image rectification for stereo vision n.
Skip this Video
Loading SlideShow in 5 Seconds..
Image Rectification for Stereo Vision PowerPoint Presentation
Download Presentation
Image Rectification for Stereo Vision

Loading in 2 Seconds...

play fullscreen
1 / 16

Image Rectification for Stereo Vision - PowerPoint PPT Presentation

  • Uploaded on

Image Rectification for Stereo Vision. Charles Loop Zhengyou Zhang Microsoft Research. Problem Statement. Compute a pair of 2D projective transforms ( homographies ). rectification. Original images. Rectified images. Motivations. To simplify stereo matching:

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Image Rectification for Stereo Vision' - royal

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
image rectification for stereo vision

Image Rectification for Stereo Vision

Charles Loop

Zhengyou Zhang

Microsoft Research

problem statement
Problem Statement
  • Compute a pair of 2D projective transforms (homographies)


Original images

Rectified images

  • To simplify stereo matching:

Instead of comparing pixels on skew lines, we now only compare pixels on the same scan lines.

  • Graphics applications: view morphing
  • Problem:

Rectifying homographies are not unique

  • Goal: to develop a technique based on

geometrically well-defined criteria minimizing image distortion due to rectification

epipolar geometry
Epipolar Geometry






Epipole at

Fundamental matrix

  • Epipoles anywhere
  • Fundamental matrix

F: a 3x3 rank-2 matrix

stereo image rectification
Stereo Image Rectification
  • Compute H and H’ such that
  • Compute rectified image points:
  • Problem:

H and H’ are not unique.

properties of h and h i
Properties of H and H’ (I)
  • Consider each row of H and H’ as a line:
  • Recall: both e and e’ are sent to [1 0 0]T
  • Observations (I):
  • v and w must go through the epipole e
  • v’ and w’ must go through the epipole e’
  • u and u’ are irrelevant to rectification
properties of h and h ii
Properties of H and H’ (II)
  • Observation (II):

Lines v and v’, and lines w and w’ must be corresponding epipolar lines.

  • Observation (III):

Lines w and w’ define the rectifying plane.

decomposition of h
Decomposition of H
  • Special projective transform:
  • Similarity transform:
  • Shearing transform:
special projective transform i
Special Projective Transform (I)
  • Sends the epipole to infinity
  • epipolar lines become parallel
  • Captures all image distortion due to projective transformation
  • Subgoal: Make Hp as affine as possible.
special projective transform ii
Special Projective Transform (II)

How to do it?

  • Let original image point be
  • the transformed point will be
  • Observation:

If all weights are equal, then there is no distortion.

  • Key idea:

minimize the variation of wi over all pixels

with weight

similarity transform
Similarity Transform
  • Rotate and translate images such that the epipolar lines are horizontally aligned.
  • Images are now rectified.
shearing transform
Shearing Transform
  • Free to scale and translate in the horizontal direction.
  • Subgoal:

Preserve original image resolution as close as possible.

  • Original image pair
intermediate result
Intermediate result
  • After special projective transform:
intermediate result1
Intermediate result
  • After similarity transform:
final result
Final result
  • After shearing transform