<< Chapter < Page Chapter >> Page >
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 mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elec 301 projects fall 2006. OpenStax CNX. Sep 27, 2007 Download for free at http://cnx.org/content/col10462/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elec 301 projects fall 2006' conversation and receive update notifications?

Ask