How to extract values from a matrix along a certain line (not vertical or horizontal).

Assume I have the following matrix:

A=[11 13 43 53 66 45 44 83 91;
   23 43 54 65 76 78 76 98 33;
   23 54 65 76 43 16 38 27 65]

I want to extract values from this matrix, along 45 degrees, to form a new matrix

B=[11 13 43 53 66 45 44;
   43 54 55 76 78 76 98;
   65 76 43 16 38 27 65]

How I can do it in MATLAB? Thanks.

Answer 1

[Image Analyst]

If you have the Image Processing Toolbox, simply use improfile().

[Image Analyst]

Or, call imrotate() to align the image with rows or columns, and extract a row or column. Should be pretty close to the same thing.

[Image Analyst]

improfile() will extract along a line at an arbitrary angle - it doesn't have to be exactly 45 degrees. You just specify the two endpoints of the line and how many points along that line you want to interpolate.

Answer 2

[Jan]

A = [11 13 43 53 66 45 44 83 91; ...
     23 43 54 65 76 78 76 98 33; ...
     23 54 65 76 43 16 38 27 65];
[m, n] = size(A);
index  = true(m, n);
index  = tril(triu(index), n - m);
B      = reshape(A(index), m, [])

[Image Analyst]

Doesn't give what he wanted, but I'm not sure how he got that anyway. For example it sort of appears that it's a rotation about the middle element, but not quite. Because using

B=imrotate(A, -45, 'crop')

will give

B =
     0    54    65    65    53    66     0     0     0
     0     0    76    76    76    45    45     0     0
     0     0     0    43    16    78    44    83     0

while Jan's code gives:

B =
    11    43    53    66    45    44    98
    13    54    65    76    78    76    27
    43    65    76    43    16    38    65

Neither of which is

B=[11 13 43 53 66 45 44;
   43 54 55 76 78 76 98;
   65 76 43 16 38 27 65]

which the user asked for. So I need Peng to explain how B was arrived at. Also, Jan's code is for 45 degrees, which is the example angle Peng wanted, but in the subject line Peng asked for an "Arbitrary angle:. So which is it?? 45 or arbitrary? And if it's just a rotation, then why is B two columns (but no rows) shorter? If anything a rotated matrix would be larger, and you can get that with the 'loose' option to imrotate() where it will expand the canvass to hold the entire rotated matrix.

[Peng]

Sorry, I did not state it clearly. I would like to extract value from a matrix along a line, e.g. for columns, the line is vertical, but now I want to extract the values along a line with 45 degrees. I am not sure if it is about the rotation of a matrix.