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This measure was explained and illustrated in the context of active appearance models where difference needs to guide model fitting. Its idea is primitive, nevertheless it is effective, especially when faced with the simplest class of tasks. Pixels are compared in two images one by one, their squared grey-level difference is calculated and a sum3.19 over all differences is returned - this obtains a sum of squared differences (SSD) in fact; MSD is simply normalised by the number of pixels which is a rational step to perform. This method is usually powerful if the two images compared are closely aligned and their intensity values are relatively continuous and low in contrast. In other words, MSD will tolerate only a low level of locally-situated difference, while contrariwise, MI and NMI rely on sparse dispersion of all pixels.
It is worth to consider suggestions on the issue of speeding up similarity measures. Some of the above measures depend heavily, from an efficiency point-of-view, on the dimensions of an image. As described in the context of active appearance models, a multi-resolution approach can be used to speed up the whole process. Blurring or averaging followed by re-sampling or sub-sampling allows for images of smaller size to be manipulated and complexity to be quadratically lessened. As the similarity measures are proportional to the images size, far better performance can be achieved by a transition from coarse to finer resolution. Pluim [] identifies the effects that this approach will have on the measurement of similarity.