Astrogeometry: toward mathematical foundations.

Details Astrogeometry: toward mathematical foundations. Astrogeometry: toward mathematical foundations.

Apr 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997ijtp...36.1009f&link_type=abstract

International Journal of Theoretical Physics, Vol. 36, No. 4, p. 1009 - 1020

Astronomy and Astrophysics

Astronomy

Image Processing: Astronomy

Scientific paper

In image processing (e.g., in astronomy), the desired black-and-white image is, from the mathematical viewpoint, a set. Hence, to process images, we need to process sets. To define a generic set, we need infinitely many parameters; therefore, if we want to represent and process sets in the computer, we must restrict ourselves to finite-parameter families of sets that will be used to approximate the desired sets. The wrong choice of a family can lead to longer computations and worse approximation. Hence, it is desirable to find the family that it is the best in some reasonable sense. In this paper, the authors show how the problems of choosing the optimal family of sets can be formalized and solved. As a result of the described general methodology, for astronomical images, they get exactly the geometric shapes that have been empirically used by astronomers and astrophysicists; thus, they have a theoretical explanation for these shapes.

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