Image Rectification

Definition

Rectification warps the two camera image planes so that they become parallel: both images are reprojected onto a common plane parallel to the baseline (with one homography per image).

After rectification:

• the epipolar lines are horizontal and the epipoles are at infinity
• corresponding points have the same $y$ coordinate, so matching is a 1D search along a scanline
• the essential matrix becomes trivial:

Formula

$$R=I,t=(T,0,0),E=[t_{\times }]=\left[\begin{array}{ccc}0& 0& 0\\ 0& 0& -T\\ 0& T& 0\end{array}\right]\Rightarrow p^{T}E{p}^{\prime }=T(v^{\prime }-v)=0$$

Trap

Rectification is a preprocessing step before stereo matching. It warps the images, it does not move the cameras and does not compute depth.

Appears in

• Lecture 4, Image Rectification
• Lecture 4, Other applications: view morphing
• Lecture 2.1, Simple stereo system: two cameras with aligned axes

Related concepts

• Epipolar Geometry
• Disparity
• Stereo Matching