If your one matrix is having less number of rows than the other image columns, you can add number of ones so as to make the number of rows same as number of columns. This is called padding.

Forget about the padding!

I assume you have a registration result in the form of a 4x4 float matrix. And when that matrix is applied to Image1, it should fit on Image2.

If you want to display it on the same GRID as Image2, then you need to invert the matrix (like you said), and loop over all GRID points of Image2.

For volumes:

x1 = mat[0] * x2 + mat[4] * y2 + mat[8]  * z2 + mat[12];

y1 = mat[1] * x2 + mat[5] * y2 + mat[9]  * z2 + mat[13];

z1 = mat[2] * x2 + mat[6] * y2 + mat[10] * z2 + mat[14];

That gives you the coordinates of each Image2 grid point in Image1. You will need to interpolate in Image1 (e.g. catmull-rom) the get the pixel-value.

For images instead of volumes, leave out the z1 line and the z2 terms. The above array of 16 floats, assumes that the translations are 12, 13 and 14. It might be that you need to transpose your matrix.

If (x1,y1,z1) is outside Image1, use a dedicated 'outside' value. One could call this 'padding', be it a very different one than the gentlemen above refer to.

Note: in this code snippet, shearing and magnification is not supported; only translations and rotations.

how about resample the images so they have same size?

Hi Darshana,

By definition, you cannot compute the product of two matrices (matrix multiplication) usless the row-column orders meet the criterion for the product AxB. So theory says what you are trying to do is not defined.

So what to do? Well you must apply one of several ad-hoc methods to change the size of one (perhaps both) of the matrices. The problem is that you will introduce your own personal bias into the results, dependiing on what ad-hoc method you chose. The value padding (zeros, ones, etc) or resampling suggested by other contributors are two of the most common. To minimize observer bias, you can also apply such things as maximum entropy row and column extrapolation. It all depends on how theoretical you want to get.

Good luck

Thank you