color image processing - ut€¦ · color image processing mtt.03.2a60 pattern recognition and...

Color Image ProcessingMTAT.03.260 Pattern Recognition and Image Analysis (MTAT)

Kristjan Krips Timo Petmanson

University of Tartu

March 18, 2011

Kristjan Krips, Timo Petmanson (University of Tartu)Color Image Processing March 18, 2011 1 / 39

Outline

1 Fundamentals

2 Color models

3 Pseudo-color processing

4 Full-color processing

5 Color transformations

6 Smoothing and sharpening

7 Color segmentation

8 Noise in color images


Visible light

Human eye is sensitive to electromagnetic radiation betweenwavelengths of approximately from 390 nm to 750 nm.


Human eye reception / primary colors

65% cones are sensitive to red light

33% of cones are sensitive to green light

2% of cones are sensitive to blue light


Primary / secondary colors

red + blue = magneta

red + green = yellow

blue + green = cyan


Color characteristics

brightness - a subjective measure of chromatic intensity of color

hue - represents the dominant color (dominant wavelenght), e.g. red,blue

saturation - the relative purity of the color, the amount of white lightmixed with the hue.

chromaticity = hue + saturation


Trichromatic coe�cients

A color can be speci�ed by its trichromatic coe�cients:

I x = X

X+Y+Z , y = Y

X+Y+Z , z =Z

X+Y+Z , where x+ y + z = 1

X =∫

∞

0 I (λ )x(λ )dλ , Y =∫

∞

0 I (λ )y(λ )dλ , Z =∫

∞

0 I (λ )z(λ )dλ

I (λ ) is the spectral power distribution of a given color,x(λ ),y(λ ),z(λ ) are color matching functions of standard observer eg.combination of three linear light detectors.


CIE chromaticity diagram

The diagram is the function of red and green. The blue is obtainedfrom equation z = 1− (x+ y).

The colors on the boundary are fully saturated, where the ticks denotethe wavelength in nanometers.


CIE chromaticity diagram

By connecting any two points with a line in the plot, we get the allpossible combinations of colors that can obtained by mixing theendpoint colors.

Grassman's Law: Any colour can be matched by a linear combinationof three other colours, provided that none of those three can bematched by a combination of the other two


sRGB color space and the gamutGamut represents the colors producable of a typical color monitor. Inexperiments carried out by W. David Wright and John Guild, thestandard observer used to set up the sRGB diagram was human.Color matching functions x(λ ), y(λ ), z(λ ) were summarized based onthe experimentsThe vertices of the triangle represent 3 primary colors easilyproducable by monochromatic lines of a mercury vapor discharge.


RGB model

Derived from primary color components red, green and blue.

Normalized into range [0,1] (in computers typically 0..255])

Color cube:

I black is (0,0,0)I white is (1,1,1)I red is (1,0,0)I green (0,1,0)I blue is (0,0,1)


RGB model

http://www.mathworks.com/help/toolbox/images/f8-15484.html


RGB <=> CIE color space

1 We need a transfer functions fr , fg , fb for each color channel of themonitor device that de�ne the relationship between input pixel valuesand displayed intensity.

2 The relationship between CIE trimulus values X,Y,Z and displayedimage pixel values R, G, B is given below.

3 The 3x3 matrix can be calculated by deom chromaticity values forthree channels and the white point usually published by themanufacturer. X

YZ

=

Xr Xg Xb

Yr Yg Yb

Zr Zg Zb

∗ fr (R)

fg (G )fb(B)

fr (R)

fg (G )fb(B)

=

Xr Xg Xb

Yr Yg Yb

Zr Zg Zb

(−1)

∗

XYZ


Calculating the 3x3 matrixManufacturer usually publishes chromaticity coordinates for theprimaries and the white point.

Colour Chromaticity coordinates

red (xr ,yr ,zr )

green (xg ,yg ,zg )

blue (xb,yb,zb)

white (xw ,yw ,zw )

Assuming that relative luminance equals to 1, we can �nd constantsar ,ag ,ab from the simulanteus equations

arxr +agxg +abxb = xnyn

aryr +agyg +abyb = 1arzr +agzg +abzb = zn

yn

=>

XYZ

=

arxr agxg abxbaryr agyg abybarzr agzg abzb

∗ fr (R)

fg (G )fb(B)


CMYK model

Derived from secondary colors.

Used as a main model in printing devices where blending of colorpigements are used to achieve colors.

Equal amounts of cyan, magneta and yellow does not give true black,thus black pigment is additionally used in blending process.

However, this simple transformation is good enough for simpergraphics, but it will produce poor results for applications with higherrequirements such as an colour printer.

CMY <=> RGB

CMY

=

111

− R

GB


CMY => CMYK

Black = min(Cyan, Magneta, Yellow)

Cyan = (Cyan - Black) / (1 - Black)

Magneta = (Magneta - Black) / (1 - Black)

Yellow = (Yellow - Black) / (1 - Black)


HSL, HSV, (HSI) model

HSL (hue, saturation, lightness) and HSV (hue, saturation, value)model is easily interpretable by humans. They are also two mostcommon cylindrical-coordinate representations of points in an RGBcolor model.


Basic idea

Starting at the red primary at 0°, passing through the green primary at120° and the blue primary at 240°, and then wrapping back to red at360°.

In each geometry, the central vertical axis comprises the neutral,achromatic, or gray colors, ranging from black at lightness 0 or value0, the bottom, to white at lightness 1 or value 1, the top.


Hue and chroma

Hue is roughly the angle of a vector representing the color, where chroma isthe length.


Hue and chroma


Lightness

The simplest de�nition is just the average of the three components, inthe HSI model called intensity.

I I = 1

3(R+G +B)

In the HSV "hexcone" model, value is de�ned as the largestcomponent of a color, our M above. This places all three primaries,and also all of the "secondary colors" � cyan, yellow, and magenta �into a plane with white, forming a hexagonal pyramid out of the RGBcube.

I V =M

In the HSL "bi-hexcone" model, lightness is de�ned as the average ofthe largest and smallest color components (�g. 11c). This de�nitionalso puts the primary and secondary colors into a plane, but a planepassing halfway between white and black.

I L= 1

2(M+m)


Lightness


Saturation


HSV => RGB


HSL => RGB


Pseudo-color (false color) processing / Basic idea

Pseudo-color (false color) processing takes a monochrome image andapplies colors to it.

The idea is to make grayscale images more easily readable andinterpretable to humans.

I mapping intensity ranges to color.I for example we can divide the intensity range [0..1] into subregions and

map a color to each range


Gray level to color transformations

Wider range of pseudocolor results, nonlinear

Independent transformation for each primary color

Results are mixed together into a composite image


Full-color image processing

Process each component image individually and form a compositeimage

I standard gray-scale image processing methods

Work directly with color pixels

I pixels are vectorsI averaging per-color-component


Basic color transformations

Processing the components of an image in a single model

I g (x ,y) = T [f (x ,y)], where f(x,y) is the input image and g(x,y) is theprocessed image

I si = Ti (r1, r2, ..., rn), where i = 1,2,...,n and si , ri denote the colorcomponents of f(x,y), g(x,y) at any point (x,y); n is the number ofcomponents; {T1,T2, ...,Tn}is a set of color transformation functions.

Cost of transformations

I In HSI model transformations are simpleI Converting from RGB, CMY(K) to HSI is di�cult, thus the gain in

total cost would be negative


Color complements

Hues that are opposite in the color circle are called complements

Analogous to the gray-scale negatives

Can bring out details in the dark regions of the image


Color slicing

Useful for separating objects from the background

Map colors in a range of intrest to a neutral color

si =

{0.5 if

[| rj −aj |> W

2

]any 1≤j≤n

ri otherwise, i = 1,2,...,n

si =

0.5 ifn

∑j=1

(rj −aj)2 > R2

0

ri otherwise, i = 1,2,...,n


Tone and color corrections

Important in printing

Tonal range (key type) - general distribution of color intensities

Calibrated imaging systems

I correct inbalances interactively and independentlyI sequential operations, tone correction �rst and then color correction

Methods

I increasing or decreasing the amount of opposite colorI changing the proportions of adjacent colors


Histogram processing

Graylevel histogram processing can be applied to color images

I doing this independently on image components results in imperfectresults

Leave colors unchanged and uniformly change the intensities of thecolors


Smoothing and sharpening

Are usually done exactly the same as with gray-scale techiques, butrequire additional steps.

I split the image into channels (R,G,B or HSI)I process all the channels or only one (I channel in HS model) with

grayscale methodsI combine back to original image


Color segmentation

Partition image into regions of interest

Segmentation in HSI

I saturation is used for isolating regions of interest

Segmentation in RGB

I better than segmentation in HSII obtain an estimate of the average color that we want to segmentI classify each RGB pixel as having a color in the speci�ed range or notI uses Euclidean distance as the similarity measureI computationally expensiveI use a bounding box as a compromise


Noise in color images

Gray-scale noise models can be applied to color images

Di�erent channels can be a�ected di�erently

Filtering out noise

I per image basisI per vector basisI averaging works on both in the same wayI median �ltering does not by default, vectors have to be orderedI more complex with vectors


Noise in color images

Sometimes it is more useful to see image in HSL, HSV, HSI colormodels, as it may reveal noisy channels better.


color image processing - ut€¦ · color image processing mtt.03.2a60 pattern recognition and...

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