Introduction
A simple camera model implies that each point in 3D space is projected to a 2D image point according to some mapping functions :
Assuming that the scene depicted by the camera is dynamic; it consists of objects moving relative each other, objects which deform, and possibly also the camera is moving relative to the scene, a fixed point in 3D space is mapped to varying points in the image. Differentiating the previous expression with respect to time gives
Here
is the motion field and the vector u is dependent both on the image position as well as on the time t. Similarly,
is the motion of the corresponding 3D point and its relation to the motion field is given by
where is the image position dependent matrix
This relation implies that the motion field, at a specific image point, is invariant to 3D motions which lies in the null space of . For example, in the case of a pinhole camera all 3D motion components which are directed to or from the camera focal point cannot be detected in the motion field.
Read more about this topic: Motion Field
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