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Sampling and interpolation of static images: a perceptual view,’’ (1993)

by M R M Nijenhuis
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Perceptual error measure and its application to sampled and interpolated single-edged images Perceptual-error measure and its application to sampled and interpolated single-edged images

by M R M Nijenhuis , F J J Blommaert
"... Error metrics quantify the difference between a reproduced image and the corresponding unprocessed original image. A drawback of the commonly used metrics such as the mean square error is their poor correlation with the perceived quality of the reproduced image. We present a framework for an altern ..."
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Error metrics quantify the difference between a reproduced image and the corresponding unprocessed original image. A drawback of the commonly used metrics such as the mean square error is their poor correlation with the perceived quality of the reproduced image. We present a framework for an alternative metric that uses the distance in a perceptual space to predict the perceived impairment of reproduced images. The perceptual space is spanned by perceptual artifacts that are introduced by image-reproduction techniques. For image reproduction using sampling and interpolation it is shown how such a multidimensional space can be determined from the image. The sensory strengths of the artifacts' periodic structure and blur are two of the orthogonal dimensions of this space. In addition, we demonstrate that, after the perceptual-error metric is calibrated to a particular observer, this metric can successfully predict experimentally determined subjective image quality of sampled and interpolated simple black-and-white images.
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... 1 ~m/m0! 3#1/3 2 1 ~m/m0! b , (10) where sv is the spread parameter of the Gaussian interpolation filter in the vertical direction, m is the modulation depth, b ' 0.7, and c is a constant such that 0 < Sp < 1. The parameter m0 is a periodic-structurethreshold parameter, and s0 is the spread parameter of a Gaussian interpolation function representing the intrinsic blur of the early visual pathway and including the optics of the eye. These last two parameters depend on the observer and must be determined experimentally. The modulation depth m is equal to m 5 2mp exp@22~p/d ! 2~s h 2 1 s 0 2!#, (11) where d is the sampling distance and sh is the spread of the Gaussian interpolation filter in the horizontal direction. We use the modulation depth of the first harmonic of the columnar structure because the first harmonic is a good predictor of the visibility of any periodic structure of not too low frequency.5 The attenuation factor mp that accounts for the interpolation of the columns of width w in Fig. 1 equals mp 5 sinc~w/d ! 5 sin~pw/d ! ~pw/d ! . (12) This factor is the attenuation of the spectral component at the sampling frequency (1/d) caused by a filter with a rectangular impulse r...

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