June 14, 99

1
June 14, 99

• COLORS
• IN
• MATLAB

2
UNDERSTANDING COLOR

• To understand color we must first understand
  color spaces
• We come in contact with color through
• Video(computers,TVs)
• 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

Colorw1redw2greenw3blue
4
RGB COLOR CUBE
Cyan
Green
White
1
Yellow
Color is represented by a point in the RGB cube
Blue
1
1
Red
Magenta
5
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 balanceto get real black
• Often black is added as the 4th color, CMYK

7
HUMAN COLOR MODEL

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

white
brightness
saturation
green
red
blue
hue
black
8
NET REFERENCE ON COLOR

• There is a comprehensive FAQ on color. You can
  reach it at
• http//www.inforamp.net/poynton/Poynton-colour.ht
  ml

9
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.

black
0
0
0
1
0
1
magenta
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FEW MATLABs COLORMAPS
Image intensity maps to color
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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)
• Whats wrong?

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Digital image

• Before going on, lets 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)
• MATLABs 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 monitors
  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
• mapcolormap
• 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?

last row
highest
Colormap
Data Values
maps to
lowest
first row
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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 k1, row 1
• Zmax km, row m
• The middle Zs 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 MATLABs 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 zlta
• assign red to zgtb
• assign a continuous color tone(blue to red) for
  altzltb

b
Z
a
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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
• zltcmin ----gtfirst row of colormap
• zgtcmax ----gtlast 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?

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MATLABS DEFAULT COLORMAP

• MATLABs 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(-40.24)
  and v90,0. Go through hsv, hot, flag, copper
  etc. colormaps. Check maps 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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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
• z132132
• pcolor(z)

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WORKING WITH IMAGES

• A two dimensional image can be modeled by
  zf(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
• mapcolormap
• 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, red0.29, green0 and
  blue0

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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
  29red. 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 zsin(sqrt(x2y2)) in the range(-pi to
  pi)in increments of 0.2
• Make the function appear red for zlt-0.5, white
  for -0.5ltzlt0.5 and blue for zgt0.5
• Do the same except for making the colors between
  red and white follow 32 gradations of colormap hot