Question about affine transformation

[mkeays]

I am trying out the affine() function with a simple example matrix, and I noticed something that puzzled me. It seems to add an extra row and column to the transformed matrix even if the scaling factors are both 1:

> pre_aff <- matrix( rep( 1, 16 ), nrow = 4 )
> pre_aff
     [,1] [,2] [,3] [,4]
[1,]    1    1    1    1
[2,]    1    1    1    1
[3,]    1    1    1    1
[4,]    1    1    1    1
> mat <- matrix( c( 1, 0, 2, 0, 1, 3 ), nrow = 3 )
> mat
     [,1] [,2]
[1,]    1    0
[2,]    0    1
[3,]    2    3
> affine( pre_aff, mat, output.dim = c( 10, 10 ), antialias = FALSE )
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
 [1,]    0    0    0    0    0    0    0    0    0     0
 [2,]    0    0    1    1    1    1    1    0    0     0
 [3,]    0    0    1    1    1    1    1    0    0     0
 [4,]    0    0    1    1    1    1    1    0    0     0
 [5,]    0    0    1    1    1    1    1    0    0     0
 [6,]    0    0    1    1    1    1    1    0    0     0
 [7,]    0    0    0    0    0    0    0    0    0     0
 [8,]    0    0    0    0    0    0    0    0    0     0
 [9,]    0    0    0    0    0    0    0    0    0     0
[10,]    0    0    0    0    0    0    0    0    0     0

Is this expected behaviour? I thought that the above transformation matrix would simply translate the matrix to a new position but leave the dimensions the same as before the transformation.

[mkeays]

I just noticed that applying the affine() function with antialias = TRUE does not do this:

> affine( pre_aff, mat, output.dim = c( 10, 10 ), antialias = TRUE )
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
 [1,]    0    0    0    0    0    0    0    0    0     0
 [2,]    0    0    0    0    0    0    0    0    0     0
 [3,]    0    0    0    1    1    1    1    0    0     0
 [4,]    0    0    0    1    1    1    1    0    0     0
 [5,]    0    0    0    1    1    1    1    0    0     0
 [6,]    0    0    0    1    1    1    1    0    0     0
 [7,]    0    0    0    0    0    0    0    0    0     0
 [8,]    0    0    0    0    0    0    0    0    0     0
 [9,]    0    0    0    0    0    0    0    0    0     0
[10,]    0    0    0    0    0    0    0    0    0     0

[aoles]

Thank you for reporting this! Might be some rounding issue occurring in bilinear filtering step, will need to investigate.

If you are interested in performing pixel transformations which have a 1:1 pixel mapping between the input and the output such as translation by whole pixel coordinates or rotation by multiplies of 90 degrees consider using affine() with filter = "none". Another option is to use wrapper functions translate() or rotate() which set the appropriate arguments to for you.

Cheers, Andrzej

[mkeays]

Hi Andrzej,

Thanks very much for looking at this! I am quite new to this sort of analysis so I was trying out the function with a simple example to see what the result would be. I have a dataset from a collaborator with images and a transformation matrix defining an affine transform to align them. I'll try out the function with filter = "none" as you suggest.

Thanks, Maria