Abstract
Linear statistical models of shape variability of identifiable point sets have previously been described and applied successfully to the empirical modeling of appearance variability in natural images. One of the limitations of these linear models has been demonstrated in the nonlinear “bending” shape variability of point sets where a length ratio is constant.
We point out that modeling point set variability with groups of transformations generated by linear vector fields constitute an algebraic frame for modeling simple nonlinear point set variability suitable for the modeling of shape variability. As an example, the very simple “bending” shape variability of three points in the complex plane is in this way generated by a linear vector field described by a complex 3 × 3 matrix.
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Olsen, N.H., Nielsen, M. (2000). Lie Group Modeling of Nonlinear Point Set Shape Variability. In: Sommer, G., Zeevi, Y.Y. (eds) Algebraic Frames for the Perception-Action Cycle. AFPAC 2000. Lecture Notes in Computer Science, vol 1888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722492_20
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DOI: https://doi.org/10.1007/10722492_20
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