Thanks so much for the clear explanation! There is a question about the transformation matrix I would like to ask. At 20:48, you have mentioned the transformation matrix was always a 4x4 matrix with 0001 in the bottom row. Could I ask what is the design logic of it? (I am sure there is some mathematical reason behind it. It would be appreciated if anyone could kindly help me to figure it out.
The affine transformation is something related to Geometric Transformations on Image Processing, this means that the transformations are related to the location of each of the pixels (or voxels), and not the intensity value of each pixel (or voxel). Imagine then, that the location of the voxel is given by a vector T = [tx, ty, tz]. Then, a Linear Transformation is a 3x3 matrix A, and an affine transformation is the sum of that plus a vector V = [vx, vy, vz], which is T' = A*T + V. You can compact that operation by appending a 1 to vector T and to vector V, and appending 0s to the columns of A. TL,DR: this is the "compact way" to do an affine transformation. Try to show this on a paper and you will see it is the case. I hope I helped ya!
Thank you so much for this. These videos are amazing. You have explained in very simple terms and easily digestible for a beginner in FSL.
Thanks for the informational video! It would be great if you show how to do rigid body/affine registration in the video.
Thanks so much for the clear explanation!
There is a question about the transformation matrix I would like to ask.
At 20:48, you have mentioned the transformation matrix was always a 4x4 matrix with 0001 in the bottom row. Could I ask what is the design logic of it? (I am sure there is some mathematical reason behind it. It would be appreciated if anyone could kindly help me to figure it out.
The affine transformation is something related to Geometric Transformations on Image Processing, this means that the transformations are related to the location of each of the pixels (or voxels), and not the intensity value of each pixel (or voxel). Imagine then, that the location of the voxel is given by a vector T = [tx, ty, tz]. Then, a Linear Transformation is a 3x3 matrix A, and an affine transformation is the sum of that plus a vector V = [vx, vy, vz], which is T' = A*T + V. You can compact that operation by appending a 1 to vector T and to vector V, and appending 0s to the columns of A.
TL,DR: this is the "compact way" to do an affine transformation. Try to show this on a paper and you will see it is the case. I hope I helped ya!