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June 14, ‘99

COLORS

IN

MATLAB

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UNDERSTANDING COLOR

To understand color we must first understand color spaces

We come in contact with color through:– Video(computers,TV’s)– Printed matter(magazines,

brochures)– Real World

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ADDITIVE COLOR MODEL

Formation of colors on video monitors is through an additive process of 3 color components– Red– Green – Blue

Concern is white balance, meaning how white is the white displayed on the monitor

Color=w1*red+w2*green+w3*blue

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RGB COLOR CUBE

Red

Blue

Green1

1

1

White

Yellow

Cyan

Magenta

Color isrepresentedby a point inthe RGB cube

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RGB CUBE

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SUBTRACTIVE COLOR MODEL

Color formation in printing industry is through the subtractive CMY model– Cyan– Magenta– Yellow

Challenge is black balance;to get real black

Often black is added as the 4th color, CMYK

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HUMAN COLOR MODEL

The most accurate model here is hue, saturation and value(brightness) HSV

white

black

hue

saturation

redgreen

blue

brightness

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NET REFERENCE ON COLOR

There is a comprehensive FAQ on color. You can reach it at

http://www.inforamp.net/~poynton/Poynton-colour.html

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UNDERSTANDING COLORMAPS

At the heart of color control in MATLAB is the concept of colormap

Colormap is a 3-column matrix with entries between 0 and 1. Each row defines a particular combination of (R,G,B) to define a color.

0 0 0

1 0 1

black

magenta

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FEW MATLAB’s COLORMAPS

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

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HSV(32)

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

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hot(32)

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

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flag(32)

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

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copper(32)

Imag

e in

ten

sit

y m

ap

s t

o c

olo

r

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Try it!

MATLAB comes with few images. To load one of them type– load clown

Now check your workspace. You will see image data stored in X and colormap stored in map

To display the image type– image(X)– What’s wrong?

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Digital image

Before going on, let’s define a digital image.

A digital image is simply a 2D matrix. Each element of the matrix, pixel, is an integer. For a black and white image pixels are between 0 (black) and 255(white)

MATLAB’s matrix oriented structure makes minced meat out of images and image processing

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Role of colormap

Type out a few values of X. You will see integers. But what is the relationship between these numbers and their actual color?

Enter colormap. Colormap is lookup table. It takes an intensity value, say 25, and connects it with some color.

To display true colors, you must set monitor’s colormap to the map used at the time the image was created

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WORKING WITH COLORMAPS

Command colormap(map) sets the colormap to one of preset or user defined values

For clown image ,type colormap(map) and watch the result.

Now try these– colormap(hot)– colormap(hsv)– colormap(gray)

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RECALLING AND SETTING COLORMAPS

Current colormap in effect can be found by

map=colormap

Any (3x1) matrix can be defined by the user and defined as the current colormap by

colormap(usermap)

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COLOR ASSIGNMENT

How is intensity connected to color?

Data Values

Colormap

lowest first row

highest last row

maps to

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COLOR MAPPING RULE

Let data range between Zmin and Zmax. Let the colormap rows k run from 1 to m.

Then

Zmin k=1, row 1

Zmax k=m, row m

The middle Z’s follow a linear mapping rule.

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Defining your first colormap

Plot the peaks function using – surf(peaks)

Define a colormap, mymap, so that the first row is blue, the second row is green, third row is white and fourth row red.

Then set MATLAB’s colormap to mymap. See code next

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Try it!

Interpret colors you see

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ARBITRARY COLOR ASSIGNMENT

Color mapping rule is simple:– take the minimum of the function and

assign it the color of the first row of colormap

– take the maximum of the function and assign it the color of last row of colormap

– in-between values take shades of color obtained by a linear mapping of the above two colors

Next slide shows you more

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ASSIGNING COLORS TO RANGES OF DATA

This is what we want to do:– assign blue to z<a– assign red to z>b– assign a continuous color tone(blue

to red) for a<z<b

a

b

Z

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How to do it? clim property

clim is a two element vector [cmin,cmax]. It can be set as follows– set(gca, ‘clim’,[cmin cmax])

Colormapping is done as follows– z<cmin ---->first row of colormap– z>cmax ---->last row of colormap

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Try it!

Plot the peaks function and display it with view(90,0)

Set cmin and cmax to [-2 2],[-3 3] and [-4 4] and see if you can explain the results?

0 5 10 15 20 25 30 35 40 45 50-8

-6

-4

-2

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10

0 5 10 15 20 25 30 35 40 45 50-8

-6

-4

-2

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10

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MATLAB’S DEFAULT COLORMAP

MATLAB’s default colormap is HSV and can be set via

colormap(‘default’) or colormap(‘hsv’)

Unless specified otherwise, colormaps are 64x3, i.e. 64 colors

Other sizes can be specified, e.g.

colormap(hot(128))

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Try it!

Plot the peaks function in the range(-4:0.2:4) and v=[90,0]. Go through hsv, hot, flag, copper etc. colormaps. Check map’s sizes

?

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DEFINING YOUR OWN COLORMAP

Want to display the peaks profile in only two colors. Negative values in red and positive values blue. Define a colormap for this purpose.

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1020

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4050

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-4

-2

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Pseudorandom color :pcolor

Command pcolor(z) draws a rectangular grid of cells with colors determined by z; function height above each cell. Mapping from z to color is determined by colormap

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OVERLAYING CONTOURS

Do the following:– get rid of the grid lines(try shading

command)– Superimpose black colored

gridlines(lookup help on contour)

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pcolor and colormap

The following will display 32 bins of current colormap– z=[1:32;1:32]’– pcolor(z)

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

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WORKING WITH IMAGES

A two dimensional image can be modeled by z=f(x,y) where (x,y) is the pixel position and z the corresponding height

The height is then mapped to either a grayscale or color range

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LOADING IMAGES

Images are loaded like sound file. For example– load clown

Now check your workspace to see which variable is “clown” loaded in.

Check the size of the image array and its min and max

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DISPLAYING IMAGES

There are a number of ways to display an image. For the start use– image(z)– z is the array your image is loaded in.

Check

Each element of z specifies the color of a rectangular patch in the image

Elements of z are used as indices into the current colormap to determine the color

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INDEXED IMAGES

MATLAB supports a number of image formats one of which is “indexed”

“intensities” in indexed images are not really intensities; they are simply entries into the colormap

If image value at (x,y)=32, this simply means that pixel color at (x,y) comes from the row 32 of the colormap

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Example of indexed image: clown

When you loaded clown you got two arrays– X: image data– map:colormap

Now check image value at position (100,100). I get 4. What color is this pixel?. MATLAB goes to the 4th row of map

This row has 3 columns, red=0.29, green=0 and blue=0

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How to display the color of a single pixel?

In the previous slide we found out that X(100,100) has no green or blue component and is 29%red. But what color is it?

Here is a way to do get it. Type– image(X(100,100))– Is it what you expect?. Is it reddish?

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PLAYING WITH COLORMAPS

Unless a digital image is accompanied by a colormap, it is impossible to determine pixel colors

Check the colormap that accompanies the loaded image; its size and its contents.

Change the colormaps to hot, hsv, cool, gray and see the results

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HOMEWORK

Plot z=sin(sqrt(x^2+y^2)) in the range(-pi to pi)in increments of 0.2– Make the function appear red for

z<-0.5, white for -0.5<z<0.5 and blue for z>0.5

– Do the same except for making the colors between red and white follow 32 gradations of colormap hot