# Row and Column Interpolations

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Ozan Can Sahin on 5 Oct 2020
Commented: Steve Eddins on 5 Oct 2020
Hi everyone,
I'm new at MATLAB and I'm trying to implement a method proposed in a paper. In that paper it says "In the second phase column interpolation is performed by using bicubic interpolated image and the filtered image obtained from the first phase.", and it also has a row interpolation version of this sentence later on. But I didn't understand what is meant by row/column interpolations. I'd be glad if you can help me with that.
Cheers,
Ozan
KSSV on 5 Oct 2020

Steve Eddins on 5 Oct 2020
Edited: Steve Eddins on 5 Oct 2020
[Update: based on the comment thread below, it appears that "column interpolation" means something different than what I wrote in this answer. I'm leaving the answer in place so that the thread will make sense.]
In image processing, "column interpolation" and "row interpolation" refer to one-dimensional interpolation operations in either the vertical or the horizontal direction. For example, suppose you have a 3x3 matrix:
>> A = magic(3)
A =
8 1 6
3 5 7
4 9 2
Suppose I want to use "column interpolation" to estimate a value for A that is halfway between A(1,1) and A(2,1). Call it A(1.5,1). Using linear interpolation between A(1,1) and A(2,1) would give 0.5*8 + 0.5*3, or 5.5.
The following call to interp1 performs 1-D interpolation down each column ("column interpolation") of A using cubic interpolation.
>> B = interp1((1:3)',A,(1:0.5:3)','cubic')
B =
8.0000 1.0000 6.0000
4.7500 3.0000 7.2500
3.0000 5.0000 7.0000
2.7500 7.0000 5.2500
4.0000 9.0000 2.0000
Now let's perform row interpolation on B. The function interp1 doesn't support a "DIM" syntax for specifying the direction of interpolation, so to get row interpolation, first transpose B, then call interp1, then transpose the result.
>> C = interp1((1:3)',B',(1:0.5:3)','cubic')'
C =
8.0000 3.0000 1.0000 2.0000 6.0000
4.7500 3.1250 3.0000 4.3750 7.2500
3.0000 4.0000 5.0000 6.0000 7.0000
2.7500 5.6250 7.0000 6.8750 5.2500
4.0000 8.0000 9.0000 7.0000 2.0000
Performing 1-D cubic interpolation in one direction, followed by 1-D cubic interpolation of the result in the other direction, is called bicubic interpolation.
Steve Eddins on 5 Oct 2020
The diagram makes absolutely no sense to me. I'm sorry, but I don't have any idea what computation you are trying to perform.

R2020a

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