Page 149 - Video Coding for Mobile Communications Efficiency, Complexity, and Resilience

126 Chapter 5. Warping-Based Motion Estimation Techniques

This synthesis process can be formulated as follows:

ˆ
f(x; y)= f r (u; v); (5.1)
c
where (x; y) are the spatial coordinates in the current frame (or its prediction)
and (u; v) are the spatial coordinates in the reference frame. This equation
indicates that the MC process applies a geometric transformation that maps
one coordinate system onto another. This is de(ned by means of the spatial
transformation functions g x and g y :
u = g x (x; y);
(5.2)
v = g y (x; y):
This spatial transformation is also referred to as texture mapping or image
warping [107].
As already discussed, the BMA method relies on a uniform translational
motion model. Thus, the transformation functions of this method are given
by

u = g x (x; y)= x + a 1 = x + d x ;
(5.3)
v = g y (x; y)= y + a 2 = y + d y :

In practice, however, a block can contain multiple moving objects, and the
motion is usually more complex and can contain translation, rotation, shear,
expansion, and other deformation components. In such cases, the simple uni-
form translational model will fail, and this will usually appear as artefacts, e.g.,
blockiness, in the motion-compensated prediction. Higher-order motion mod-
els can be used to overcome such problems. Examples of such models are
the a ne, bilinear, and perspective spatial transformations given by Equations
(5.4), (5.5), and (5.6), respectively:

A ne:

u = g x (x; y)= a 1 x + a 2 y + a 3 ;
(5.4)
v = g y (x; y)= a 4 x + a 5 y + a 6 :

Bilinear:
u = g x (x; y)= a 1 xy + a 2 x + a 3 y + a 4 ;
(5.5)
v = g y (x; y)= a 5 xy + a 6 x + a 7 y + a 8 :