is no mention of transfer function but non-linear (video-like) coding is implicit, which make those images not suitable for linear-light data manipulation. Standardisation of the transfer function is necessary in order that image formats meet the usersŽs expectations.
IV.5.2. DETECTOR RESPONSE
All previous statements also imply an optical lineal response of the detector, that have to be tested in any case, under appropriate conditions. As shown in the previous figure, video voltage can be considered linear in a Video camera but linear intensity is only obtained if their is no gamma correction because this is a non-linear transformation. Linearity of the optical systems is a sine-quanon condition for densitometric measurements.
FIGURE IV.4. Grey values given by the Texcan system [1]
using a B/W CCD camara and B/W frame grabber, in front of a densitrometric slide test (optical
density) and the internal optical density values of the system obtained by software [3] (Texcan).
IV.5.2.1. LIGHT SPECTRUM SENSITIVITY
The problem is even more complex if we consider that the detectors present on the video cameras do not have, up to now, the same sensitivity throughout the whole light spectrum and therefore modify the eye colour detection that also have limited sensitivity as shown in the figure IV.5.
Microscopic spectrum of Blue (400-510 nm), Red (590-660) and Green (515-560) is covered in most of the pathology images that are mainly based on H-E (Hemathoxylin-Eosine=B-R). Therefore, any modification of the white balance of the camera or display (point of equal energy for the 3 primary colours) modify the colour response.
Figure IV.5. Sensititivy of the detectors
This, together with the fact that CCD cameras as well as analogue cameras (except vidicon) are less sensitive than the eye on the blue region, produces colour aberrations when compared with eye perception.
IMPORTANT: Please note that each vendor camera have different sensitivity spectrum, and only few vendors provide the response curve of their sensors
IV.5.2.2 DENSITOMETRY ASPECTS
| If=Final intensity | |
| OD=- log T=- log (If/Io) | OD=Optical density |
| Io=Original light intensity of the background |
Obviously each colour has its maximum absorvance at a specific range of the light spectrum, therefore for the densitrometric analysis the maximum absorvance of the pigments should be known in advance. That is the case in Pathology slides stained with different dyes for histology recognition or quantitation, whose maximum absorvance spectrum (with a narrow band filter of 20 nm wave length) using a stabilised illumination provided by an halogen lamp of 100W are summarised in the following table [2].
Table IV.2. Absorvance peak of the most common histological dyes
| STAINING (DYE) | Maximum absorvance |
| Toluidine Blue | 640 nm |
| Feulgen | 560 nm |
| DAB (Diamino Bencidine) | 547 nm |
| Gallocianine | 580 nm |
| Haemathoxyline alone | 600 nm |
| Haemathoxyline-Eosine | 530 nm |
| Haemathoxyline-Light Green | 635 nm |
| PAP standard | 545 nm |
| Thionine | 570 nm |
| Methyl Green | 660 nm |
Under those premises the densitometric measurements of transmitted light (Transmission densitometry) work in the ACHROMATIC space in which only grey values are considered.
Nevertheless the Surround Effect or light present around of the object pays an important role. For example a white area around a dark dense object may favour the visual contrast but the bright light coming from the surroundings decrease its densitometric measurements (Glare effect on the borders). This is controlled in the video environment for visual perception applying a power function (in general 0.45) with an exponent of about 1/1.1 or 1/1.2 to correct the bright surround. Recently some image format (i.e. TIFF 6.0) incorporates a tag that includes an appropriate transfer function for the viewing environment.
The Contrast ratio or relation between the brightest white and the darkest black of a particular detector is very important for densitometric devices. It differs from displayed images affected by environmental lights (Projected cinema 80:1 in a dark theatre, TV 30:1 in the living room, CRT in an office environment 5:1). In Black and white B/W capture systems, it is manipulated by the offset and gain control that adjust the dynamic range of the capture system to an artificial LUT that fixed the detector offset (acquiring a black image) in the 0 values and the detector gain (acquiring a white image) at the maximum level (i.e. 255 in 8 bits LUTs). In true colour framegrabbers, the pixel value of each colour in the frame buffer is mapped through one of three (RGB) lookuptables of 8 bits (0-255); each mapped value plus or minus de black level (offset) error is proportional to voltage.
| L=Luminance | |
| L=(V+epsilon) gamma | V=Voltage |
| epsilon=Black-level offset |
while the gain is indirectly corrected doing a white balance of the colour in the video-camera.
FIGURE IV.6. Plot of the densitometric measurements (Y) express as ISC (Immuno
Score=sum of densitometric values over a background level) versus real steroid receptors
in the breast tissue (X) in fmol/mg of protein obtained by biochemical measurements.
Furthermore, in densitometric measurements the saturation level
of the detector is linked to the impossibility to distinguish variations at the black
or offset level (see also Chapter 1- x-ray laser scanners). This is particularly
important if we would like to quantify in real units and not in arbitrary units. As an
example the figure IV.6 shows how a CCD detector can be saturated by the darkness of the
high substrate content, giving a logarithmic response with a plateau over a given content.
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