Colors and images

(MMG640 / MVE080)

Overview

• Brief history of color models
• Color models: RGB, HSV, HSL, CMYK
• Color images on the computer
• Loading images in Python (exercise)
• Gray scale images
• 'meshgrid' command
• Creating and saving images in Python (exercise)
• Color maps (gradients)
• Contour plots

slides.com/kmodin/mmg640-colors-images/live#

Pioneers of color models

Isaac Newton's prism and color wheel

Other early contributors:

Thomas Young, Hermann von Helmholtz, James Clerk Maxwell

Standard color model: Red Green Blue (RGB)

• Color specified by 3-tuple [R, G, B]
• Each value integer between 0 and 255
• Black is [0, 0, 0]
• White is [255, 255, 255]
• Additive model (large means bright)

RGB color codes

Typically three different ways

• Decimal, integer [0,255]
  Example: [125, 13, 67]
   
• Decimal, floating-point [0,1]   (used in Matplotlib)
  Example: [0.5, 0.24353, 0.8983]
   
• Hexa-decimal  (often used in HTML)
  Example: #0F3ABC

Other color models

HSV (Hue, Saturation, Value)

Resembles the way colors mix spectrally

HSL (Hue, Saturation, Lightness)

Resembles perceptual color models such as the Natural Color System (NCS)

Color pickers

Color bitmap images

• Array of dimension height*width*3
   
• Think of it as matrix of 'pixels'
   
• Each pixel is an RGB tuple
   
• Sometimes a fourth 'alpha-channel' representing opacity (cf. RGBA)
  0 % = fully transparent pixel
  100 % = fully opaque pixel

Image file formats

• For storage efficiency, bitmap image arrays are compressed
   
• Commonly used image file formats:
  
  JPEG (Joint Photographic Experts Group), *.jpg
  Lossy compression
  Good for photos
  
  GIF (Graphics Interchange Format), *.gif
  Lossless compression
  Good for few color images: shapes, logos, cartoons
  
  PNG (Portable Network Graphics), *.png
  Lossless compression
  Modern replacement of GIF, also handles photos

Gray scale images

• Image with only one channel = matrix
• Scalar functions \(f: [a,b]\times[c,d] \to \mathbb{R}\) are usually approximated by gray scale images

• meshgrid command in Numpy is useful

Example: \(f(x,y) = \sin(x y)\) as gray scale image in Numpy

x = np.arange(-3,4); y = np.arange(-3,3)

xx,yy = np.meshgrid(x,y); ff = np.sin(xx*yy)

xx

yy

Color maps (gradients)

• Matplotlib function imshow can display gray images

Example (cont.):

>> plt.imshow(ff)

Why is it not in gray scale?

Answer: color map used to assign color to each gray value

A colormap is \(n\times 3\) matrix where \(n\) is number of 'gray levels'

Convert to RGB image

• Matplotlib function imsave can convert gray images to RGB using a specific color map

Example: (with ff as before)

>> imsave('mycolorfunction.jpg', ff, cmap='viridis')

or

>> imsave('mygrayfunction.jpg', ff, cmap='gray')

Contour plots

• Level-set of \(f:[a,b]\times[c,d] \to \mathbb{R}\) is \(S_v = \{ (x,y)\mid f(x,y) = v \}\)
• Each level set gives a curve
• Matplotlib functions contour plots level set curves

Example: (with x,y,ff as before)

>> plt.contour(x,y,ff)

>> plt.colorbar()