Convergence properties of multi-dimensional stack filters
Peter Wendt
Electronic Imaging: Advanced Devices and Systems 1990
We consider Steiner minimum trees (SMT) in the plane, where only orientations with angle iπ/σ, 0 ≤ i ≤; σ - 1 and σ an integer, are allowed. The orientations define a metric, called the orientation metric, λσ, in a natural way. In particular, λ2 metric is the rectilinear metric and the Euclidean metric can be regarded as λ∞ metric. In this paper, we provide a method to find an optimal λσ SMT for 3 or 4 points by analyzing the topology of λσ SMT's in great details. Utilizing these results and based on the idea of loop detection first proposed in Chao and Hsu, IEEE Trans. CAD, vol. 13, no. 3, pp. 303-309, 1994, we further develop an O(n2) time heuristic for the general λσ SMT problem, including the Euclidean metric. Experiments performed on publicly available benchmark data for 12 different metrics, plus the Euclidean metric, demonstrate the efficiency of our algorithms and the quality of our results.
Peter Wendt
Electronic Imaging: Advanced Devices and Systems 1990
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering
Leo Liberti, James Ostrowski
Journal of Global Optimization
R.A. Brualdi, A.J. Hoffman
Linear Algebra and Its Applications