Linear filter

Question 1

What is a linear filter

Answer 1

Generally, when dealing with linear filters, we have neighbourhood and some weights on the neighbourhood and we try to apply a weight som

Question 2

explain the spacial frequencies

Answer 2

when speaking about frequencies, we usually notice high frequencies for edges and low frequencies for continuous parts, spatial frequencies

Question 3

what is Fourier Transform

Answer 3

it is a way to analyze a signal in the form of a series of different sin and cosine functions

Question 4

explain the inverse Fourier transform

Answer 4

the inverse Fourier Transform allows, allows returning from the Fourier space to the signal space

Question 5

what is |F(u)|^2

Answer 5

reflects the power spectrum in the Fourier domain

Question 6

what is 2D Fourrier transform

Answer 6

the same Fourrier transform domain but extended to dimension generally for images we are interested by this

Question 7

what is the relation between the Fourier transform

Answer 7

the idea is that we can transform an image into a Fourier function where the size of Fourier domain correspond to the size of the image

Question 8

why do have the same size between the Fourier Transform and image

Answer 8

since we can not have a frequency that is higher than the difference of the two pixels

Question 9

what is the discrete Fourrier Tranform

Answer 9

Since images are actually discrete, we are more interested in representing the images discrete Fourier ing transform

Question 10

what is the fast fourrier transoform

Answer 10

it is simply an improved version of the Fourier Transform that runs in N log2 instead of N2

Question 11

Why using the Fourier Transform in the linear filter s

Answer 11

Since the convolution in the signal, space is equivalent to a term by term product in the frequency domain
which corresponds to the linear filter here.
Meaning we have the Fourier transform of the image and of the structuring element, then we apply there multiplication

Question 12

what is a low pass filter

Answer 12

in low pass filter, we simply keep the low frequencies generally used to blurr the image

Question 13

how can a sharp structuring element impacts the image

Answer 13

we ll notice some ripples on the image that reflect the edge of the images; a solution that is to have a less sharp transition

Question 14

How does the Fourier transform contain all the image information

Answer 14

the whole Fourier transform information is actually contained in the phase, so if we flip the image, we notice a difference in the phase

Question 15

what is the high pass filter

Answer 15

we only keep the high frequencies and enhance the edges

Question 16

how would it be possible to have a bandpass filter a filter only have frequencies on a certain domain

Answer 16

we can simply omit both low frequencies and high frequencies

Question 17

what is the bandpass filter utilities

Answer 17

it can be user to detect some edges by detecting some noise

Question 18

what is correlation

Answer 18

correlation can be used to detect some patterns in the image, for a given image containing a piece of the image, we will notice that the whom image is blurred except that small piece that correspond to the structuring element

Question 19

how does the size of the structuring element affect the resulted image

Answer 19

the bigger is the structuring element the more we get back to the original image