3D Skeletons: A State-of-the-Art Report

Andrea Tagliasacchi, Thomas Delame, Michela Spagnuolo, Nina Amenta, Alexandru Telea
2016 Computer graphics forum (Print)  
a) (b) (c) (d) Figure 1: Four alternative definitions of medial skeletons: (a) centers of maximally-inscribed balls; (b) shock graph of the grassfire surface flow; (c) as points with more than one corresponding images on the surface; (d) local axis of reflectional symmetry. Abstract Given a shape, a skeleton is a thin centered structure which jointly describes the topology and the geometry of the shape. Skeletons provide an alternative to classical boundary or volumetric representations, which
more » ... s especially effective for applications where one needs to reason about, and manipulate, the structure of a shape. These skeleton properties make them powerful tools for many types of shape analysis and processing tasks. For a given shape, several skeleton types can be defined, each having its own properties, advantages, and drawbacks. Similarly, a large number of methods exist to compute a given skeleton type, each having its own requirements, advantages, and limitations. While using skeletons for two-dimensional (2D) shapes is a relatively well covered area, developments in the skeletonization of three-dimensional (3D) shapes make these tasks challenging for both researchers and practitioners. This survey presents an overview of 3D shape skeletonization. We start by presenting the definition and properties of various types of 3D skeletons. We propose a taxonomy of 3D skeletons which allows us to further analyze and compare them with respect to their properties. We next overview methods and techniques used to compute all described 3D skeleton types, and discuss their assumptions, advantages, and limitations. Finally, we describe several applications of 3D skeletons, which illustrate their added value for different shape analysis and processing tasks. A. Tagliasacchi, T. Delame, M. Spagnuolo, N. Amenta, A. Telea / 3D Skeletons: A State-of-the-Art Report shape properties. Such tasks are favored by a compact shape representation that encodes the key properties for the tasks at hand in a computationally efficient way. Expressiveness Different shape analysis and processing applications focus on different properties of a shape. Examples are shape topology and symmetry (for shape retrieval) or shape thickness (for metrology applications). Modeling and animation applications need to intuitively support complex forms of interactive shape manipulation. All such applications benefit from using shape representations beyond the classical volumetric and surface ones. Skeletons are one such alternative representation. Informally, skeletons are descriptors which jointly describe the geometry, topology, and symmetry properties of a shape in compact and intuitive ways, providing a mean to capture the 'essence' of a shape. The concept originated with medial skeletons in 2D shape understanding, as a way to reduce the large amount of data carried by a shape down to the key information that can be more readily assimilated [Blu67] . An example of a medial skeleton for a 2D shape is shown in Fig. 2a . The concept was next extended to 3D shapes, yielding a wide family of variations, including surface skeletons [SBTZ02], curve skeletons [CSM07], and centerlines [WLK * 02, AB02].
doi:10.1111/cgf.12865 fatcat:dpyylsn5kffwxkjw4cza3zzcyu