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Varying Weights

In May 2004, a further investigation of the ratio between shape and intensity began. As a result, ways of stabilising the objective function at a low convergence point, may have been identified. Otherwise, with this ratio improperly set, convergence (though not a full one) continuously appeared well above the correct solution. Figure shows what happens when the ratio is inadequately picked.

In the past (and seldom at present) the value of was chosen either to be a pre-set constant provided by the user, a value which is derived from the image derivatives, or a value that is proportional to the variances. In either case, it was always found to be overly high. When this value winds up taking shape into account, the objective function quickly fails to improve as shown below.

Figure: The old model-based objective function which gets stuck due to Ws inappropriately set.

Going back to Figurecap:Warps-shown-as, it can be seen what the shape is actually defined to be. The combined model is that which takes into account image intensity values along with the warps that accompany these newly-deformed values. The problem encountered resulted from the fact that all these curves were initially linear^7.15 and mutually identical. In other words, the shape defined for all data instances had no variance at all. It was therefore hard, using a proper combined model, to 'lure' the objective function to depart from that point of low variance. Warps were simply thrown away once they had been chosen.