ROBOT VISION
Sponsored Links
This presentation is the property of its rightful owner.
1 / 33

Content PowerPoint PPT Presentation


  • 157 Views
  • Uploaded on
  • Presentation posted in: General

ROBOT VISION Lesson 4: Camera Models and Calibration Matthias Rüther Slides partial courtesy of Marc Pollefeys Department of Computer Science University of North Carolina, Chapel Hill. Content. Camera Models Pinhole Camera CCD Camera Finite Projective Camera Affine Camera Pushbroom Camera

Download Presentation

Content

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


ROBOT VISIONLesson 4: Camera Models and CalibrationMatthias RütherSlides partial courtesy of Marc Pollefeys Department of Computer ScienceUniversity of North Carolina, Chapel Hill


Content

  • Camera Models

    • Pinhole Camera

    • CCD Camera

    • Finite Projective Camera

    • Affine Camera

    • Pushbroom Camera

  • Calibration

    • Inner Orientation

    • Nonlinear Distortion

    • Calibration using Planar Targets

    • Calibration using a 3D Target

The Cyclops, 1914 by Odilon Redon


Basic Pinhole Camera Model


Basic Pinhole Camera Model


Basic Pinhole Camera Model


Principal Point Offset

principal point


Principal Point Offset

calibration matrix


Camera Rotation and Translation


CCD Camera


non-singular

Finite Projective Camera

11 dof (5+3+3)

decompose P in K,R,C?

{finite cameras}={P3x4 | det M≠0}

If rank P=3, but rank M<3, then cam at infinity


(pseudo-inverse)

Action of Projective Cameras on Points

Forward projection (3D -> 2D)

D…direction

Back-projection (2D -> 3D)


Projective Depth of Points

(PC=0)

(dot product)

If ,

then m3 unit vector in positive direction


arctan(1/s)

g

1

When is skew non-zero?

for CCD/CMOS, always s=0

Image from image, s≠0 possible

(non coinciding principal axis)

resulting camera:


Moving the Camera Center to Infinity

Camera center at infinity

Affine and non-affine cameras

Definition: affine camera has P3T=(0,0,0,1)


Affine Cameras


Parallel Projection: Summary

canonical representation

affine calibration matrix

principal point is not defined


A Hierarchy of Affine Cameras

Orthographic projection

(5dof)

Scaled orthographic projection

(6dof)


A Hierarchy of Affine Cameras

Weak perspective projection

(7dof)


A Hierarchy of Affine Cameras

Affine camera

(8dof)

  • Affine camera=camera with principal plane coinciding with P∞

  • Affine camera maps parallel lines to parallel lines

  • No center of projection, but direction of projection PAD=0

  • (point on P∞)


Pushbroom Cameras

(11dof)

Straight lines are not mapped to straight lines!

(otherwise it would be a projective camera)


Line Cameras

(5dof)

Null-space PC=0 yields camera center

Also decomposition


Camera calibration


Problem Statement


Basic Equations


minimize subject to constraint

Basic Equations

minimal solution

P has 11 dof, 2 independent eq./points

  • 5½ correspondences needed (say 6)

Over-determined solution

n  6 points


Geometric Error


Gold Standard algorithm

  • Objective

  • Given n≥6 2D to 2D point correspondences {Xi↔xi’}, determine the Maximum Likelyhood Estimation of P

  • Algorithm

  • Linear solution:

    • Normalization:

    • DLT:

  • Minimization of geometric error: using the linear estimate as a starting point minimize the geometric error:

  • Denormalization:

~

~

~


Example


Exterior Orientation

Calibrated camera, position and orientation unkown

 Pose estimation

6 dof  3 points minimal (4 solutions in general)


Nonlinear Distortion

  • Radial Component

short and long focal length


Nonlinear Distortion

  • Radial Component


Correction of radial Distortion

Correction of radial distortion

Choice of the distortion function and center

  • Computing the parameters of the distortion function

  • Minimize with additional unknowns

  • Straighten lines


Nonlinear Distortion

  • Tangential Component

Distortion function:


  • Login