## A New Complex Basis for Implicit Polynomial Curves and
its Simple Exploitation for Pose Estimation and Invariant Recognition

#### Abstract

- New representations are developed for 2D IP (implicit polynomial)
curves ofarbitrary degree. These representations permit shape recognition
and pose estimation with essentially single, rather than iterative,
computation, and extract and use all the information in the polynomial
coefficients. This is accomplished by decomposing polynomial coefficient
space into a union of orthogonal subspaces for which rotations within
two dimensional subspaces or identity transformations within one dimensional
subspaces result from rotations in x,y measured-data space. These rotations
in the two dimensional coefficient subspaces are related in simple ways to
each other and to rotation in the x,y data space. By recasting this approach
in terms of complex polynomials, i.e, z=x+iy and complex coefficients,
further simplification occurs for rotations and some simplification occurs
for translation.

#### Reference

@inproceedings{jpt-cvpr98,
author = {Tarel, J.-P. and Cooper, D. B.},
title = {A New Complex Basis for Implicit Polynomial Curves and its Simple Exploitation for Pose Estimation and Invariant Recognition},
booktitle = {Proceedings of IEEE Conference on Computer Vision and Pattern Recognition},
address = {Santa Barbara, California, USA},
date = {23-25},
year = {1998},
month = {June},
pages = {111-117},
note = {http://perso.lcpc.fr/tarel.jean-philippe/publis/cvpr98.html}
}

** Compressed postscript file (100 Kb)**

** Pdf file (157 Kb)**

** (c) IEEE**