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Gives the highlights of the projective flow algorithm we used for image registration.

Overview

Superresolution is based on the idea that images with slight shifts can be aligned and combined into a single, higher resolution image. While aligning images with respect to one another may not seem too complex at first, there are a number of technical details that muddy the waters. Additionally, superresolution requires registration results that are accurate to the subpixel level. While an error of one or two pixels sounds just fine, it would lead to a poor quality image after combination.

Motivation

Let's first look at the impact of registration before delving into the details of the algorithm we chose. Consider the following two test images:

Registration test images

Two slightly shifted images (Source: http://lcavwww.epfl.ch/software/superresolution/superresolution_dataset1.tar.gz)

While these two images may appear to be the same, they are actually just slightly different from each other. While we could try to combine the images as they are now, we need to register them first to achieve a better result. Below two difference graphs illustrate the impact of registration, the first showing the difference before registration, and the other after.

Difference graphs

Before registration
After registration

Even though it is hard to see a visible difference when viewing the two images separately, the difference graphs above show how registration can still detect difference and account for them.

Algorithm

While there are a number of different techniques that can be used to register images, many of them are feature-based . They attempt to track the same set of points as they move from image to image. This can work well, but only if the points are detect accurately each time. Instead, we chose to use a featureless algorithm, which avoids feature points by using the flow of all pixels in the image. It improves upon the optical flow concept discussed in a previous module by allowing for changes in translation, rotation, scale, pan, and tilt between each image. The algorithm is detailed below.

  • Calculate the vertical, horizontal, and time derivatives between the two images. This is same process mentioned in Optical Flow .
  • From these spatiotemporal derivatives, estimate an approximate model (q) of the projective parameters. There are several models that can be used, such as bilinear and pseudo-projective. The system used to estimate the bilinear model is shown below.

    Bilinear approximation model

    System of equations that relates derivative to the bilinear approximation model (Source: 1)
  • Using the four corners of the image, calculate their new coordinates from the approximate model. In the formulas for the bilinear model below, u m + x and v m + y denote the new x and y coordinates respectively.

    Bilinear coordinate formulas

    Relates old and new coordinate via approximate (q) parameters (Source: 1)
  • These old and new coordinates now completely determine the projective parameters in the exact model (p).
  • Apply these new parameters (p) to one of the images and iterate until the difference is negligible.

Improving accuracy

To get better results, we can create a multi-resolution pyramid for each image first. This means that we generate several levels of increasingly blurry images. Starting at the blurriest level, we apply several iterations of the algorithm as described above. Then, we move up to a less blurry level and repeat, but we carry over the result from the previous level and use that as our starting point.

Questions & Answers

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
what school?
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 to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
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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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