Hidden Space Dynamics using Relaxation HBR 180898

Now that the hidden dynamic system has been expressed in terms of a network of springs, the next problem is to evaluate the hidden dynamic sequence given the targets, target pliancies and segmentation/labelling.

One obvious solution is to simulate the physical system, and starting from some initial condition, release the beads to assume the rest position. Finding a solution this way is often referred to as "relaxation". To avoid these beads and springs oscillating (especially as it's a discrete-time simulation), we apply some damping (put the whole thing in treacle so the beads can't accelerate).

Such a simulation is shown in Fig 1. The initial condition is to set all of the beads to the same vertical position. There are 150 frames here divided into three segments, so for each frame there is an (unshown) spring attached to the target value, and 149 springs between the moving "beads".

Of course, using this iterative method requires quite a lot of computation. Fortunately, a solution to this problem can be found using a much more efficient Kalman filter algorithm.

This Kalman filter approach is described on the next page.