Journal Article
@Article
Artikel in Fachzeitschrift


Show entries of:

this year (2019) | last year (2018) | two years ago (2017) | Notes URL

Action:

login to update

Options:








Author, Editor(s)

Author(s):

Rosenhahn, Bodo
Sommer, Gerald

dblp
dblp

Not MPG Author(s):

Sommer, Gerald

BibTeX cite key*:

RosenhahnJMIV2004a

Title

Title*:

Pose Estimation in Conformal Geometric Algebra. Part I: The stratification of mathematical spaces

Journal

Journal Title*:

Journal of Mathematical Imaging and Vision

Journal's URL:

http://www.springerlink.com/(rm0acsrmmui1lyqzcq4totfx)/app/home/journal.asp?referrer=parent&backto=linkingpublicationresults,1:100293,1

Download URL
for the article:

http://www.ingentaconnect.com/content/klu/jmiv/2005/00000022/00000001

Language:

English

Publisher

Publisher's
Name:

Springer Science+Business Media B.V.

Publisher's URL:

http://www.springerlink.com

Publisher's
Address:

Heidelberg, Germany

ISSN:

0924-9907

Vol, No, pp, Date

Volume*:

22

Number:

1

Publishing Date:

January 2005

Pages*:

27-48

Number of
VG Pages:

22

Page Start:


Page End:


Sequence Number:


DOI:


Note, Abstract, ©

Note:


(LaTeX) Abstract:

2D-3D pose estimation means to estimate the relative position and orientation of a 3D object with respect to a reference camera system. This work has its main focus on the theoretical foundations of the 2D-3D pose estimation problem: We discuss the involved mathematical spaces and their interaction within higher order entities. To cope with the pose problem (how to compare 2D projective image features with 3D Euclidean object features), the principle we propose is to reconstruct image features (e.g. points or lines) to one dimensional higher entities (e.g. 3D projection rays or 3D reconstructed planes) and express constraints in the 3D space. It turns out that the stratification hierarchy [11] introduced by Faugeras is involved in the scenario. But since the stratification hierarchy is based on pure point concepts a new algebraic embedding is required when dealing with higher order entities. The conformal geometric algebra (CGA) [24] is well suited to solve this problem, since it subsumes the involved mathematical spaces. Operators are defined to switch entities between the algebras of the conformal space and its Euclidean and projective subspaces. This leads to another interpretation of the stratification hierarchy, which is not restricted to be based solely on point concepts. This work summarizes the theoretical foundations needed to deal with the pose problem. Therefore it contains mainly basics of Euclidean, projective and conformal geometry. Since especially conformal geometry is not well known in computer science, we recapitulate the mathematical concepts in some detail. We believe that this geometric model is useful also for many other computer vision tasks and has been ignored so far. Applications of these foundations are presented in Part II [36].

URL for the Abstract:

http://www.springerlink.com/(rm0acsrmmui1lyqzcq4totfx)/app/home/contribution.asp?referrer=parent&backto=issue,3,6;journal,5,49;linkingpublicationresults,1:100293,1

Categories,
Keywords:

2D-3D pose estimation, stratification hierarchy, conformal geometric algebra

HyperLinks / References / URLs:


Copyright Message:

Springer

Personal Comments:


Download
Access Level:

Public

Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Computer Graphics Group

Appearance:

MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort


BibTeX Entry:

@ARTICLE{RosenhahnJMIV2004a,
AUTHOR = {Rosenhahn, Bodo and Sommer, Gerald},
TITLE = {Pose Estimation in Conformal Geometric Algebra. Part I: The stratification of mathematical spaces},
JOURNAL = {Journal of Mathematical Imaging and Vision},
PUBLISHER = {Springer Science+Business Media B.V.},
YEAR = {2005},
NUMBER = {1},
VOLUME = {22},
PAGES = {27--48},
ADDRESS = {Heidelberg, Germany},
MONTH = {January},
ISBN = {0924-9907},
}


Entry last modified by Christine Kiesel, 07/06/2006
Show details for Edit History (please click the blue arrow to see the details)Edit History (please click the blue arrow to see the details)
Hide details for Edit History (please click the blue arrow to see the details)Edit History (please click the blue arrow to see the details)

Editor(s)
Bodo Rosenhahn
Created
12/22/2005 09:39:31 AM
Revisions
4.
3.
2.
1.
0.
Editor(s)
Christine Kiesel
Christine Kiesel
Christine Kiesel
Bodo Rosenhahn
Bodo Rosenhahn
Edit Dates
06.07.2006 14:58:43
31.05.2006 11:36:42
31.05.2006 11:33:44
04/25/2006 05:04:52 PM
12/22/2005 09:39:31 AM
Show details for Attachment SectionAttachment Section
Hide details for Attachment SectionAttachment Section