How to Find a Khalimsky-Continuous Approximation of a Real-Valued Function

نویسنده

  • Erik Melin
چکیده

Given a real-valued continuous function defined on n-dimensional Euclidean space, we construct a Khalimsky-continuous integer-valued approximation. From a geometrical point of view, this digitization takes a hypersurface that is the graph of a function and produces a digital hypersurface—the graph of the digitized function.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Continuous digitization in Khalimsky spaces

A real-valued function defined on R can sometimes be approximated by a Khalimsky-continuous mapping defined on Z. We elucidate when this can be done and give a construction for the approximation. This approximation can be used to define digital Khalimsky hyperplanes that are topological embeddings of Z into Z. In particular, we consider Khalimsky planes in Z and show that the intersection of tw...

متن کامل

Digital Geometry and Khalimsky Spaces

Melin, E. 2008. Digital Geometry and Khalimsky Spaces (Digital geometri och Khalimskyrum). Uppsala Dissertations in Mathematics 54. vii+47 pp. Uppsala. ISBN 978-91-506-1983-6 Digital geometry is the geometry of digital images. Compared to Euclid’s geometry, which has been studied for more than two thousand years, this field is very young. Efim Khalimsky’s topology on the integers, invented in t...

متن کامل

Universal Approximation of Interval-valued Fuzzy Systems Based on Interval-valued Implications

It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  A formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

متن کامل

Pointfree topology version of image of real-valued continuous functions

Let $ { mathcal{R}} L$ be the ring of real-valued continuous functions on a frame $L$ as the pointfree  version of $C(X)$, the ring of all real-valued continuous functions on a topological space $X$. Since $C_c(X)$ is the largest subring of $C(X)$ whose elements have countable image, this motivates us to present the pointfree  version of $C_c(X).$The main aim of this paper is to present t...

متن کامل

Approximation of fixed points for a continuous representation of nonexpansive mappings in Hilbert spaces

This paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a Hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   The main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004