表示二进制矩阵中每列随机化的图形

Question

Imagine the following binary image exemplified by the matrix below. This is a simplified version of the images I'll be working with:

0 1 0 1
0 1 1 1
0 0 0 1
0 1 1 1

I want to construct a graph that will represent the randomness of each column. My thought is to develop a random index = the total transitions between each value in the column / by the total possible transitions. In the matrix above, each column could have a total possible of 3 transitions.

For the example above:

Column 1 would have a random index of 0% (0/3)

Column 2 would have a random index of 66.7% (2/3)

Column 3 = 100% (3/3)

Column 4 = 0% (0/3) even though they are 1's and not 0's. Doesn't matter, I just want the transitions.

Can I draw a boundary around all the 1 values and then have MATLAB sum all of the boundaries?

Answer 1

Let your image be defined as

im = [ 0 1 0 1
       0 1 1 1
       0 0 0 1
       0 1 1 1 ];

The random index you want can be computed as

result = sum(diff(im)~=0) / (size(im,1)-1);

Explanation: diff computes the difference between consecutive elemtents down each column. The result is compared against zero ( ~=0 ), and all nonzero values within each row are added (with sum ). Finally, the result is divided by the maximum number os transitions, which is the number of rows minus 1 ( size(im,1)-1 )

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Equivalently, you could use xor between consecutive rows:

result = sum(xor(im(1:end-1,:), im(2:end,:))) / (size(im,1)-1)

Answer 2

To calculate what you are suggesting you can just do:

sum( diff(A) ~= 0 )

The diff(A) will take the forward difference down the columns and the sum will count the number of non-zero changes. So if you do this you will get:

ans =
     0     2     3     0