An algebraic approach to Hough transforms

作者：Beltrametti Mauro C; Robbiano Lorenzo^*

来源：Journal of Algebra, 2012, 371: 669-681.

DOI：10.1016/j.jalgebra.2012.09.012

• Hough transform
• Grobner basis
• Family of schemes
• Hough regularity

The 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 Grobner 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]).

• 出版日期2012-12-1