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Visibility functions measure the relative visibility of noise added to a picture at those points where some measure of local activity exceeds a given threshold. The functions are obtained from a series of subjective experiments and vary with the content of the picture. Visibility functions have been used to design quantizing characteristics for DPCM coding of monochrome and color signals and for three-dimensional transform coding. We consider an alternative approach to determining the visibility function that obviates the need for repeated picture-dependent subjective tests. The visibility function is assumed to consist of two parts, a picture-dependent component and viewer-dependent component (referred to as the masking function). The visibility function may be approximated by the quotient of a probability density function raised to a power and the masking function. The role of probability is found to be weaker where the viewer has more opportunity to scrutinize the picture.