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The estimation of the length of a continuous curve from discrete data is considered. For ideal straight chaincode strings, optimal estimators are given. Comparisons are performed with known methods and recommendations given. A sampling density vs. accuracy trade-off theorem is presented. The applicability to nonstraight strings is discussed. For curves that(More)
  • Leo Dorst
  • IEEE Transactions on Pattern Analysis and Machine…
  • 2005
The well-known Procrustes method determines the optimal rigid body motion that registers two point clouds by minimizing the square distances of the residuals. In this paper, we perform the first order error analysis of this method for the 3D case, fully specifying how directional noise in the point clouds affects the estimated parameters of the rigid body(More)
If a continuous straight line segment is digitized on a regular grid, obviously a loss of information occurs. As a result, the discrete representation obtained (e.g., a chaincode string) can be coded more conveniently than the continuous line segment, but measurements of properties (such as line length) performed on the representation have an intrinsic(More)
This paper describes an approach to implementing geometric algebra. The goal of the implementation was to create an efficient, general implementation of geometric algebras of relatively low dimension, based on an orthogonal basis of any signature, for use in applications like computer graphics, computer vision, physics and robotics. The approach taken is to(More)
rical objects in fields like computer graphics, robotics, and computer vision routinely uses vectors to characterize constructions. Doing this effectively means extending the basic concept of a vector as an element of a linear space by an inner product and a cross product and by some additional constructions such as homogeneous coordinates. This compactly(More)