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One method for interpolating the pixel values of several low-resolution (LR) images to create a single high-resolution (HR) image is to approximate the patches of a Delaunay triangulation with bivariate polynomials.

In data processing applications, it often occurs that certain points on a surface are known and are all samples of a common function (ex: an image). However, if these samples are too few for a particular purpose (ex: viewing an image in high resolution), then the question arises: how can the value of this function at other points be found? If there is no formula that, given (x,y) will return the function's value, then such a formula must be approximated. Interpolation is the generation of such an approximation.

The task of creating a high-resolution (HR) image from a set of low-resolution (LR) images requires interpolation. One method, Bose-Lertrattanapanich interpolation, is described below.

  • Given a set of LR images and a registration algorithm, apply the registration algorithm to obtain a set of non-uniformly distributed points. These points represent the relative locations of all LR pixel values.
  • Construct a Delaunay triangulation of the points.

    Delaunay triangulation example

    MATLAB Delaunay triangulation of registered points from a set of LR images.
  • Estimate the gradient vector of image intensity (dz/dx,dz/dy) at each triangle vertex from the normal vectors of surrounding regions.

    Normal vector at a vertex

    The gradient vector at a vertex (dz/dx,dz/dy) can be estimated from the normal vector at the vertex: n = [nx,ny,nz]. n is calculated by summing the normal vectors of the surrounding triangle patches weighted by their areas, then dividing this sum by the total area of these triangles. The result is dz/dx = -nx/nz, dz/dy = -ny/nz. (Source: 2)
  • Approximate the image intensity values (z) for each triangle patch by a continuous surface.
    Bivariate polynomial to model surface; c values are based on the gradient vectors. (Source: 2)
  • For each point (x,y) on the HR grid, apply the appropriate polynomial to calculate the pixel value.

There are many simpler implementations of the last three steps of this process. The algorithm our code implements generates a constant function for each triangle patch, rather than a bivariate polynomial. In our implementation, the interpolated pixel value in each triangle patch (pT) is the average of the pixel values at the three vertices of each triangle (pA,pB,pC): pT = (pA + pB + pC)/3. This function is less accurate than the bivariate polynomial, but is more intuitive and cost-efficient to implement.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
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Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Elec 301 projects fall 2006. OpenStax CNX. Sep 27, 2007 Download for free at http://cnx.org/content/col10462/1.2
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