Formation et Analyse dImages Session 3

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Formation et Analyse dImagesSession 3

• Daniela Hall
• 3 October 2005

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Course Overview

• Session 1 (19/09/05)
• Overview
• Human vision
• Homogenous coordinates
• Camera models
• Session 2 (26/09/05)
• Tensor notation
• Image transformations
• Homography computation
• Session 3 (3/10/05)
• Camera calibration
• Reflection models
• Color spaces
• Session 4 (10/10/05)
• Pixel based image analysis
• 17/10/05 course is replaced by Modelisation
  surfacique

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Course overview

• Session 5 6 (24/10/05) 945 1245
• Kalman filter
• Tracking of regions, pixels, and lines
• Session 7 (7/11/05)
• Gaussian filter operators
• Session 8 (14/11/05)
• Scale Space
• Session 9 (21/11/05)
• Contrast description
• Hough transform
• Session 10 (5/12/05)
• Stereo vision
• Session 11 (12/12/05)
• Epipolar geometry
• Session 12 (16/01/06) exercises and questions

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Session Overview

• Camera calibration
• Light
• Reflection models
• Human color perception
• Color spaces

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Bi-linear interpolation
The bilinear approach computes the weighted
average of the four neighboring pixels. The
pixels are weighted according to the area.
D
C
A
B
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Camera calibration

• Assuming that the camera performs a exact
  perspective projection, the image formation
  process can be expressed as a projective mapping
  from R3 to R2.
• PIMIS PS
• Camera calibration process of estimating MIS
  from a set of point correspondences RS PI .
• Advantage intrinsic and extrinsic camera
  parameters don't need to be known. They are
  estimated automatically.

Ref CVonline, LOCAL_COPIES/MOHR_TRIGGS/node16.htm
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Calibration

• Construct a calibration object whose 3D position
  is known.
• Measure image coordinates
• Determine correspondences between 3D point RSk
  and image point PIk.
• We have 11 DoF. We need at least 5 ½
  correspondences.

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Calibration

• For each correspondence scene point RSk and image
  point PIk
• which gives following equations for k1, ..., 6
• from wich MIS can be computed

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Calibration using many points

• For k5 ½ M has one solution.
• Solution depends on precise measurements of 3D
  and 2D points.
• If you use another 5 ½ points you will get a
  different solution.
• A more stable solution is found by using large
  number of points and do optimisation.

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Calibration using many points

• For each point correspondence we know (i,j) and
  R(x,y,z,1)T.
• We want to know MIS. Solve equation with your
  favorite algorithm (least squares,
  levenberg-marquart, svd,...)

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Estimation of MIS

• When intrinsic (Ci, Cj, Di, Dj, F) and extrinsic
  camera (3d camera position and orientation)
  parameters are known, compute MIS directly
• If one parameter is not precisely known or you
  wish a stable estimation of MIS, do calibration
  with a large number of points.

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Session Overview

• Camera calibration
• Light
• Reflection models
• Human color perception
• Color spaces

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Light

• N surface normal
• i angle between incoming light and normal
• e angle between normal and camera
• g angle between light and camera

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Spectrum

• Light source is characterised by its spectrum.
• The spectrum consists of a particular quantity of
  photons per frequency.
• The frequency is described by its wavelength
• The visible spectrum is 380nm to 720nm
• Cameras can see a larger spectrum depending on
  their CCD chip

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Albedo

• Albedo is the fraction of light that is reflected
  by a body or surface.
• Reflectance function

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Reflectance functions

• Specular reflection
• example mirror
• Lambertian reflection
• diffuse reflection, example paper, snow

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Specular reflection
light
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camera
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Lambertian reflection
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Di-chromatic reflectance model

• the reflected light R is the sum of the light
  reflected at the surface Rs and the light
  reflected from the material body RL
• Rs has the same spectrum as the light source
• The spectrum of Rl is  filtered  by the
  material (photons are absorbed, this changes the
  emitted light)
• Luminance depends on surface orientation
• Spectrum of chrominance is composed of light
  source spectrum and absorption of surface
  material.

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Session Overview

• Camera calibration
• Light
• Reflection models
• Human color perception
• Color spaces

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Color perception

• The retina is composed of rods and cones.
• Rods - provide "scotopic" or low intensity
  vision.
• Provide our night vision ability for very low
  illumination,
• Are a thousand times more sensitive to light than
  cones,
• Are much slower to respond to light than cones,
• Are distributed primarily in the periphery of the
  visual field.

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Color perception

• Cones - provide "photopic" or high acuity vision.
  
• Provide our day vision,
• Produce high resolution images,
• Determine overall brightness or darkness of
  images,
• Provide our color vision, by means of three types
  of cones
• "L" or red, long wavelength sensitive,
• "M" or green, medium wavelength sensitive,
• "S" or blue, short wavelength sensitive.
• Cones enable our day vision and color vision.
  Rods take over in low illumination. However, rods
  cannot detect color which is why at night we see
  in shades of gray.
• source http//www.hf.faa.gov/Webtraining/VisualDi
  splays/

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Color perception

• Rod Sensitivity- Peak at 498 nm.
• Cone Sensitivity- Red or "L" cones peak at 564
  nm. - Green or "M" cones peak at 533 nm.  - Blue
  or "S" cones peak at 437 nm.
• This diagram shows the wavelength sensitivities
  of the different cones and the rods. Note the
  overlap in sensitivity between the green and red
  cones.

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Camera sensitivity

• observed light intensity depends on
• source spectrum S(?)
• reflectance of the observed point (i,j) P(i,j,?)
• receptive spectrum of the camera c(?)
• p0 is the gain

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Classical RGB camera

• The filters follow a convention of the
  International Illumination Commission.
• They are functions of ? r(?), g(?), b(?)
• They are close to the sensitivity of the human
  color vision system.

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Color pixels
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Color bands (channels)

• It is not possible to perceive the spectrum
  directly.
• Color is a projection of the spectrum to the
  spectrum of the sensors.
• Humans (and cameras) probe the spectrum at 3
  positions.

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Session Overview

• Camera calibration
• Light
• Reflection models
• Human color perception
• Color spaces

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Color spaces

• RGB color space
• CMY color space
• YIQ color space
• HLS color space

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RGB color space

• A CCD camera provides RGB images
• The luminance axis is rgb (diagonal)
• Each axis has 256 (8 bit) different values
• RGB colors 256316777216

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Hering color space

• Opponent color space
• Is obtained from RGB space by transformation.
• Luminance, C1 (red-green), C2 (redgreen-blue)

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CMY color space

• Cyan, magenta, yellow
• CMYK CMY black color channel

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YIQ color space

• This is an approximation of
• Y luminance,
• I red cyan,
• Q magenta - green
• Used US TVs (NTSC coding). Black and white TVs
  display only Y channel.

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HLS space

• Hue, luminance, saturation space.
• LRGB
• S1-3min(R,G,B)/L

L
T
S
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Influence of color spaces for image analysis

• According to dichromatic reflectange model
• Luminance depends on surface orientation
• Spectrum of chrominance is composed of light
  source spectrum and absorption of surface
  material.
• In HLS space, luminance is separated from
  chrominance. For object recognition robust to
  changes in light source direction, use only
  chrominance plane for identification.
• In RGB space, changes in luminance influence all
  3 channels. The above technique can not be used
  directly (do transformation to Hering space
  first).