Defining the Pose of any 3D Rigid Object and an Associated Distance
This addresses a foundational issue in computer vision and robotics for handling symmetric objects, but it is incremental as it builds on existing pose representation methods.
The paper tackles the problem of defining pose for symmetric 3D rigid objects by proposing a frame-invariant metric based on geometric considerations, enabling efficient neighborhood queries and pose averaging without arbitrary tuning. This is applied to pose estimation from depth maps using Mean Shift, though no concrete performance numbers are provided.
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.