1. Computer Vision Lecture 4: Color
Image Resampling
Example: Downscaling from 5×5 to 3×3 pixels
Centers of output pixels mapped onto input image
February 8, 2018
Computer Vision Lecture 4: Color

2. Computer Vision Lecture 4: Color
Image Resampling
Nearest-neighbor method: For each output pixel, intensity is taken from the input pixel whose center is closest to the mapped output pixel’s center. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9
Centers of output pixels mapped onto input image
February 8, 2018
Computer Vision Lecture 4: Color

3. Computer Vision Lecture 4: Color
Image Resampling
Bilinear interpolation method: Consider the four closest neighbors (2×2) of each mapped output pixel. Then use linear interpolation in horizontal and vertical direction to determine output pixel intensity.
Bicubic interpolation method: Consider the 16 closest neighbors (4×4) of each mapped output pixel. Then use cubic interpolation (polynomials of degree 3) in horizontal and vertical direction to determine output pixel intensity.
Many current image processing applications use bicubic interpolation.
February 8, 2018
Computer Vision Lecture 4: Color

4. Computer Vision Lecture 4: Color
Nearest neighbor
Bilinear interpolation
Bicubic interpolation
February 8, 2018
Computer Vision Lecture 4: Color

5. Computer Vision Lecture 4: Color
February 8, 2018
Computer Vision Lecture 4: Color

6. Computer Vision Lecture 4: Color
Our retina has three different types of color receptors. Their maximum responses occur for the colors red, green, and blue, respectively.
Our color perception is entirely based on these three responses. Any two input spectra that create the same pattern of responses are perceived as identical colors.
February 8, 2018
Computer Vision Lecture 4: Color

7. Computer Vision Lecture 4: Color
How can we quantitatively describe a color?
As computer programmers, we usually treat colors as RGB triples.
The three components define the amount of red, green, and blue, respectively, whose combination results in the desired color on a computer screen.
Typically, each channel uses discrete values from 0 to 255.
The color space formed by all possible RGB values is also called the RGB cube.
February 8, 2018
Computer Vision Lecture 4: Color

8. Computer Vision Lecture 4: Color
The RGB color space is easy to use and represents color in the same way as the monitor requires it for its display.
However, for computer vision applications such as the recognition of objects, other color spaces are more useful.
We will discuss the HSI color model, standing for hue, saturation, and intensity.
These dimensions characterize important object properties more naturally as compared to the RGB components.
February 8, 2018
Computer Vision Lecture 4: Color

9. Computer Vision Lecture 4: Color
Hue is determined by the dominant wavelength in the spectral distribution of light wavelengths.
Saturation is the magnitude of the hue relative to other wavelengths.
It is defined as the amount of light at the dominant wavelength divided by the amount of light at all wavelengths.
Intensity is a measure of the overall amount of light within the visible spectrum.
It is a scale factor that is applied across the entire spectrum.
February 8, 2018
Computer Vision Lecture 4: Color

10. Computer Vision Lecture 4: Color
Hue
Saturation
Brightness
February 8, 2018
Computer Vision Lecture 4: Color

11. Computer Vision Lecture 4: Color
Hue is (ideally) independent of the lighting conditions and the distance between object and observer. It is thus a reliable parameter for object recognition.
Saturation decreases with the amount of particles between object and observer. We can use it to estimate our distance from a known object.
Intensity is the only variable that changes when the lighting conditions vary. It can be used to infer shading and, in turn, three-dimensional structure.
February 8, 2018
Computer Vision Lecture 4: Color

12. Computer Vision Lecture 4: Color
RGB HSI
February 8, 2018
Computer Vision Lecture 4: Color

13. Conversion from RGB to HSI
It is not too difficult to convert RGB values into HSI values to facilitate color processing in computer vision applications.
First of all, we normalize the range of the R, G, and B components to the interval from 0 to 1.
For example, for 24-bit color information, this can be done by dividing each value by 255.
Then we compute the intensity I as
I = 1/3*(R + G + B).
Obviously, intensity also ranges from 0 to 1.
February 8, 2018
Computer Vision Lecture 4: Color

14. Conversion from RGB to HSI
Then we compute the values r, g, b that are independent of intensity:
r = R/(R + G + B)
g = G/(R + G + B)
b = B/(R + G + B)
When we consider the RGB cube, then all possible triples (r, g, b) lie on a triangle with corners (1, 0, 0), (0, 1, 0), and (0, 0, 1).
We could call this the rgb-subspace of our RGB cube.
February 8, 2018
Computer Vision Lecture 4: Color

15. Conversion from RGB to HSI
red (pr)
green
blue
p - w
p = (r, g, b)
pr - w H
w = (1/3, 1/3, 1/3) (white)
The hue is the angle H from vector pr – w to vector p – w.
The saturation is the distance from w to p relative to the distance from w to the fully saturated color of the same hue as p (on the edge of the triangle).
February 8, 2018
Computer Vision Lecture 4: Color

16. Conversion from RGB to HSI
Then we have:
Since w = (1/3, 1/3, 1/3):
And since pr = (1, 0, 0):
February 8, 2018
Computer Vision Lecture 4: Color

17. Conversion from RGB to HSI
We can also compute:
With the above formulas, including those for deriving r, g, and b from R, G, and B, we can determine an equation for computing H directly from R, G, and B:
February 8, 2018
Computer Vision Lecture 4: Color

18. Conversion from RGB to HSI
Note that when we use the arccos function to compute H, arccos always gives you a value between 0 and 180 degrees.
However, H can assume values between 0 and 360 degrees.
If B > G, then H must be greater than 180 degrees.
Therefore, if B > G, just compute H as before and then take (360 degrees – H) as the actual hue value.
February 8, 2018
Computer Vision Lecture 4: Color

19. Conversion from RGB to HSI
The saturation is the distance on the triangle in the rgb-subspace from white relative to the distance from white to the fully saturated color with the same hue.
Fully saturated colors are on the edges of the triangle.
The derivation of the formula for saturation S is very lengthy, so we will just take a look at the result:
February 8, 2018
Computer Vision Lecture 4: Color

20. Computer Vision Lecture 4: Color
February 8, 2018
Computer Vision Lecture 4: Color

21. Limitations of RGB and HSI
Using three individual wavelengths to represent color can never cover the entire visible range of colors:
February 8, 2018
Computer Vision Lecture 4: Color

22. Limitations of any Color Representation
It is important to note (again) that our perception of an object’s color does not only depend on the frequency spectrum emitted from the object’s location.
It also depends on the spectra of other objects or regions in the visual field.
This mechanism called color constancy allows us to assign a color to a given object that is invariant to shading or illumination of the scene by varying light sources.
February 8, 2018
Computer Vision Lecture 4: Color

23. Computer Vision Lecture 4: Color
Color Constancy
February 8, 2018
Computer Vision Lecture 4: Color