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128 Chapter 5. Warping-Based Motion Estimation Techniques

u x
v y

A' B' A B
grid (nodal)
points
C' D' C D

reference frame current frame
A' A B
B'

C' D' warping C D
(spatial transformation)
Figure 5.1: Warping-based motion estimation and compensation

5.2.1 Shape of Patches
The most widely used shapes are triangles and quadrilaterals. Nakaya and
Harashima [114] showed that equilateral triangles are optimal, in the prediction-
quality sense, when the a ne transformation is used, whereas squares are
optimal when the bilinear transformation is used. Square patches are some-
times preferred because they are compatible with current block-based video
coding methods and standards. Triangular patches are more compatible with
model-based coding methods, where wireframe models are usually de(ned in
terms of triangles.

5.2.2 Type of Mesh

The mesh structure can be (xed or adaptive. A 'xed mesh is one that is
built according to a predetermined pattern, e.g., a regular mesh with square
patches. An adaptive mesh, on the other hand, is one that is adaptively built
according to frame contents and motion. Adaptive meshes can be content-
based or motion-based. In content-based adaptive meshes, nodes are placed
to (t important features like contours and edges [111, 121]. In motion-based
adaptive meshes, more nodes are placed in moving areas. This is usually
achieved using a hierarchical (usually, quad-tree) mesh structure [109, 120,