Majorization Algorithms for Inspecting Circles, Ellipses, Squares, Rectangles, and Rhombi

References

• Ahn S. J., Rauh W., Warnecke H.-J. Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognition (2001) 34:2283–2303Crossref, Google Scholar
• De Leeuw J., Bock H. H., Lenski W., Richter M. M. Block relaxation algorithms in statistics. Information Systems and Data Analysis (1994) (Springer-Verlag, Berlin, Germany) 308–325Crossref, Google Scholar
• De Leeuw J., Heiser W. J., Krishnaiah P. R. Multidimensional scaling with restrictions on the configuration. Multivariate Analysis V (1980) (North-Holland, Amsterdam, The Netherlands) 501–522Google Scholar
• Drezner Z., Steiner S., Wesolowsky G. O. On the circle closest to a set of points. Comput. Oper. Res. (2002) 29:637–650Crossref, Google Scholar
• Eiselt H. A., Laporte G., Drezner Z. Objectives in location problems. Facility Location: A Survey of Applications and Methods (1995) (Springer, New York) 151–180Crossref, Google Scholar
• Fonseca M. J., Jorge J. A. Experimental evaluation of an online scribble recognizer. Pattern Recognition Lett. (2001) 22:1311–1319Crossref, Google Scholar
• Groenen P. J. F. Iterative majorization algorithms for minimizing loss functions in classification. (2002) . Working paper, 8th Conf. IFCS. Krakow, PolandGoogle Scholar
• Groenen P. J. F., Heiser W. J., Meulman J. J. Global optimization in least-squares multidimensional scaling by distance smoothing. J. Classification (1999) 16:225–254Crossref, Google Scholar
• Groenen P. J. F., Mathar R., Heiser W. J. The majorization approach to multidimensional scaling for Minkowski distances. J. Classification (1995) 12:3–19Crossref, Google Scholar
• Groenen P. J. F., van Os B. J., Meulman J. J. Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis. Psychometrika (2000) 65:511–524Crossref, Google Scholar
• Heiser W. J., Krzanowski W. J. Convergent computation by iterative majorization: Theory and applications in multidimensional data analysis. Recent Advances in Descriptive Multivariate Analysis (1995) (Oxford University Press, Oxford, UK) 157–189Google Scholar
• Kiers H. A. L. Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems. Comput. Statist. Data Anal. (2002) 41:157–170Crossref, Google Scholar
• Kiers H. A. L., Groenen P. J. F. A monotonically convergent algorithm for orthogonal congruence rotation. Psychometrika (1996) 61:375–389Crossref, Google Scholar
• Langbein F. C., Mills B., Marshall A. D., Martin R. R. Approximate geometric shapes. Internat. J. Shape Model. (2001) 7:129–162Crossref, Google Scholar
• Lange K., Hunter D. R., Yang I. Optimization transfer using surrogate objective functions. J. Comput. Graphics Statist. (2000) 9:1–20Google Scholar
• Rorres C., Romano D. G. Finding the center of a circular starting line in an ancient Greek stadium. SIAM Rev. (1997) 39:745–754Crossref, Google Scholar
• Van-Ban L., Lee D. T. Out-of-roundness problem revisited. IEEE Trans. Pattern Anal. (1991) 13:217–223Crossref, Google Scholar
• Van Deun K., Groenen P. J. F., Heiser W. J., Busing F. M. T. A., Delbeke L. Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model. Psychometrika (2005) 70:45–69Crossref, Google Scholar
• Yeralan S., Ventura J. A. Computerized roundness inspection. Internat. J. Production Res. (1988) 26:1921–1935Crossref, Google Scholar