[Insight-users] resampling and linear interpolation

[Michael Kuhn]

Hi,

I'm doing 3D registration. Unfortunately, my data sizes are too big to 
do a registration on the original data. Therefore I'm using a resample 
image filter to downscale my images. I assign it a linear interpolate 
image function and an affine transform. The idea of the affine transform 
is to

1) transform the output spacing into unit spacing (along all axis)
2) resample the output image at a less dense grid than the grid of the 
input image

This basically means, a scaling matrix has to be set for the affine 
transform, and unit spacing has to be set as the output spacing for the 
resample image filter.

The transform itself seems to work fine. However, when doing a 
registration of the pre transformed (downscaled, unit spacing) images, 
it turns out that the resulting (meansquares) metric value is always 
lower for non integer downscale factors than for integer ones (see 
sample below). I wonder if there is a mathematical or numerical cause 
for this problem (I thought about the linear interpolation that does not 
need to do any interpolation in the integer case).

Thanks,

Michael

Sample:
(1st column: downscale factor, 2nd column best meansquare metric value 
achieved for a registration run)
3    671076
3.01    493154
3.02    507410
3.03    519153
3.04    526705
3.05    530006
3.06    519486
3.07    506158
3.08    525221
3.09    511372
3.1    507557
3.11    501830
3.12    503091
3.13    514344
3.14    508190
3.15    504942
3.16    502145
3.17    508199
3.18    508164
3.19    509470
3.2    512111
3.21    499700
3.22    491668
3.23    510329
3.24    498813
3.25    502576
3.26    490604
3.27    494706
3.28    511005
3.29    510030
3.3    494550
3.31    496548
3.32    482143
3.33    471736
3.34    488468
3.35    494607
3.36    487787
3.37    480632
3.38    479595
3.39    499615
3.4    497371
3.41    493534
3.42    485106
3.43    481086
3.44    480180
3.45    488807
3.46    482753
3.47    481374
3.48    473041
3.49    466220
3.5    497818
3.51    468225
3.52    479928
3.53    466164
3.54    472708
3.55    461543
3.56    469550
3.57    457421
3.58    473226
3.59    469654
3.6    467439
3.61    460392
3.62    458992
3.63    457589
3.64    473349
3.65    462462
3.66    457830
3.67    453209
3.68    452390
3.69    462715
3.7    450983
3.71    466169
3.72    468178
3.73    459741
3.74    467537
3.75    463755
3.76    453383
3.77    451812
3.78    459649
3.79    461948
3.8    461665
3.81    454432
3.82    450894
3.83    444630
3.84    447712
3.85    455920
3.86    466395
3.87    456363
3.88    449726
3.89    452826
3.9    454229
3.91    446022
3.92    434137
3.93    440316
3.94    453348
3.95    447570
3.96    448920
3.97    447767
3.98    412571
3.99    432648
4    596577