This module extends the ideas of the Discrete Fourier Transform (DFT) into two-dimensions, which is necessary for any image processing.
2d dft
To perform image restoration (and many other useful image
processing algorithms) in a computer, we need a FourierTransform (FT) that is discrete and two-dimensional.
where the above equation (
)
has finite support for an
$N$ x
$N$ image.
Inverse 2d dft
As with our regular fourier transforms, the 2D DFT also has
an inverse transform that allows us to reconstruct an imageas a weighted combination of complex sinusoidal basis
functions.
Below we go through the steps of convolving two
two-dimensional arrays. You can think of
$f$ as representing an image and
$h$ represents a PSF, where
$h(m, n)=0$ for
$m\land n> 1$ and
$m\land n< 0$ .
$$h=\begin{pmatrix}h(0, 0) & h(0, 1)\\ h(1, 0) & h(1, 1)\\ \end{pmatrix}$$$$f=\begin{pmatrix}f(0, 0) & & f(0, N-1)\\ & & \\ f(N-1, 0) & & f(N-1, N-1)\\ \end{pmatrix}$$ Step 1 (Flip
$h$ ):
We use the standard 2D convolution equation (
) to find the first element of
our convolved image. In order to better understand what ishappening, we can think of this visually. The basic idea is
to take
$h(-m, -n)$ and place it "on top" of
$f(k, l)$ , so that just the bottom-right element,
$h(0, 0)$ of
$h(-m, -n)$ overlaps with the top-left element,
$f(0, 0)$ , of
$f(k, l)$ . Then, to get the next element of our convolved
image, we slide the flipped matrix,
$h(-m, -n)$ , over one element to the right and get the
following result:
$$g(0, 1)=h(0, 0)f(0, 1)+h(0, 1)f(0, 0)$$ We continue in this fashion to find all of the elements ofour convolved image,
$g(m, n)$ . Using the above method we define the general
formula to find a particular element of
$g(m, n)$ as:
Using this equation, we can calculate the value for each
position on our final image,
$\stackrel{~}{g}(m, n)$ . For example, due to the periodic extension of
the images, when circular convolution is applied we willobserve a
wrap-around effect.
where in the above equation,
$\sum_{n=0}^{N-1} f(m, n)e^{-i\frac{2\pi ln}{N}}$ is simply a 1D DFT over
$n$ .
This means that we will take the 1D FFT of each row; if wehave
$N$ rows, then it will
require
$N\lg N$ operations per row. We can rewrite this as
In this morden time nanotechnology used in many field .
1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc
2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc
3- Atomobile -MEMS, Coating on car etc.
and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change .
maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.