A New Metric for Grey-Scale Image Comparison

Error measures can be used to numerically assess the differences between two images. Much work has been done on binary error measures, but little on objective metrics for grey-scale images. In our discussion here we introduce a new grey-scale measure, ^g, aiming to improve upon the most common grey-scale error measure, the root-mean-square error. Our new measure is an extension of the authors' recently developed binary error measure, ^b, not only in structure, but also having both a theoretical and intuitive basis. We consider the similarities between ^b and ^g when tested in practice on binary images, and present results comparing ^g to the root-mean-squared error and the Sobolev norm for various binary and grey-scale images. There are no previous examples where the last of these measures, the Sobolev norm, has been implemented for this purpose.