Shape analysis is the automatic analysis of geometric shapes, for example using a computer to detect similarly shaped objects in a database or parts that fit together. For a computer to automatically analyze and process geometric shapes, the objects have to be represented in a digital form. Most commonly a boundary representation is used to describe the object with its boundary. However, other volume based representations or point based representations can be used to represent shape. Once the objects are given, either by modeling, by scanning or by extracting shape from 2D or 3D images, they have to be simplified before a comparison can be achieved. The simplified representation is often called a shape descriptor. These simplified representations try to carry most of the important information, while being easier to handle, to store and to compare than the shapes directly. A complete shape descriptor is a representation that can be used to completely reconstruct the original object.
Application fields
Shape analysis is used in many application fields:
archeology for example, to find similar objects or missing parts
architecture for example, to identify objects that spatially fit into a specific space
Shape descriptors can be classified by their invariance with respect to the transformations allowed in the associated shape definition. Many descriptors are invariant with respect to congruency, meaning that congruent shapes will have the same descriptor. Another class of shape descriptors is invariant with respect to isometry. These descriptors do not change with different isometric embeddings of the shape. Their advantage is that they can be applied nicely to deformable objects as these deformations do not involve much stretching but are in fact near-isometric. Such descriptors are commonly based on geodesic distances measures along the surface of an object or on other isometry invariant characteristics such as the Laplace–Beltramispectrum. There are other shape descriptors, such as graph-based descriptors like the medial axis or the Reeb graph that capture geometric and/or topological information and simplify the shape representation but can not be as easily compared as descriptors that represent shape as a vector of numbers. From this discussion it becomes clear, that different shape descriptors target different aspects of shape and can be used for a specific application. Therefore, depending on the application, it is necessary to analyze how well a descriptor captures the features of interest.
