Shows a decomposition of the Jacobian matrix for different self-motions.

This matrix Jflow is decomposed into divergence, curl, Type I shear, and Type II shear using the function gflow considering only a translation (vx, vy, vz) (second row), only a rotation (ωx, ωy, ωz) (third row), only a fixating rotation (fourth row), or a translational motion toward a plane with the normal (nx, ny, nz) and distance d (fifth row). Note, and are the differential displacements on the image plane or pixel velocities. Rotations are independent of the depth and its partial derivatives.
1The roll rotation ωz is independent of the surface. Furthermore, this roll rotation appears only and exclusively in the curl component.
2The divergence 2•vz/Z is present, independent of the spatial derivatives of the depth Z and this component only appears for the divergence.