Almost vanishing polynomials and an application to the Hough transform

作者：Torrente Maria Laura^*; Beltrametti Mauro C

来源：Journal of Algebra and Its Applications, 2014, 13(8): 1450057.

DOI：10.1142/S0219498814500571

• Weighted matrix norm
• crossing area algorithm
• Hough transform

We consider the problem of deciding whether or not an affine hypersurface of equation f = 0, where f = f(x(1) , ... , x(n)) is a polynomial in R[x(1) , ... , x(n)], crosses a bounded region T of the real affine space A(n). We perform a local study of the problem, and provide both necessary and sufficient numerical conditions to answer the question. Our conditions are based on the evaluation of f at a point p is an element of T, and derive from the analysis of the differential geometric properties of the hypersurface z = f(x(1) , ... , x(n)) at p. We discuss an application of our results in the context of the Hough transform, a pattern recognition technique for the automated recognition of curves in images.

• 出版日期2014-12