Digital Image Processing

T. Peynot

Chapter 5
Colour Image Processing

Colour Image Processing

1. Colour Fundamentals
2. Colour Models
3. Pseudocolour Image Processing
4. Basics of Full-Colour Image Processing
5. Colour Transformations
6. Smoothing and Sharpening
7. Image Segmentation based on Colour

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Introduction

Motivation to use colour:

Powerful descriptor that often simplifies object identification and extraction
from a scene
Humans can discern thousands of colour shades and intensities, compared to
about only two dozen shades of gray

Two major areas:

Full-colour processing: e.g. images acquired by colour TV camera or colour
scanner
Pseudo-colour processing: assigning a colour to a particular monochrome
intensity or range of intensities

Some of the gray-scale methods are directly applicable to colour images

Others require reformulation
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1. Colour Fundamentals

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Perception of colours by the human eye

Cones can be divided into 3 principal sensing categories: (roughly) red, green and blue
~65% are sensitive to red light, ~33% to green light and ~2% to blue (but most sensitive)
Colours are seen as variable combinations of the primary colours: Red, Green, Blue
From CIE* (1931), wavelengths: blue = 435.8nm, green = 546.1nm, red = 700nm

* CIE = Commission Internationale de lEclairage

(the International
19922008 Commission
R. C. Gonzalez & R. E. on Illumination)
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Primary colours can be added to produce

the secondary colours of light:
Magenta (red plus blue)
Cyan (green plus blue)
Yellow (red plus green)

Mixing the three primaries in the right

intensities produce white light

Primary colours of pigment: absorb a

primary colour of light and reflects or
transmits the other two
magenta, cyan and yellow

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Characteristics of a colour:
Brightness: embodies the achromatic notion of intensity
Hue: attribute associated with the dominant wavelength in a mixture of light waves
Saturation: refers to the relative purity or the amount of white light mixed with a hue
(The pure spectrum colours are fully saturated; e.g. Pink (red and white) is less
saturated, degree of saturation being inversely proportional to the amount of white light
added)

Hue and Saturation together = chromaticity

Colour may be characterized by its brightness and chromaticity

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Tristimulus values = amounts of red (X), green (Y) and blue (Z) needed to form a
particular colour. A colour can be specified by its trichromatic coefficients:

NB:

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Content:
62% green
Another approach for specifying colours: 25% red
The CIE chromaticity diagram: 13% blue
Shows colour composition as a function of x (red)
and y (green)
For any value of x and y: z (blue) is obtained
by:

Pure colours of the spectrum (fully saturated):

boundary
Equal fractions of the 3
primary colours (CIE
standard for white light)

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Typical range of colours (colour gamut) produced by RGB monitors:

Colour gamut of todays high-

quality colour printing devices

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2. Colour Models

Also called: colour spaces or colour systems

Purpose: facilitate the specification of colours in some standard way
Colour model = specification of a coordinate system and a subspace within it where
each colour is represented by a single point

Most commonly used hardware-oriented models:

RGB (Red, Green, Blue), for colour monitors and video cameras
CMY (Cyan, Magenta, Yellow) and CMYK (CMY+Black) for colour printing
HSI (Hue, Saturation, Intensity)

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2.1 The RGB Colour Model

Each colour appears in its primary spectral components of Red, Green and Blue
Model based on a Cartesian coordinate System
Colour subspace = cube
RGB primary values: at 3 opposite corners (+ secondary values at 3 others)
Black at the origin, White at the opposite corner

Gray scale

Convention: all colour values normalized

=> unit cube and all values of R,G,B in [0,1]

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Number of bits used to represent each pixel in the RGB space = pixel depth
Example: RGB image in which each of the red, green and blue images is a 8-bit image
Each RGB colour pixel (i.e. triplet of values (R,G,B)) is said to have a depth of 24
bits (full-colour image)

Total number of colours in a 24-bit RGB image is: (28)3 = 16,777,276

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NB: acquiring an image = reversed process:

Using 3 filters sensitive to red, green and blue, respectively (e.g. Tri-CCD sensor)

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Colour Image acquisition: Colour MonoCCD and Bayer Filter Mosaic

Bayer Mosaic Diagonal Mosaic Columns Mosaic

[Avia Cervantes
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Demosaicking: Interpolating the values of missing pixels in the component images

Example:
Bilinear demosaicking:

[Avia Cervantes 2005]

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Demosaicking

Other methods :
Nearest Neighbour Method
Demosaicking by median filter
Demosaicking by constant hue
Demosaicking by gradients detection
Adaptive interpolation by Laplacian

[Avia Cervantes 2005]

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2.2 XYZ (CIE)

Official definition of the CIE XYZ standard (normalised matrix):

Commonly used form: w/o leading fraction => RGB=(1,1,1) Y=1

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2.2 The CMY and CMYK Colour Models

CMY: Cyan, Magenta, Yellow (secondary colours of light, or primary colours of

pigments)
CMY data input needed by most devices that deposit coloured pigments on paper,
such as colour printers and copiers
or RGB to CMY conversion:

(assuming normalized colour values)

Equal amounts of cyan, magenta and yellow => black, but muddy-looking in practice
=> To produce true black (predominant colour in printing) a 4th colour, black, is added
=> CMYK model (CMY + Black)
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2.3 The HSI Colour Model

RGB and CMY models: straightforward + ideally suited for hardware implementations
+ RGB system matches nicely the human eye perceptive abilities
But, RGB and CMY not well suited for describing colours in terms practical for human
interpretation

Human view of a colour object described by Hue, Saturation and Brightness (or Intensity)
Hue: describes a pure colour (pure yellow, orange or red)
Saturation: gives a measure of the degree to which a pure colour is diluted by white light
Brightness: subjective descriptor practically impossible to measure. Embodies the
achromatic notion of intensity => intensity (gray level), measurable

=> HSI (Hue, Saturation, Intensity) colour model

(or HSL: Lightness, HSB: Brightness, HSV: Value)

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2.3 The HSI Colour Model

Intensity is along the line joining white and black in the RGB cube
To determine the intensity component of any colour point: pass a plane
perpendicular to the intensity axis and containing the colour point. Intersection of the
plane with the axis is the normalized intensity value
Saturation (purity) of a colour increases as a function of distance from the intensity
axis (on the axis, saturation = 0, gray points)

Intensity axis

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Colour planes, perpendicular to the intensity axis:

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The HSI Colour Models based on:

Triangular colour planes

Circular colour planes

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Conversion from RGB to HSI

Given an RGB pixel: then normalise H

with

Saturation:

Intensity: NB: RGB values normalised to [0,1],

Theta measured w.r.t. red axis of the HSI space

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Conversion from HSI to RGB

Three sectors of interest:

RG sector (0 H 120 ):

GB sector (120 H 240 ):

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Conversion from HSI to RGB

BR sector (240 H 360 ):

Then normalise H

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Conversion from HSI to RGB

Hue Saturation Intensity

=>

RGB 24-bit colour cube Corresponding HSI values

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Manipulation of HSI images:

Primary and secondary

RGB colours
H

S I

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H
Manipulation of HSI images: Modified HSI image

I
H S
S I

I RGB
image
Original image

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2.4 The L*a*b* model

Example of Colour Management System (CMS):

CIE L*a*b* model, or CIELAB:

Where:

XW, YW and ZW are reference white tristimulus

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The L*a*b* colour space is:

Colorimetric (colours perceived as matching are encoded identically)
Perceptually uniform (colour differences among various hues are perceived
uniformly)
Device independent

Other characteristics:
Not a directly displayable format
Its gamut encompasses the entire visible spectrum
Can represent accurately the colours of any display, print, or input device
Like HSI, excellent decoupler of intensity (represented by lightness L*) and
colour (a* for red minus green, b* for green minus blue)

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4. Basics of Full-Colour Image Processing

2 major categories:
Processing of each component image individually
=> composite processed colour image
Work with colour pixels (vectors) directly

Vector in RGB colour space:

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4. Basics of Full-Colour Image Processing

Per-colour-component and vector-based processing equivalent iff:

1. The process is applicable to both vectors and scalars
2. The operation on each component of a vector is independent of the other
components

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5. Colour Transformations
NB: Context of a single colour model (no conversion between models)

5.1 Formulation
(cf. 3.1)

(processed) colour
output image Colour input image
Operator defined over a
spatial neighbourhood of
point (x,y)

Set of transformation of colour mapping functions

Basic transformations:
e.g. RGB or HSI: n=3. CMYK: n=4

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Example: modify the intensity of the full-colour image using:

In HSI:
In RGB:
In CMY:

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5.2 Colour complements

Hues directly opposite one another on the colour circle = complements

Complements are analogous to gray-scale negatives (section 3.2.1)

Useful for enhancing detail embedded in dark regions

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5.2 Colour complements

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5.3 Colour slicing

Highlighting a specific range of colours to separate objects from surroundings
Display the colour of interest, or:
Use the region defined by colours as a mask

If colours of interest enclosed by a cube (or hypercube) of width W and centered at a

prototypical (e.g. average) colours with components (a1, a2,, an), then:

=> Highlight the colours around the prototype by forcing all other colours to the
midpoint of the reference colour space (e.g. middle gray in RGB: (0.5,0.5,0.5))

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5.3 Colour slicing

=>

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5.4 Tone and Colour Corrections

Effectiveness of these transformations judged ultimately in print

But developed, refined and evaluated on monitors
Need to maintain a high degree of colour consistency between monitors used and
eventual output devices
Device-independent colour model, relating the colour gamuts of the monitors
and output devices

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1. Tonal transformations

Boosting contrast
Typical transformations for correcting
three common tonal imbalances:

Cf. power-law
transformations

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2. Colour balancing

Goal: move the white point of a given image closer to pure white
(R=G=B)
Example of strongly coloured illuminant: incandescent indoor lighting
(=> yellow or orange hue)
NB: using white may not always be a good idea

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2. Colour balancing

Analyze (spectrometer) a known

colour in an image

When white areas: accurate visual

assessments are possible
Other example: skin tones

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Colour Adaptation

White Flash

Adaptive
Illumination

Vasilescu et al., Color-Accurate Underwater Imaging Using 44

Perceptual
19922008 R. C. Gonzalez
Adaptive & R. E. WoodsRSS
Illumination, 2010.
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5.5 Histogram Processing

Example: Histogram Equalisation in the HSI colour space

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6 Smoothing and Sharpening

6.1 Colour Image Smoothing

: Set of coordinates of a neighbourhood centered at (x,y) in an RGB image

Average of the RGB component vectors in this neighbourhood:

Can be carried out on a per-colour-plane basis (same as averaging using RGB vectors)

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Colour Image Smoothing: Example

RGB

G B

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Colour Image Smoothing: Example

RGB

H S I

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Colour Image Smoothing: Example

Smoothing each RGB

component image Smoothing the I of HSI Difference

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Colour Image Smoothing: Example

Smoothing each RGB

component image Smoothing the I of HSI Difference

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6.1 Colour Image Sharpening

In RGB, the Laplacian of vector c is:

=> Can be computed on each component image separately

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Original image
7 Image Segmentation Based on Colour
7.1 Segmentation in HSI Colour Space Hue

Typically: segmentation on
Hue image
Saturation Intensity

Example:

Binary saturation mask

Mask * Hue image
(threshold=10% of max value)

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7.2 Segmentation in RGB Colour Space

Given a set of sample colour points of interest, obtain an average colour to segment:
=> RGB vector a
Segmentation: classify each RGB pixel as having a colour in the specified range or not

z in RGB space is said similar to a if the distance between them is less than a specified
threshold
Euclidean distance:

Segmentation criteria:

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7.2 Segmentation in RGB Colour Space

Generalization of the distance measure:

(Mahalanobis distance)
Where C is the covariance matrix of the samples representative of the colour we
wish to segment

Bounding box
Euclidean Generalized
distance distance

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Example:
1. Compute mean vector a of colour points
in rectangle
2. Compute the standard deviation of red,
green and blue values
3. Box centered on a, dimensions along
each RGB axes: 1.25 R

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References:
R.C. Gonzalez and R.E. Woods, Digital Image Processing, 3rd Edition, Prentice Hall, 2008
D.A. Forsyth and J. Ponce, Computer Vision A Modern Approach, Prentice Hall, 2003
J.G. Avia Cervantes, Navigation visuelle d'un robot mobile dans un environnement
d'extrieur semi-structur (Visual Navigation of a Mobile Robot in semi-structured outdoor
environment), PhD Thesis, Institut National Polytechnique de Toulouse, 2005

19922008 R. C. Gonzalez & R. E. Woods