Time-space registration is what you do all your waking time. Objects move, shake, jump, but it does not prevent you from recognizing & understanding their characteristics. The brain does the registration for you. For example, let's mimic what your eyes might see when you observe living cells through a microscope. (Movies below show epithelial cells with karotin). On the top left panel you see image distructed by a motion: the cells are moving, the microscope or the table is shaking. Can we make the movie steady without altering the image quality? Yes, we can. I wrote a Matlab registration algorithm that determines how far to shift each image in order to make the whole movie steady. The top right panel shows the result of the registration algorithm: the "calm" cells. There are 10 frames in the movie, as 10 consequtive microscope images.

acquired data

registered data

Now, lets imagine a more realistic scenario, at each acquisition the microscope zooms in (or the cell/tissue swells). Thus, in addition to the image shift, there is a non-uniform image transformation that occured over 15 steps (the lower left panel). The registration algorithm still works! (the lower right panel).

acquired data

registered data

Each color image consists of 256-by-256-by-3 pixels, which are acquired in 10 time steps, each time for 15 depths. Therefore, the algorithm works with a 5-D matrix.