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- Abel_transform abstract "In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions. The Abel transform of a function f(r) is given by:Assuming f(r) drops to zero more quickly than 1/r, the inverse Abel transform is given byIn image analysis, the forward Abel transform is used to project an optically thin, axially symmetric emission function onto a plane, and the reverse Abel transform is used to calculate the emission function given a projection (i.e. a scan or a photograph) of that emission function.In absorption spectroscopy of cylindrical flames or plumes, the forward Abel transform is the integrated absorbance along a ray with closest distance y from the center of the flame, while the inverse Abel transform gives the local absorption coefficient at a distance r from the center. Abel transform is limited to applications with axially symmetric geometries. For more general asymmetrical cases, more general-oriented reconstruction algorithms such as Algebraic Reconstruction Technique (ART), Maximum Likelihood Expectation Maximization (MLEM), Filtered Back-Projection (FBP) algorithms should be employed.In recent years, the inverse Abel transformation (and its variants) has become the cornerstone of data analysis in photofragment-ion imaging and photoelectron imaging. Among recent most notable extensions of inverse Abel transformation are the Onion Peeling and BAsis Set Expansion (BASEX) methods of photoelectron and photoion image analysis.".
- Abel_transform thumbnail AbelTransform.png?width=300.
- Abel_transform wikiPageID "1499595".
- Abel_transform wikiPageRevisionID "584774582".
- Abel_transform hasPhotoCollection Abel_transform.
- Abel_transform subject Category:Image_processing.
- Abel_transform subject Category:Integral_transforms.
- Abel_transform subject Category:Niels_Henrik_Abel.
- Abel_transform comment "In mathematics, the Abel transform, named for Niels Henrik Abel, is an integral transform often used in the analysis of spherically symmetric or axially symmetric functions.".
- Abel_transform label "Abel transform".
- Abel_transform label "Abelsche Integralgleichung".
- Abel_transform label "Transformada de Abel".
- Abel_transform label "Интегральное преобразование Абеля".
- Abel_transform sameAs Abelsche_Integralgleichung.
- Abel_transform sameAs Transformada_de_Abel.
- Abel_transform sameAs m.0565lb.
- Abel_transform sameAs Q4666656.
- Abel_transform sameAs Q4666656.
- Abel_transform wasDerivedFrom Abel_transform?oldid=584774582.
- Abel_transform depiction AbelTransform.png.
- Abel_transform isPrimaryTopicOf Abel_transform.
