Hough变换的代数方法
An Algebraic Approach to Hough Transforms
摘要：
本文的主要目的是奠定基础的一般理论，其中包括经典的霍夫变换的功能，并将其扩展到一般的代数对象，如仿射计划。主要动机来自于医学和天文图像中特殊形状的检测问题。经典的Hough变换主要用于检测直线和圆等简单曲线。我们推广这一概念使用减少Groebner基地的平面家庭的仿射计划。为此，我们引进和发展霍夫正则性理论。该理论是非常有效的，我们给出了一些例子计算与CoCoA。
英文摘要：
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.
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