How can interpolation result be larger or smaller than the minimal/maximal values of the original signal?

Question

If I have a matrix

>> M=[0 0 1 1 0 ]
M =
     0     0     1     1     0

and resize it

>> imresize(M,[1,size(M,2)*2])

I get an answer

ans =
         0   -0.0234   -0.0703    0.2031    0.7969    1.0938    1.0938    0.7969    0.2031   -0.0703

My original array did not have any value less than 0 or greater than 1. How come it contains values greater than 1 or values lesser than 0?

Answer 1

I assume that your question was, "How come that the outcome of interpolation can be larger or smaller than the maximal or minimal value of the original signal".

The answer is that it depends on your interpolation type. For instance, if you do nearest-neighbor interpolation, it will not happen:

imresize(M,[1,size(M,2)*2],'nearest')
ans =

 0     0     0     0     1     1     1     1     0     0

It will not happen in bilinear as well:

imresize(M,[1,size(M,2)*2],'bilinear')
ans =
     0         0         0    0.2500    0.7500    1.0000    1.0000    0.7500    0.2500         0

It does happen in bicubic interpolation, which is the default:

 imresize(M,[1,size(M,2)*2],'bicubic')

That is indeed one of the properties of bicubic interpolation. To understand why it happens, take a look at the one-dimensional case (cubic interpolation):