Abstract
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, Δg, 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, Δb, not only in structure, but also having both a theoretical and intuitive basis. We consider the similarities between Δb and Δg when tested in practice on binary images, and present results comparing Δg 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.
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References
Abdou, I. E. and Pratt, W. K. 1979. Quantitative design and evaluation of enhancement/thresholding edge detectors. Proc. I. E. E. E., Vol. 67, No. 5, pp. 753-763.
Baddeley, A. J. 1992a. An error metric for binary images. In Robust Computer Vision, W. Förstner and S. Ruwiedel (Eds.), Karlsruhe, Wichmann, pp. 59-78.
Baddeley, A. J. 1992b. Errors in binary images and an Lp version of the Hausdorff metric. Nieuw Archief Voor Wiskunde, 10:157-183.
Borgefors, G. 1986. Distance transformations in digital images. Computer Vision, Graphics and Image Processing, 34:344- 371.
Bracewell, R. N. 1986. The Fourier Transform and its Applications. McGraw-Hill Book Company Inc.: NY.
Bryant, V. 1985. Metric Spaces: Iteration and Application. Cambridge University Press: Cambridge.
Canny, J. 1986. A computational approach to edge detection. I. E. E. E. Transactions on Pattern Analysis and Machine Intelligence, PAMI-8(6):679-698.
Choquet, G. 1966. Topology. Academic Press: NY, pp. 138-139.
Cornsweet, T. N. 1970. Visual Perception. Academic Press: NY, pp. 249-253.
Daly, S. 1993. The visible differences predictor: an algorithm for the assessment of image fidelity. In Digital Images and Human Vision, A. B. Watson (Ed.), MIT Press: Cambridge, Massachusetts, pp. 179-206.
Delp, E. J. and Mitchell, O. R. 1979. Image compression using block truncation coding. I. E. E. E. Trans. on Comm., COM-27(9):1335- 1342.
Dugundji, J. 1966. Topology. Allyn and Bacon, Inc.: Boston, pp. 83-85.
Gonzalez, R. C. and Woods, R. E. 1993. Digital Image Processing. Addison-Wesley, pp. 307-407.
Habibi, A. 1974. Hybrid coding of pictorial data. I. E. E. E. Trans. on Comm., COM-22(5):614-624.
Jain, A. K. 1981. Image data compression: A review. Proc. I. E. E. E., Vol. 69, No. 3, pp. 349-369.
Linde, Y., Buzo, A., and Gray, R. M. 1980. An algorithm for vector quantization design. I. E. E. E. Trans. on Comm., COM-28(1):84- 95.
Matheron, G. 1975. Random Sets and Integral Geometry. John Wiley & Sons: NY, pp. ix-x, 12-21, 128.
Natterer, F. 1986. The Mathematics of Computerized Tomography. John Wiley & Sons: Chichester, pp. 200-203.
Netravali, A. N. and Haskell, B. G. 1988. Digital Pictures, Representation and Compression. Plenum Press: NY, London, pp. 301- 501.
Peli, T. and Malah, D. 1982. A study of edge detection algorithms. Computer Graphics and Image Processing, 20:1-21.
Pratt, W. K. 1991. Digital Image Processing, second edition, John Wiley & Sons, Inc.: NY, pp. 538-543.
Rabbini, M. and Jones, P. W. 1991. Digital Image Compression Techniques. SPIE Optical Engineering Press.
Rosenfeld, A. 1969. Picture Processing by Computer. Academic Press: NY, pp. 1-5.
Serra, J. 1982. Image Analysis and Mathematical Morphology. Academic Press: London, pp. 34-90.
Tagare, H. D. and deFigueiredo, R. J. P. 1990. On the localisation performance measure and optimal edge detection. I. E. E. E. Transactions on Pattern Analysis and Machine Intelligence, 12(12):1186- 1190.
Teo, P. C. and Heeger, D. J. 1994a. Perceptual image distortion. In First International Conference on Image Processing.
Teo, P. C. and Heeger, D. J. 1994b. Perceptual image distortion (in press).
Vervaat, W. 1988. Narrow and vague convergence of set functions. Statistics and Probability Letters, 6:295-298.
Wallace, G. K. 1992. The JPEG still compression standard. I. E. E. E. Transactions on Consumer Electronics, 38(1):18-34.
Watson, A. B. (Ed.) 1993. Digital Images and Human Vision. MIT Press: Cambridge, Massachusetts, Chap. 3, pp. 139-140.
Woods, J. W. and O'Neil, S. D. 1986. Subband coding of images. I. E. E. E. Trans. Acoust. Speech Signal Processing, ASSP-34(5):1278-1288.
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Wilson, D.L., Baddeley, A.J. & Owens, R.A. A New Metric for Grey-Scale Image Comparison. International Journal of Computer Vision 24, 5–17 (1997). https://doi.org/10.1023/A:1007978107063
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DOI: https://doi.org/10.1023/A:1007978107063