A New Metric for Grey-Scale Image Comparison

  • Authors:
  • Dale L. Wilson;Adrian J. Baddeley;Robyn A. Owens

  • Affiliations:
  • Department of Engineering Science, The University of Oxford. E-mail: dale@robots.ox.ac.uk;Department of Mathematics, The University of Western Australia. E-mail: adrian@maths.uwa.edu.au;Department of Computer Science, The University of Western Australia. E-mail: robyn@cs.uwa.edu.au

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

Error measures can be used to numerically assess the differencesbetween two images. Much work has been done on binary error measures,but little on objective metrics for grey-scale images. In ourdiscussion here we introduce a new grey-scale measure,Δ_g, aiming to improve upon the most commongrey-scale error measure, the root-mean-square error. Our new measureis an extension of the authors‘ recently developed binary errormeasure, Δ_b, not only in structure, but alsohaving both a theoretical and intuitive basis. We consider thesimilarities between Δ_b andΔ_g when tested in practice on binary images, andpresent results comparing Δ_g to theroot-mean-squared error and the Sobolev norm for various binary andgrey-scale images. There are no previous examples where the last ofthese measures, the Sobolev norm, has been implemented for thispurpose.