3D Shape Analysis in a Nutshell - Mathematical Tools for Shape Analysis and Description - page 10

2. 3D SHAPE ANALYSIS IN A NUTSHELL
• Matching (comparison): How can we compute a measure of similarity between 3D mod-
els? e evaluation of shape similarity finds application in several problems, from product
design to computational biology. Usually, shape comparison is carried out by first abstract-
ing 3D objects as shape descriptors (or signatures), then using shape descriptors to perform
similarity assessment. In chapter 7 , algebraic topology helps casting the complex problem
of comparing two shapes as the comparison of combinatorial objects, which turns out to be
computationally efficient and stable to noise, as demonstrated by applications such as the
monitoring of the effects of orthodontics treatments.

• Retrieval: How can we find a given 3D model in a large database? e increasing avail-
ability of powerful modeling software and 3D acquisition devices has led to rapidly growing
repositories of 3D models. For example, the Trimble 3D Warehouse ¹ contains millions of
3D models in many different classes and thus should be a valuable resource for people work-
ing with 3D objects. Yet, the task of exploring such large 3D repositories and retrieving the
models of interest remains an important and challenging problem. One key challenge is
that users may be interested in exploring different types of shape properties. e definition
of shape descriptors coding different attributes, along with proper comparison strategies, is
the first step towards the definition of effective 3D retrieval techniques. In chapter 12 we
will see how the combination of tools from topological persistence and differential geom-
etry yielded to a technique for 3D textured shape retrieval, which is able to analyze both
colorimetric and geometric properties.

• Classification and clustering: How can we assign a 3D model to its proper class? Classi-
fying and clustering 3D shapes is an important issue for many applications. For example, in
3D cultural heritage the shape-based categorization of unknown objects, such as vessels or
coins, helps their attribution to given time periods, to a given society, or to a given author. In
chapter 9 an example of multi-class 3D classification technique is presented, which is based
on the description of 3D objects via spectral features computed on topological skeletons
and augmented by a feature selection technique.

2.2 APPLICATIONS

e entertainment industry has been the driving force behind the explosion of applications and
technological advances in 3D media: highly efficient GPUs are now available at a reasonable price,
and commodity hardware is connected to the internet at high speed. e technological infras-
tructure is now ready to allow the sharing, creation and storage of huge volumes of 3D data over
the web. e creation of 3D models is within reach of everybody and not only of experienced
professionals as it was before, and sources for really heavy amounts of 3D data like scanning,
photogrammetry or procedural/parametric design make it even easier to produce digital shapes.

¹ https://3dwarehouse.sketchup.com/