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.
for
and
.
where the above equation (
)
has finite support for an
x
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
as representing an image and
represents a PSF, where
for
and
.
Step 1 (Flip
):
Step 2 (Convolve):
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
and place it "on top" of
, so that just the bottom-right element,
of
overlaps with the top-left element,
, of
. Then, to get the next element of our convolved
image, we slide the flipped matrix,
, over one element to the right and get the
following result:
We continue in this fashion to find all of the elements ofour convolved image,
. Using the above method we define the general
formula to find a particular element of
as:
Using this equation, we can calculate the value for each
position on our final image,
. For example, due to the periodic extension of
the images, when circular convolution is applied we willobserve a
wrap-around effect.
Where the last three terms in
are a result of the wrap-around effect caused
by the presence of the images copies located all around it.
Zero padding
If the support of
is
x
and
is
x
,
then we zero pad
and
to
x
(see
).
Circular Convolution = Regular Convolution
Computing the 2d dft
where in the above equation,
is simply a 1D DFT over
.
This means that we will take the 1D FFT of each row; if wehave
rows, then it will
require
operations per row. We can rewrite this as
where now we take the 1D FFT of each column, which means
that if we have
columns,
then it requires
operations per column.
Therefore the overall complexity of a 2D FFT is
where
equals the number of pixels in the image.
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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