1. Computer Vision
Chapter 6
Color

2. Visible light Color Wavelength violet 380–450 nm blue 450–495 nm
green 495–570 nm
yellow 570–590 nm
orange 590–620 nm
red 620–750 nm
(high frequency/shorter wavelength)

3. White light So what is “white” light?
White light is composed of approx. equal energy in all wavelengths of the visible spectrum.

4. Perception of color
A blue surface appears blue when illuminated by white light.
The same surface appears violet when illuminated by red light.

5. Perception of color Dependent on: Spectrum of light source
Characteristics of illuminated object
Spectral sensitivity of the sensor

6. Perception of color Additional factors:
Surface is specular or matte (lambertian)
Distance of surface from light
Orientation of surface and light

8. Surface normals
Say we have 3 points, p1, p2, and p3 on our surface element.
Form two vectors, U=p2-p1 V=p3-p1.
Then N=UxV is the surface normal (cross product).
Nx = UyVz – UzVy
Ny = UzVx – UxVz
Nz = UxVy – UyVx
Analog in 2D is UxVy – UyVx
Note regarding length of N; note regarding direction of N.

9. Sensitivity of receptors

10. Types of images Binary image = range of I is in {0,1}
Gray-scale image = range of I is in {0,1,…,max}
Multispectral image = vector-valued
Ex. Color image = range is in {<r,g,b> | (r,g,b) in {0,1,…,max} }, for 8 bits, max=255 (28-1)
<0,0,255> = ?
<255,0,0> = ?
<100,100,100> = ?

11. Representing color RGB (red green blue) CMY (cyan magenta yellow)
Additive (to black: <0,0,0>)
CMY (cyan magenta yellow)
Subtractive (from white: <0,0,0>); based on printing inks on white paper
Often CMYK (K=key=black) because black from CMY is poor.
HSI (hue saturation intensity)
aka HSV (hue saturation value)

12. Additive (left) vs. subtractive (right)

14. Color cube (note RGB values in [0.0..1.0])

15. color cube vs. color wheel

16. Interactive:
Hue angle in [0..2Pi].
Saturation in [0..1].
Intensity in [0..255].

18. Other systems Luminance + 2 chromaticity values YIQ luminance red-cyan
Y = 0.3 R G B
red-cyan
I = 0.6 R – 0.28 G – 0.32 B
magenta-green
Q = 0.21 R – 0.52 G B
Used by color and black & white broadcast TV (before digital).

19. Other systems Luminance + 2 chromaticity values YUV
Y = 0.3 R G B
U = (B – Y)
V = (R – Y)
Used by JPEG and MPEG (compresses better than RGB)

20. Color histograms

21. Color histograms
How can one construct a color histogram?

22. Color histograms How can one construct a color histogram?
as 3D color clouds

23. Color histograms How can one construct a color histogram?
as histograms of each individual component

24. Color histograms Another method for constructing a color histogram:
Given an RGB value, construct an integer i = R2G2B2
where R2 = the 2 high order bits of the R component (and similarly for G and B)
= 26 = 64 bins in histogram
Maps 3D RGB values into 1D.

25. 64 bin color histogram example

26. 64 bin color histogram example

27. Color histograms Another method of constructing a color histogram:
Quantize RGB into 16 levels (4 bits for each component, 24 = 16)
Create a histogram of red values
Create a histogram of green values
Create a histogram of blue values
Concatenate these 3 histograms into one single 16x3 = 48 bin histogram
Also maps 3D RGB values into 1D.

28. Comparing histograms

29. Comparing color histograms
Say we have a database of images and their color histograms.
Given an image that is not in our database, we can calculate its histogram.
And see what histogram it best matches.
But how can we compare histograms?

30. Method 1: Comparing two (1D) histograms hI and hM
Note: match is not symmetric. I.e., match(a,b) <> match(b,a) for all a and b.

31. Method 2: Comparing two (1D) histograms hI and hM
Normalize (divide) each hI and hM by total number of pixels (to approximate probabilities).
Calculate distance d( hI, hM ) as (or 48-) dimensional points.
How do we calculate the distance between or 48-) dimensional points?

32. Method 2: Comparing two (1D) histograms hI and hM cont’d.
Normalize (divide) each hI and hM by total number of pixels (to approximate probabilities).
Calculate distance d( hI, hM ) as (or 48-) dimensional points.
How do we calculate the distance between or 48-) dimensional points?

33. Method 3: Relative entropy (or the Kullback Leibler distance)
from “Elements of Information Theory,” 2nd ed., (Wiley Series in Telecommunications and Signal Processing) by Thomas M. Cover and Joy A. Thomas (Hardcover - Jul 18, 2006), p. 18.
(all logs are base 2)

34. Method 4: Mutual information
from “Elements of Information Theory,” 2nd ed., (Wiley Series in Telecommunications and Signal Processing) by Thomas M. Cover and Joy A. Thomas (Hardcover - Jul 18, 2006)
(all logs are base 2)

35. Method 4: Mutual information cont’d.
How to calculate the joint distribution or joint p.m.f., p(x,y):

36. Color segmentation example

37. Color segmentation example
Problem: Find (segment) face in workstation camera image.
Approach:
Training phase:
Determine clusters from pixels from known faces using red-green values.
Classification phase:
Given a pixel that we need to classify (as either face or not), produce a labeled image which is then filtered according to region size.

38. non face pixel colors
cluster of face pixel colors

40. End color segmentation example

41. Color histograms
Yet another method is to map 3D RGB values into a 3D histogram.
Note that K-means can also be easily applied to any of these 3 color histogram methods.

42. Homework
Exercises 6.6, 6.8, and 6.9.

43. Homework Exercise 6.6. Using Algorithm 6.1 (procedure RGB_to_HSI),
convert the RGB value (100,150,200) into an HSI value and,
convert the RGB value (0.0, 1.0, 0.0) to HSI.

44. Homework
Exercise Suppose a color camera encodes a given pixel in RGB as (200, 50, 100), where 255 is the highest (most energy) value.
What should be the equivalent triple in the HSI system?
What should be the equivalent triple in the YIQ system?

45. Homework
Exercise Is the transformation from RGB to YIQ invertible? Is so, compute the inverse.

46. Color is a key feature in identifying the real tiger.

47. original increased saturation decreased saturation
HSI is a natural representation for increased or decreasing the amount of color in an image.
Hue angle in [0..2Pi].
Saturation in [0..1].
Intensity in [0..255].

48. image after segmentation and labeling (coloring)

49. Storing images in file

50. { P2 = ASCII gray PGM header ASCII max data value data comments height
(rows)
width
(cols)

51. P3 = ASCII color PPM
Each pixel’s color is represented as <red,green,blue>. P3
w h
maxval
v1r v1g v1b v2r v2g v2b
. . .
vw*hr vw*hg vw*hb

52. 2D Images Stored as 1D Arrays
Say our 2D color (RGB) image is stored as a 1D array, I.
How do we calculate the offset to a particular element given a particular row and column?
First, do you recall how it’s done for a 2D gray image?