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One possible definition of the length of a digitized curve in 3D is the length of the shortest polygonal curve lying entirely in a cube curve. In earlier work the authors proposed an iterative algorithm for the calculation of this minimal length polygonal curve (MLP). This paper reviews the algorithm and suggests methods to speed it up by reducing the set of possible locations of vertices of the MLP,...
We propose in this paper an arithmetical definition of 3-D discrete lines as well as an efficient construction algorithm. From this notion, an algorithm of 3-D discrete lines segmentation has been developed. It is then used to calculate the length of a discrete curve. Ap roof of the multigrid convergence of length estimators is presented.
Jordan, Peano and others introduced digitizations of sets in the plane and in the 3D space for the purpose of feature measurements. Features measured for digitized sets, such as perimeter, contents etc., should converge (for increasing grid resolution) towards the corresponding features of the given sets before digitization. This type of multigrid convergence is one option for performance evaluation...
This paper looks at the problem of approximating the length of the unknown parametric curve γ : [0, 1] → ℝn from points qi = γ(ti), where the parameters ti are not given. When the ti are uniformly distributed Lagrange interpolation by piecewise polynomials provides efficient length estimates, but in other cases this method can behave very badly [15]. In the present paper we apply this simple algorithm...
The 1-D Leap-Frog Algorithm [12] is an iterative scheme for solving a class of nonlinear optimization problems. In the present paper1 we adapt Leap-Frog to solve an optimization problem in computer vision. The vision problem in the present paper is to recover (as far as possible) an integrable vector field (over an orthogonal grid) from a field corrupted by noise or the effects of digitization of...
A polyhedral approximation of closed Jordan surfaces is described. The approximation is based on the notion of a relative convex hull in a polyhedrally bounded compact set obtained by gridding technique and can be applied also to approximation of surfaces of functions.
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