Spatial Relationship Pattern

A spatial relationship pattern denotes a subproblem in a complex tracking or calibration setup graph for which one or more known algorithms exist. The pattern defines the ‘signature’ of an algorithms to solve the specific problem in a general setup.

These algorithms have as input a set of measurements as defined by the problem and return a set of measurements that is part of the solution to the overall problem. But other than function signatures in programming languages, spatial relationship patterns do not merely define the type of arguments and return values, but also impose restrictions on the geometric relationship between them.

Basic Patterns

• Inversion
• Concatenation^?
• Fusion

Advanced Patterns

• 3D-3D Pose Estimation (Absolute Orientation)
• 2D-3D Pose Estimation
• 2D-3D Triangulation
• 2D-3D Projective Calibration
• Hand Eye Calibration
• Pointing Device Calibration (Tip Calibration, Pivoting)

References

	D. Pustka, M. Huber, M. Bauer, G. Klinker Spatial Relationship Patterns: Elements of Reusable Tracking and Calibration Systems The Fifth IEEE and ACM International Symposium on Mixed and Augmented Reality, Santa Barbara, CA, USA, Oct. 22 - 25, 2006, pp. 88-97. (bib)
	With tracking setups becoming increasingly complex, it gets more difficult to find suitable algorithms for tracking, calibration and sensor fusion. A large number of solutions exists in the literature for various combinations of sensors, however, no development methodology is available for systematic analysis of tracking setups. When modeling a system as a spatial relationship graph (SRG), which describes coordinate systems and known transformations, all algorithms used for tracking and calibration correspond to certain patterns in the graph. This paper introduces a formal model for representing such spatial relationship patterns and presents a small catalog of patterns frequently used in augmented reality systems. We also describe an algorithm to identify patterns in SRGs at run-time for automatic construction of data flows networks for tracking and calibration.
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