3D Motion

In computer vision the motion field is an ideal representation of 3D motion as it is projected onto a camera image. Given a simplified camera model, each point in the image is the projection of some point in the 3D scene but the position of the projection of a fixed point in space can vary with time. The motion field can formally be defined as the time derivative of the image position of all image points given that they correspond to fixed 3D points. This means that the motion field can be represented as a function which maps image coordinates to a 2-dimensional vector. The motion field is an ideal description of the projected 3D motion in the sense that it can be formally defined but in practice it is normally only possible to determine an approximation of the motion field from the image data

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 to 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.