Light Field Parametrization
A 4D light field can be thought of as a collection of pinhole views, where the view points all lie in a common focal plane $\Pi$, and the views are projected onto a common image plane $\Omega$. We parametrize $\Pi$ with coordinates $(s,t)$, and $\Omega$ with coordinates $( x,y )$.
Cuts through a 4D light field exhibits an interesting structure, which is related to the epipolar plane geometry. One can observe this by fixing a vertical camera coordinate $t^*$ and a vertical image plane coordinate $y^*$.
The resulting cut in the \((x,s)\) plane is called an epipolar plane image.
Epipolar Plane Images (EPIs)
Each camera location \( (s^*,t^*) \) in the image plane \( \Pi \) yields a different pinhole view of the scene. By fixing a horizontal line of constant \( y^* \) in the image plane and a constant camera coordinate \( t^* \) as above, one obtains an epipolar plane image (EPI) in \((x,s)\) coordinates. A scene point \( P \) is projected onto a line in the EPI due to a linear correspondence between its \(s\)- and projected \(x\)-coordinate.
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| Light field geometry | Pinhole view at \( (s^*,t^*) \) and epipolar plane image \( S_{y^*,t^*}\) |
The slope of the projected line in an EPI is inversely proportional to the depth of the corresponding scene point. We exploit this property in our work on consistent depth reconstruction from 4D light fields.