Apart from technical difficulties (contact me privately if so), I would recommend the gray-scale extensions of Baddeley's Delta Metric to compare those images. The first one (by Wilson, Baddeley and Owen [1]) does not recover the original metric for binary images, but the second attempt (Coquin and Bolon [2]) does it. They hold nice properties for recognition but also face the most common problem in grayscale image comparison: how should we compensate (modulate) the variations in the spatial and tonal domain in one single metric output.
cheers,
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[1] A New Metric for Grey-Scale Image Comparison
[2] Application of Baddeley's distance to dissimilarity measurement between gray scale images