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The visual efficiency of an image compression technique depends directly on the amount of visually significant information it retains. By "visually significant" we mean information to which a human observer is most sensitive. The overall sensitivity depends on aspects such as contrast, color, spatial frequency, and so forth. One important aspect is the inverse relationship between contrast sensitivity and spatial frequency. This is described by the contrast sensitivity function (CSF). In compression algorithms the CSF can be exploited to regulate the quantization step-size to minimize the visibility of compression artifacts. Existing CSF implementations for wavelet-based image compression use the same quantization step-size for a large range of spatial frequencies. This is a coarse approximation of the CSF. This paper presents two new techniques that implement the CSF at significantly higher precision, adapting even to local variations of the spatial frequencies within a decomposition subband. The approaches can be used for luminance as well as color images. For color perception three different CSFs describe the sensitivity. The implementation technique is the same for each color band. Implemented into the JPEG2000 compression standard, the new techniques are compared to conventional CSF-schemes. The proposed techniques turn out to be visually more efficient than previously published methods. However, the emphasis of this paper is on how the CSF can be implemented in a precise and locally adaptive way, and not on the superior performance of these techniques.