Page 118 - Video Coding for Mobile Communications Efficiency, Complexity, and Resilience

Section 4.2. Motion Estimation 95

intensity rotates about its center, it has a rotational projected motion but zero
apparent motion. Another example is a still object with change of illumination
between frames. Although the object has zero projected motion, the change in
illumination will result in some apparent motion. Hereafter, unless otherwise
stated, the term motion will be used to refer to apparent motion rather than
true projected motion.
Two-dimensional motion can be represented in terms of either 2-D displace-
T
ment vectors, d =[d x ;d y ] , or 2-D instantaneous velocity vectors, v =[v x ;v y ] T
dx dy T
=[ ; ] . A set of such vectors representing motion in a frame is called
dt dt
the motion eld of the frame. The two representations are called the dis-
placement eld and the velocity eld in the case of projected motion, or the
correspondence eld and the optical "ow eld in the case of apparent motion.
However, in the video coding literature, it has become a convention to ignore
this distinction and to use the terms displacement eld and velocity eld to
refer to the apparent correspondence eld and optical *ow eld, respectively.
Hereafter, this convention will be adopted. Furthermore, this book uses the
displacement eld representation rather than the velocity eld representation.
Thus, the term motion eld will always refer to the apparent correspondence
eld and the term motion vector will always refer to a displacement vector
within this eld.

4.2.2 Problem Formulation
Two-dimensional apparent motion can be attributed to three main causes. The
rst cause is global, or camera, motion. Even when there is no object motion
in the frame, the motion of the camera induces a global motion. The second
cause is local motion. This is the intrinsic motion of the objects in the scene.
The third cause is illumination changes. Even when there is no object motion
in the scene, changes in lighting conditions in*uence apparent motion.
All techniques considered in this chapter make no distinction between global
and local motions, and they do not take into account illumination changes.
Thus, they assume that global motion is taken into account through local
motion and that the impact of illumination changes can be ignored. It should be
pointed out, however, that some other techniques use a two-stage global=local
motion estimation, e.g., Ref. 77, or estimate illumination changes, e.g., Ref. 78.
The 2-D apparent motion estimation problem can be formulated as a for-
ward or a backward estimation problem depending on the temporal location
of the reference frame with respect to the current frame.
In backward motion estimation, a pel s =[x; y] T in the current frame at
time t is related to a pel in a previous reference frame at time t − @t by

f t (s)= f t−@t (s − d(s)): (4.1)