Motion field

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Motion Field in computer vision refers to the 2-D projection of velocities of the image points, induced by the relative motion between camera and scene. Motion field is not directly measurable from an image. Motion field is different than optical flow which is a vector field subject to Image Brightness Constancy Equation. The motion field $\mathbf{v}$ is defined as:

$\mathbf{v} = f\frac{Z\mathbf{V} - V_z\mathbf{P}}{Z^2}$

where

$\mathbf{V}=-\mathbf{T}-\mathbf{\omega}\times\mathbf{P}$ .

$\mathbf{P}$ is a point in the scene where Z is the distance to that scene point. $\mathbf{V}$ is the relative motion between the camera and the scene, $\mathbf{T}$ is the translational component of the motion, and $\mathbf{\omega}$ is the angular velocity of the motion.