  Object data analysis is concerned with statistical methodology for datasets
whose elements reside in an arbitrary, unspecified metric space. In this work
we propose the object shape, a novel measure of shape/symmetry for object data.
The object shape is easy to compute and interpret, owing to its intuitive
interpretation as interpolation between two extreme forms of symmetry. As one
major part of this work, we apply object shape in various metric spaces and
show that it manages to unify several pre-existing, classical forms of
symmetry. We also propose a new visualization tool called the peeling plot,
which allows using the object shape for outlier detection and principal
component analysis of object data.
