  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
Groebner 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.
