  The pose of a rigid object is usually regarded as a rigid transformation,
described by a translation and a rotation. However, equating the pose space
with the space of rigid transformations is in general abusive, as it does not
account for objects with proper symmetries -- which are common among man-made
objects.In this article, we define pose as a distinguishable static state of an
object, and equate a pose with a set of rigid transformations. Based solely on
geometric considerations, we propose a frame-invariant metric on the space of
possible poses, valid for any physical rigid object, and requiring no arbitrary
tuning. This distance can be evaluated efficiently using a representation of
poses within an Euclidean space of at most 12 dimensions depending on the
object's symmetries. This makes it possible to efficiently perform neighborhood
queries such as radius searches or k-nearest neighbor searches within a large
set of poses using off-the-shelf methods. Pose averaging considering this
metric can similarly be performed easily, using a projection function from the
Euclidean space onto the pose space. The practical value of those theoretical
developments is illustrated with an application of pose estimation of instances
of a 3D rigid object given an input depth map, via a Mean Shift procedure.
