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SHAPE AND SHAPE ANALYSIS
Modeling shapes is part of both cognitive and creative processes, and from the outset, models of
physical shapes have satisfied the desire to see in advance the result of a project. For over a century
philosophers and psychologists have tried to understand how the human visual perception system
recognizes objects from images as picked up from the human eye. Sensory input and perceived
shape geometry are two of the key elements, but not the only, which influence humans' under-
standing of objects. Prior knowledge about an object's place and functional context, perceived
similarity to other presented objects, or current task demands, can equally contribute to an object
description.
Shape analysis may be defined as a set of theories, methods and algorithms that concur to
the formalization and computation of properties useful to characterize the geometrical appearance
of objects. Initiated by computer vision and pattern recognition, the focus of shape analysis was
on the identification of objects in images. A large number of methods was developed, relying on
experimentation on how humans' representations of objects are built bottom-up from low-level
2D image features. Object recognition and reconstruction are particularly challenging in vision
because 2D images contain only partial information about objects due to occlusions and lighting
conditions.
Over the last decades, advances in acquisition and modeling techniques made 3D objects
as common as images and videos. With the advancements of geometric modeling and computer
graphics, shape analysis of 3D digital representations of objects is now maturing to a key discipline
penetrating many applied domains, spanning from entertainment to life sciences, from cultural
heritage to industrial design, from manufacturing to urban planning. Over the years, computer
graphics started addressing the same basic issues targeted by computer vision, from shape recog-
nition to shape segmentation and understanding. Yet, new techniques had to be developed, as 3D
models are different from 2D images: they portrait the complexity of the 3D world, whereas they
do not suffer from the sensory gap. Objects represented by 3D models can be analyzed relying
on a complete digital model of their shape, and therefore it is possible to evaluate them not only
using local low-level features, but also global high-level geometric and topological properties.
In the last years, we observed an explosion of methods for the analysis of 3D shapes and
shape collections, targeting a variety of tasks, such as shape design and synthesis, content-based
retrieval, and automatic classification. is suggests how 3D shape analysis is likely to become
fundamental in the development of future interfaces with the digital worlds. Emerging new tech-
