Page 137 - Video Coding for Mobile Communications Efficiency, Complexity, and Resilience

114 Chapter 4. Basic Motion Estimation Techniques

Orchard et al. [102, 103] used this view to formulate OMC as a linear
estimator of the form

ˆ
f (s)= w n (s) f t−@t (s − d n ); (4.32)
t
d n ∈N(s)
where N(s)= {d n (s)} is the set of motion vectors used to compensate the
pel at location s and w n (s) is the weight given to the prediction provided
by vector d n . Using this formulation, they solve two optimization problems:
overlapped-motion compensation and overlapped-motion estimation. Given the
set of motion vectors N(s) estimated by the encoder, they propose a method
for designing optimal windows, w n (s), to be used at the decoder for motion
compensation. Also, given a xed window that will be used at the decoder,
they propose a method for nding the optimal set of motion vectors at the
encoder. Note that the latter problem is much more complex than the BMA,
since in this case the estimated motion vectors are interdependent. For this
reason, their proposed method is based on an iterative procedure. A number
of methods have been proposed to alleviate this complexity, e.g., Ref. 104.
As a linear estimator of intensities, OMC belongs to a more general set of
motion compensation methods called multihypothesis motion compensation.
Another member in this set is bidirectional motion compensation. The theoret-
ical motivations for such methods were presented by Sullivan in 1993 [105].
Recently, Girod [106] analyzed the rate-distortion e!ciency of such meth-
ods and provided performance bounds and comparisons with single-hypothesis
motion compensation (e.g., the BMA).
Figure 4.9 compares the performance of OMC to that of the BMA when
applied to the FOREMAN sequence. In the case of OMC, the same BMA motion
vectors were used for compensation (i.e., the motion vectors were not opti-
mized for overlapped compensation). Each motion vector was used to copy
a32 × 32 block from the reference frame and center it around the current
16 × 16 block in the current frame. Each copied block was weighted by a
bilinear window function de ned as [103]

1 (z + 1 ) for z =0;:::; 15;
w(x; y)= w x · w y ; where w z = 16 2 (4.33)
w 31−z for z =16;:::; 31:
Border blocks were handled by assuming “phantom” blocks outside the frame
boundary with motion vectors equal to those of the border blocks. Despite the
fact that the estimated vectors, the window shape, and the overlapping weights
were not optimized for overlapped compensation, OMC provided better objec-
tive (Figure 4.9(a)) and subjective (Figures 4.9(b)–4.9(d)) quality compared
to the BMA. In particular, the annoying blocking artefacts have clearly been
reduced.