A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates

Gallego Bonet, Guillermo and Yezzi, Anthony (2015). A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates. "Journal of Mathematical Imaging and Vision", v. 51 (n. 3); pp. 378-384. ISSN 0924-9907. https://doi.org/10.1007/s10851-014-0528-x.

Description

Title: A Compact Formula for the Derivative of a 3-D Rotation in Exponential Coordinates
Author/s:
  • Gallego Bonet, Guillermo
  • Yezzi, Anthony
Item Type: Article
Título de Revista/Publicación: Journal of Mathematical Imaging and Vision
Date: March 2015
ISSN: 0924-9907
Volume: 51
Subjects:
Freetext Keywords: Cross-product matrix, Derivative of rotation, Exponential map, Lie group, Rodrigues parameters, Rotation, Rotation vector
Faculty: E.T.S.I. Telecomunicación (UPM)
Department: Señales, Sistemas y Radiocomunicaciones
UPM's Research Group: Tratamiento de Imágenes GTI
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We present a compact formula for the derivative of a 3-D rotation matrix with respect to its exponential coordinates. A geometric interpretation of the resulting expression is provided, as well as its agreement with other less-compact but better-known formulas. To the best of our knowledge, this simpler formula does not appear anywhere in the literature. We hope by providing this more compact expression to alleviate the common pressure to reluctantly resort to alternative representations in various computational applications simply as a means to avoid the complexity of differential analysis in exponential coordinates.

Funding Projects

TypeCodeAcronymLeaderTitle
FP7246565UNITEUniv. Politecnica de MadridUPM - Marie Curie International Mobility Programme
Government of SpainTEC2010-20412Enhanced 3DTVUnspecifiedUnspecified
Government of SpainTEC2013-48453MR-UHDTVUnspecifiedUnspecified
FP7610691BRIDGETUnspecifiedBRIDGING THE GAP FOR ENHANCED BROADCAST

More information

Item ID: 35479
DC Identifier: http://oa.upm.es/35479/
OAI Identifier: oai:oa.upm.es:35479
DOI: 10.1007/s10851-014-0528-x
Official URL: https://link.springer.com/article/10.1007%2Fs10851-014-0528-x
Deposited by: Dr Guillermo Gallego Bonet
Deposited on: 29 May 2015 09:53
Last Modified: 30 May 2019 18:03
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