^{1} Image Analysis and Computer Graphics, Department of Informatics and Mathematical Modeling, Technical University of Denmark^{2} Department of Informatics and Mathematical Modeling, Technical University of Denmark^{3} Department of Applied Mathematics and Computer Science, Technical University of Denmark^{4} unknown

Abstract:

We express the alignment of 2D shapes as the minimization of the norm of a linear vector function. The minimization is done in the \$l\_1\$, \$l\_2\$ and the \$l\_\$\backslash\$infty\$ norms using well known standard numerical methods. In particular, the \$l\_1\$ and the \$l\_\$\backslash\$infty\$ norm alignments are formulated as linear programming problems. The linear vector function formulation along with the different norms results in alignment methods that are both resistant from influence from outliers, robust wrt. errors in the annotation and capable of handling missing datapoints. Another reason for using other norms than the \$l\_2\$ norm is to minimize the effect of the choice of landmarks. Examples that illustrate the properties of the different norms are given on simulated as well as real datasets.