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Section 5.2. Warping-Based Methods: A Review 129

115, 123]. Although adaptive meshes can improve prediction quality, they have
the disadvantages of increased computational complexity (for the generation
and adaptation processes) and increased overhead (to describe the structure of
the mesh). The structure overhead can be removed by applying the adaptation
process based on previous frames that are available at the decoder.

5.2.3 Spatial Transformation

As shown by Seferidis and Ghanbari [119], the perspective transform achieves
the best prediction-quality performance. However, the high computational com-
plexity of this transformation limits its use in practice. The a ne transforma-
tion is the least computationally complex, but it has the fewest degrees of
freedom. The performance of the bilinear transformation is very close to that
of the perspective transformation, with the advantage of reduced computational
complexity. However, a study by Nakaya and Harashima [114] showed that the
a ne and bilinear transformations have almost the same performance when the
patch shape is optimized (equilateral triangles and squares, respectively). In
fact, the same study showed that the performance of the a ne transformation
can be superior as the number of nodes decreases.

5.2.4 Continuous Versus Discontinuous Methods

Adjacent patches in the current frame have common vertices between them.
There are two main methods for estimating the motion of such common ver-
tices. If the motion of common vertices is estimated independent from each
other (i.e., common vertices are assigned di>erent motion vectors), then this
will result in a discontinuous motion (eld with discontinuities along the bound-
aries of the patches. This is known as the discontinuous method. The motion
(eld in this case has similarities with that produced by the BMA. If, how-
ever, a restriction is applied such that common vertices have the same motion
vector, then this will result in a continuous motion (eld and the method
is known as the continuous method. The two methods are illustrated in
Figure 5.2.
As pointed out by Ghanbari et al. [115], the discontinuous method is more
Dexible and can compensate for more general complex motion. However, as
pointed out by Nakaya and Harashima [114], since discontinuities are allowed
along the boundaries of patches, this method can su>er from blocking artefacts.
Another disadvantage of the discontinuous method is that it generates more
motion overhead (four motion vectors per patch) compared to the continuous
method (about one motion vector per patch).