how 2x2 median filter works

hi I tried this

• a = [ 1 2 3 ; 4 5 6; 7 8 9]
• b = medfilt2(a);

Output is [0,2,0;2,5,3;0,5,0]

How were values of b calculated from a ?

I can't figure out the logic.

Thanks.

Answer 1

[KSSV]

When ever you use a function in MATLAB.....it should be a common practice to read the documentation part of it. Read the documentation: https://in.mathworks.com/help/images/ref/medfilt2.html. The doc mentions the reference for the function. You may refer that for further idea.

Lim, Jae S., Two-Dimensional Signal and Image Processing, Englewood Cliffs, NJ, Prentice Hall, 1990, pp. 469-476.

[sumeet]

sorry for late reply. I had read the link - still , it does not explain the output. Why did 1,3,7,9 from original matrix got replaced by zeroes ?

Thanks.

[Image Analyst]

Because when the window is centered such that most of the window is "off the image", the off image pixels are considered 0. Since most of the pixels are 0, 0 is the median.

[sumeet]

The problem is how is window decided for a particular pixel ? The documentation taught that medfilt2 will take 4 values , find their average , discard the fraction and give whole number as output . Is that right ? Then , let the window have values called top left , top right , bottom left and bottom right . 1 maps to 0 would mean that avg of 4 values < 1 . similiarly for 3,7,9 .

2 maps to 2 would mean that avg of 4 values >= 2 and <3 . similairly for 4.

5 maps to 5 would mean that avg of 4 values >= 5 and <6 . similairly for 8.

6 maps to 3 would mean that avg of 4 values >= 3 and <4 .

Now can you tell me four values considered for each case above ? I am unable to find neighbour choosing criterion such that above mapping happens .

Thanks a lot.

Answer 2

[Image Analyst]

When the image is this:

a =
     1     2     3
     4     5     6
     7     8     9

and you're using a 2x2 window, and the 2x2 window is in the upper left, it will see

0 0
0 1

The zeros are where the window is off the array. So the median of three zeros and a 1 is zero, so that's why you got a zero in the upper left element of your output.

[sumeet]

that explains 1->0 .

now for 2 the window must be

0 0

1 2

the average is 3 . 3/4 is 0.75 so output should be 0.

how do we get 2 there ?

[Image Analyst]

Are you using a 2x2, like your subject line says, or a 3x3 like your code does?

a = [ 1 2 3 ; 4 5 6; 7 8 9]
am3x3 = medfilt2(a)
am2x2 = medfilt2(a, [2, 2])

a =
     1     2     3
     4     5     6
     7     8     9
am3x3 =
     0     2     0
     2     5     3
     0     5     0
am2x2 =
       3        4         1.5
       6        7         3
       3.5      4         0