Defining the Pose of Any 3D Rigid Object and an Associated Distance

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-ma...

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Bibliographic Details
Published in:International journal of computer vision 2018-06, Vol.126 (6), p.571-596
Main Authors: Brégier, Romain, Devernay, Frédéric, Leyrit, Laetitia, Crowley, James L.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computer Imaging
Computer Science
Computer Vision and Pattern Recognition
Euclidean geometry
Euclidean space
Image Processing and Computer Vision
Image processing systems
Mathematical Physics
Mathematics
Mechanics
Metric Geometry
Pattern Recognition
Pattern Recognition and Graphics
Physics
Searching
Solid mechanics
Transformations
Vision
Vision systems
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Summary: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 to 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 a 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.
ISSN:0920-5691
1573-1405
DOI:10.1007/s11263-017-1052-4