A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing

136 Dimensionality Reduction

in Figure 9.2. To appreciate the problem’s difficulty, we first need

to understand how motion sequences are represented.

Figure 9.3: A series of skeletal poses in a motion sequence.

An animation or motion sequence typically consists of a series

of skeletal poses, as illustrated in Figure 9.3. The skeleton is de-

fined by a number of bones connected by joints and the poses are

parameterized by spatial or physical attributes including positions,

angles, and velocities associated with the bones and joints. Rich

and realistic motions necessitate a large number of such attributes.

Thus, the animation traces out a high-dimensional