Reeb Graphs - Mathematical Tools for Shape Analysis and Description - page 73

Figure 9.2: From left to right, 3D description via Reeb graph extraction, computation of histograms
of spectral features, feature selection [ 85 ].

scriptor could be used to code the model subparts, this descriptor satisfies the requirements of
being rotation and scale invariant, computationally efficient, synthetic and able to store the dis-
tribution of each sub-part. Nodes and edges are uniformly indexed using an array, whose entries
correspond on the spherical harmonic values of the related sub-part.
Figure 9.3 shows a set of contours and the Reeb graph of a tea-pot model with the cor-
responding shape parts. In case of multiple connection between the nodes v 1 and v 2 , each edge
stores the geometric information related to a single portion of the surface.

Figure 9.3: Characterization, ERG and model parts associated with graph nodes and edges.

, most
of them derived from graph matching techniques [ 201 ]. e approach followed in [ 12 ] adopts a
matching techniques based on kernels [ 109 , 119 , 206 , 207 ].
e definition of the ERG is flexible with respect to the choice of the function f : this prop-
erty makes the ERG adaptable to the characteristics of the specific domain where the similarity
needs to be evaluated. erefore, given a 3D model database composed of N models, a NF
graph table T is created (being F the number of real functions). e element T.i;j/ is the ERG

Several methods are available to measure the similarity between graphs G and G

0