Those are the slides for the book: Visual Computing: Geometry, Graphics, and Vision. by Frank Nielsen (2005) http://www.sonycsl.co.jp/person/nielsen/visualcomputing/ http://www.amazon.com/Visual-Computing-Geometry-Graphics-Charles/dp/1584504277

1. © 2011 Frank Nielsen
INF555
Fundamentals of 3D
Lecture 7:
Colors
Randomized algorithms
RANSAC/MINIBALL
Frank Nielsen
nielsen@lix.polytechnique.fr
2nd November 2011

2. © 2011 Frank Nielsen
Supersampling: Averaging
Uniform versus non-uniform sampling
(raytracing software: Povray, Blender)
The essence of pixels: Integration !

3. © 2011 Frank Nielsen
Color and perception
Commission Internationale de
l’ ´ Eclairage in French, CIE, http:// www.cie.co.at/

4. © 2011 Frank Nielsen
A candela unit is defined as the luminous intensity of
a light source emitting a monochromatic light of frequency
540 × 10^12 Hz that has a radiant intensity of 1 683 watt per
steradian.
A luminous flux is measured in lumen units (lm).
A lumen unit is defined as the amount of light that falls on a unit
area at unit distance from a light source of one candela.
The lux (lx) represents the luminance and defined as one lumen
per square meter.
Color and measurements

5. © 2011 Frank Nielsen
Cone responses in human eyes
Cones (color) and rods (B&W) in human eyes

6. © 2011 Frank Nielsen
Additive and subtractive color modes
Display/printing industries
Color checking in printing industry

7. © 2011 Frank Nielsen
Choosing colors: Colors pick-up

8. © 2011 Frank Nielsen
Pseudo-coloring
Volume rendering and transfer function

9. © 2011 Frank Nielsen
Color spaces
Normalizing coefficient
converts the spectrum absorption of light L to XYZ colors

10. © 2011 Frank Nielsen
The basic response functions for CIE XYZ hypothetical colors.
Observe the artificial response curve x(·) of color X.
The basic response functions for CIE XYZ hypothetical colors.
Observe the artificial response curve x(·) of color X.

11. © 2011 Frank Nielsen
Color cube

12. © 2011 Frank Nielsen
HLS/HSV color spaces
(hue, lightness, saturation (hue, saturation, value)

13. © 2011 Frank Nielsen

14. © 2011 Frank Nielsen
CMYK color space (for printing)

15. © 2011 Frank Nielsen
CIE L*a*b
Perceptual difference between two colors:
CIE L*a*b (where Euclidean distance make sense)

16. © 2011 Frank Nielsen
Many standards....

17. © 2011 Frank Nielsen
Gamma color correction:
Bayer tile

18. © 2011 Frank Nielsen
Half-toning and dithering
t=127 Random t

19. © 2011 Frank Nielsen
Dithering: Trade space for grey level perception

20. © 2011 Frank Nielsen
Error-diffusion process: Floyd-Steinberg

21. © 2011 Frank Nielsen
Low dynamic range images (LDRs) versus
High dynamic range images (HDRs)

22. © 2011 Frank Nielsen
Low dynamic range image
High dynamic range image
Tone mapping

23. © 2011 Frank Nielsen
Tone mapping

24. © 2011 Frank Nielsen
Quicksort:
O(n log n) expected
O(n^2) worst-case
O(n) best case

25. © 2011 Frank Nielsen
Randomization: A Powerful principle
Analysis:

26. © 2011 Frank Nielsen
RANSAC on Harris-Stephens points.
Epipolar points intersect on their epipoles
RANSAC: Random Sample Consensus

27. © 2011 Frank Nielsen

28. © 2011 Frank Nielsen
Probability of failure of picking two inliers
Macthing points: Inliers/outliers

29. © 2011 Frank Nielsen
RANSAC: Bounding failure probability
Probability of failure after one round
Probability of failure after k independent rounds

30. © 2011 Frank Nielsen

31. © 2011 Frank Nielsen
Estimating homographies with RANSAC

32. © 2011 Frank Nielsen
Adaptive RANSAC: Guessing the ratio of inliers

33. © 2011 Frank Nielsen
Demo of autostich:

34. © 2011 Frank Nielsen
Bounding sphere hierarchy

35. © 2011 Frank Nielsen
MINIBALL: Smallest enclosing ball
UNIQUE
http://www.inf.ethz.ch/personal/gaertner/miniball.html

36. © 2011 Frank Nielsen
LP-type problem in optimization

37. © 2011 Frank Nielsen
MINIBALL: Solving for basis of 2 and 3 points
Intersection of bisectors
(use cross-product on homogeneous
coordinates)
Intersection of bisector/segment
linking the two points:
Circumcenter=half-point