(slides 7) visual computing: geometry, graphics, and vision
Post on 05-Dec-2014
121 Views
Preview:
DESCRIPTION
TRANSCRIPT
© 2011 Frank Nielsen
INF555
Fundamentals of 3D
Lecture 7: ColorsRandomized algorithms
RANSAC/MINIBALL
Frank Nielsennielsen@lix.polytechnique.fr
2nd November 2011
© 2011 Frank Nielsen
Supersampling: Averaging
Uniform versus non-uniform sampling(raytracing software: Povray, Blender)
The essence of pixels: Integration !
© 2011 Frank Nielsen
Color and perceptionCommission Internationale del’ ´ Eclairage in French, CIE, http:// www.cie.co.at/
© 2011 Frank Nielsen
A candela unit is defined as the luminous intensity ofa 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
© 2011 Frank Nielsen
Cone responses in human eyes
Cones (color) and rods (B&W) in human eyes
© 2011 Frank Nielsen
Additive and subtractive color modes
Display/printing industries
Color checking in printing industry
© 2011 Frank Nielsen
Choosing colors: Colors pick-up
© 2011 Frank Nielsen
Pseudo-coloring
Volume rendering and transfer function
© 2011 Frank Nielsen
Color spaces
Normalizing coefficient
converts the spectrum absorption of light L to XYZ colors
© 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.
© 2011 Frank Nielsen
Color cube
© 2011 Frank Nielsen
HLS/HSV color spaces
(hue, lightness, saturation (hue, saturation, value)
© 2011 Frank Nielsen
© 2011 Frank Nielsen
CMYK color space (for printing)
© 2011 Frank Nielsen
CIE L*a*b
Perceptual difference between two colors:
CIE L*a*b (where Euclidean distance make sense)
© 2011 Frank Nielsen
Many standards....
© 2011 Frank Nielsen
Gamma color correction:
Bayer tile
© 2011 Frank Nielsen
Half-toning and dithering
t=127 Random t
© 2011 Frank Nielsen
Dithering: Trade space for grey level perception
© 2011 Frank Nielsen
Error-diffusion process: Floyd-Steinberg
© 2011 Frank Nielsen
Low dynamic range images (LDRs) versusHigh dynamic range images (HDRs)
© 2011 Frank Nielsen
Low dynamic range imageHigh dynamic range imageTone mapping
© 2011 Frank Nielsen
Tone mapping
© 2011 Frank Nielsen
Quicksort:
O(n log n) expectedO(n^2) worst-caseO(n) best case
© 2011 Frank Nielsen
Randomization: A Powerful principle
Analysis:
© 2011 Frank Nielsen
RANSAC on Harris-Stephens points.Epipolar points intersect on their epipoles
RANSAC: Random Sample Consensus
© 2011 Frank Nielsen
© 2011 Frank Nielsen
Probability of failure of picking two inliers
Macthing points: Inliers/outliers
© 2011 Frank Nielsen
RANSAC: Bounding failure probability
Probability of failure after one round
Probability of failure after k independent rounds
© 2011 Frank Nielsen
© 2011 Frank Nielsen
Estimating homographies with RANSAC
© 2011 Frank Nielsen
Adaptive RANSAC: Guessing the ratio of inliers
© 2011 Frank Nielsen
Demo of autostich:
© 2011 Frank Nielsen
Bounding sphere hierarchy
© 2011 Frank Nielsen
MINIBALL: Smallest enclosing ballUNIQUE
http://www.inf.ethz.ch/personal/gaertner/miniball.html
© 2011 Frank Nielsen
LP-type problem in optimization
© 2011 Frank Nielsen
MINIBALL: Solving for basis of 2 and 3 points
Intersection of bisectors(use cross-product on homogeneous coordinates)
Intersection of bisector/segmentlinking the two points:Circumcenter=half-point
top related