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TitleAn algebraic approach to Hough transforms
Author(s) Mauro C. Beltrametti, Lorenzo Robbiano
TypeArticle in Journal
AbstractThe main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from problems of detection of special shapes in medical and astronomical images. The classical Hough transform has been used mainly to detect simple curves such as lines and circles. We generalize this notion using reduced Gröbner bases of flat families of affine schemes. To this end we introduce and develop the theory of Hough regularity. The theory is highly effective and we give some examples computed with CoCoA (see [1]).
KeywordsHough transform, Gröbner basis, Family of schemes, Hough regularity
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S002186931200453X
LanguageEnglish
JournalJournal of Algebra
Volume371
Pages669 - 681
Year2012
Edition0
Translation No
Refereed No
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