Error measures quantify the difference between a reproduced image and the corresponding unprocessed “original” image. Unfortunately, most of the existing error measures such as the mean-square-error (MSE) correlate poorly with the perceived quality of the reproduced images. The reason is that these measures either do not or insufficiently take the properties of the human visual system into account. The distance in a perceptual space spanned by artifacts relevant to the image reproduction techniques is used as a measure of the impairment of the reproduced image relative to the original image. For sampling and interpolation, we show how a two-dimensional perceptual space with the sensorial strengths of periodic structure and blur along the axes can be constructed from the physical parameters. The quantitative perceptual error measure can be used to determine a perceptually optimal combination of sampling and interpolation. The optimization problem is shown to be equivalent to minimizing a cost function known from standard regularization theory. The optimal solution is a compromise between conflicting demands in the perceptual space.