## Details

Originalsprache | Englisch |
---|---|

Seiten (von - bis) | 267-289 |

Seitenumfang | 23 |

Fachzeitschrift | International Journal of Computer Vision |

Jahrgang | 62 |

Ausgabenummer | 3 |

Publikationsstatus | Veröffentlicht - 1 Nov. 2004 |

Extern publiziert | Ja |

## Abstract

In this article we discuss the 2D-3D pose estimation problem of 3D free-form contours. In our scenario we observe objects of any 3D shape in an image of a calibrated camera. Pose estimation means to estimate the relative position and orientation (containing a rotation and translation) of the 3D object to the reference camera system. The fusion of modeling free-form contours within the pose estimation problem is achieved by using the conformal geometric algebra. The conformal geometric algebra is a geometric algebra which models entities as stereographically projected entities in a homogeneous model. This leads to a linear description of kinematics on the one hand and projective geometry on the other hand. To model free-form contours in the conformal framework we use twists to model cycloidal curves as twist-depending functions and interpret n-times nested twist generated curves as functions generated by 3D Fourier descriptors. This means we use the twist concept to apply a spectral domain representation of 3D contours within the pose estimation problem. We will show that twist representations of objects can be numerically efficient and easily be applied to the pose estimation problem. The pose problem itself is formalized as implicit problem and we gain constraint equations which have to be fulfilled with respect to the unknown rigid body motion. Several experiments visualize the robustness and real-time performance of our algorithms.

## ASJC Scopus Sachgebiete

- Informatik (insg.)
**Software**- Informatik (insg.)
**Maschinelles Sehen und Mustererkennung**- Informatik (insg.)
**Artificial intelligence**

## Zitieren

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**Pose estimation of 3D free-form contours.**/ Rosenhahn, Bodo; Perwass, Christian; Sommer, Gerald.

in: International Journal of Computer Vision, Jahrgang 62, Nr. 3, 01.11.2004, S. 267-289.

Publikation: Beitrag in Fachzeitschrift › Übersichtsarbeit › Forschung › Peer-Review

*International Journal of Computer Vision*, Jg. 62, Nr. 3, S. 267-289. https://doi.org/10.1007/s11263-005-4883-3

*International Journal of Computer Vision*,

*62*(3), 267-289. https://doi.org/10.1007/s11263-005-4883-3

}

TY - JOUR

T1 - Pose estimation of 3D free-form contours

AU - Rosenhahn, Bodo

AU - Perwass, Christian

AU - Sommer, Gerald

PY - 2004/11/1

Y1 - 2004/11/1

N2 - In this article we discuss the 2D-3D pose estimation problem of 3D free-form contours. In our scenario we observe objects of any 3D shape in an image of a calibrated camera. Pose estimation means to estimate the relative position and orientation (containing a rotation and translation) of the 3D object to the reference camera system. The fusion of modeling free-form contours within the pose estimation problem is achieved by using the conformal geometric algebra. The conformal geometric algebra is a geometric algebra which models entities as stereographically projected entities in a homogeneous model. This leads to a linear description of kinematics on the one hand and projective geometry on the other hand. To model free-form contours in the conformal framework we use twists to model cycloidal curves as twist-depending functions and interpret n-times nested twist generated curves as functions generated by 3D Fourier descriptors. This means we use the twist concept to apply a spectral domain representation of 3D contours within the pose estimation problem. We will show that twist representations of objects can be numerically efficient and easily be applied to the pose estimation problem. The pose problem itself is formalized as implicit problem and we gain constraint equations which have to be fulfilled with respect to the unknown rigid body motion. Several experiments visualize the robustness and real-time performance of our algorithms.

AB - In this article we discuss the 2D-3D pose estimation problem of 3D free-form contours. In our scenario we observe objects of any 3D shape in an image of a calibrated camera. Pose estimation means to estimate the relative position and orientation (containing a rotation and translation) of the 3D object to the reference camera system. The fusion of modeling free-form contours within the pose estimation problem is achieved by using the conformal geometric algebra. The conformal geometric algebra is a geometric algebra which models entities as stereographically projected entities in a homogeneous model. This leads to a linear description of kinematics on the one hand and projective geometry on the other hand. To model free-form contours in the conformal framework we use twists to model cycloidal curves as twist-depending functions and interpret n-times nested twist generated curves as functions generated by 3D Fourier descriptors. This means we use the twist concept to apply a spectral domain representation of 3D contours within the pose estimation problem. We will show that twist representations of objects can be numerically efficient and easily be applied to the pose estimation problem. The pose problem itself is formalized as implicit problem and we gain constraint equations which have to be fulfilled with respect to the unknown rigid body motion. Several experiments visualize the robustness and real-time performance of our algorithms.

KW - 2D-3D pose estimation

KW - Algebraic curves

KW - Conformal geometry

KW - Free-form contours

KW - Geometric algebra

UR - http://www.scopus.com/inward/record.url?scp=14844342883&partnerID=8YFLogxK

U2 - 10.1007/s11263-005-4883-3

DO - 10.1007/s11263-005-4883-3

M3 - Review article

AN - SCOPUS:14844342883

VL - 62

SP - 267

EP - 289

JO - International Journal of Computer Vision

JF - International Journal of Computer Vision

SN - 0920-5691

IS - 3

ER -