Relative Orientation

Fundamental Matrix

Used for uncalibrated cameras (intrinsics are unknown). Essential Matrix is used for calibrated cameras.

The fundamental matrix relates corresponding points in stereo images (epipolar geometry).

Resources

• Fundamental and Essential Matrix - 5 Minutes with Cyrill

The matrix $F$ is the fundamental matrix (for uncalibrated cameras): $F=(K^{\prime }{)}^{-T}{R}^{\prime }{S}_b{R}^{\prime \prime {}^T}(K^{\prime \prime }{)}^{-1}$

It allow for expressing the Coplanarity Constraint by $x^{\prime {}^T}F{x}^{\prime \prime }=0$

The fundamental matrix is the matrix that fulfills the equation $x^{\prime {}^T}F{x}^{\prime \prime }=0$ for corresponding points

The fundamental matrix contains the all the available information about the relative orientation of two images from uncalibrated camera.

Related

• Essential Matrix