Digital Representations of the Real World

244 Digital Representations of the Real World

Figure 16.3: A 3D shape histogram of 5 shells, 10 bins for θ, and 20 bins

for φ together with the space partitions on the 5th shell is illustrated.

The volumetric shape histogram H(M ) partitions the space which contains

a 3D object into disjoint cells and counts the number of occupied voxels

falling in each bin to construct a histogram as a signature for this 3D object.

The space is represented in a spherical coordinate system (R, θ, φ) around

the center of mass. An example of a 3D shape histogram is shown in Figure

16.3.

A frame-to-frame static similarity matrix C = [c

r,s

]

N×N

, where N de-

notes the total ...