In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, the Abel transform, named for Niels Henrik Abel

Niels Henrik Abel

Niels Henrik Abel was a Norwegian mathematician who proved the impossibility of solving the quintic equation in radicals.-Early life:...

, 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 by


In image analysis

Image analysis

Image analysis is the extraction of meaningful information from images; mainly from digital images by means of digital image processing techniques...

, 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.