## The complex representation of algebraic curves and its simple exploitation for pose estimation and invariant recognition

#### TAREL ; COOPER

Type de document

CHAPITRE D'OUVRAGE (CO)

Langue

anglais

Auteur

TAREL ; COOPER

Résumé / Abstract

New representations are introduced for handling 2d algebraic curves (implicit polynomial curves) of arbitrary degree in the scope of computer vision applications. These representations permit fast, accurate pose-independent shape recognition under Euclidian transformations with complete sets of invariants, and fast accurate pose-estimation based on all the polynomial coefficients. The latter is accomplished by a new centering of a polynomial based on its coefficients, followed by rotation estimation 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. Angles of these rotations in the two-dimensional coefficient sub-spaces are proportional to each other and are integer multiples of the rotation angle in the X,Y data space. By recasting this approach in terms of a complex variable, I.E; X + IY = Z, and complex polynomial coefficients, further conceptual and computational results. Application to shape-based indexing into databases is presented to illustrate the usefulness and the robustness of the complex representation of algebraic curves.