Details:
Title  Hyperplane sections, Gröbner bases, and Hough transforms  Author(s)  Lorenzo Robbiano  Type  Article in Journal  Abstract  Abstract The purpose of this paper is twofold. In the first part we concentrate on hyperplane sections of algebraic schemes, and present results for determining when Gröbner bases pass to the quotient and when they can be lifted. The main difficulty to overcome is the fact that we deal with nonhomogeneous ideals. As a byproduct we hint at a promising technique for computing implicitization efficiently. In the second part of the paper we deal with families of algebraic schemes and the Hough transforms. We compute the dimension of the Hough transforms, and show that in some interesting cases it is zero. Then we concentrate on their hyperplane sections; some results and examples hint at the possibility of reconstructing external and internal surfaces of human organs from the parallel crosssections obtained by tomography.  ISSN  00224049 
URL 
http://www.sciencedirect.com/science/article/pii/S0022404914002461 
Language  English  Journal  Journal of Pure and Applied Algebra  Volume  219  Number  6  Pages  2434  2448  Year  2015  Edition  0  Translation 
No  Refereed 
No 
