Beyond Geometry and Topology - Mathematical Tools for Shape Analysis and Description - page 89

C H A P T E R 12

Beyond Geometry and
Topology

roughout this topic we have focused on mathematical tools for shape analysis, where the term
shape mainly referred to geometrical and topological properties of objects. Nonetheless, there is
much more to deal with the problem of 3D shape analysis.
A first issue concerns appearance properties, coded by texture . Nowadays 3D textured mod-
els can be easily obtained, as most sensors are able to acquire both 3D shape and texture with
reasonable accuracy, and multiple-view stereo techniques enable the recovery of both geomet-
ric and colorimetric information directly from images. Examples of textured 3D models can be
seen in Figure 12.1 . Texture and colorimetric features contain rich information about the visual
appearance of real objects. For example, in 3D cultural heritage the visual appearance of objects
(materials, decorations, etc.) conveys essential historical and artistic information. It enables the
categorization of objects according to surface decorations, or to attribute the fabric of furnishings
to a given producer, or even to match degradation phenomena on element surfaces (e.g., for con-
servation and restoration purposes). ough most of the shape analysis techniques developed so
far did not take texture into account, the attention towards appearance properties has considerably
grown over the last few years, and the first techniques which analyze both shape and appearance
properties have been proposed [ 20 , 121 , 129 , 160 , 172 , 199 , 213 ].

Figure 12.1: Models from the “Retrieval of textured 3D models” track of the SHREC'13 benchmark
[ 42 ].

Besides geometry and texture, semantic aspects are of fundamental importance to 3D shape
analysis. Here semantics refers to the meaning, or functionality , of an object in a given context. A
variety of recent 3D shape analysis techniques are meant to derive semantic (high-level) informa-
tion from low-level properties. A first example is semantic annotation , which is the automatic or
semi-automatic labeling of objects (or parts of objects) with a tag describing their content [ 7 , 122 ].
en, attribute transfer techniques study how to automatically transfer labels from a single ob-