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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
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Crow Reply
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RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
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What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Stoney Reply
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Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
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Smarajit Reply
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