This paper focuses on the link between a visible linear and local distortion in a pictorial scene and its cost in terms of information theory quantities. In particular, a formal relation between the Michelson visual contrast and the Jensen-Shannon divergence (JSD) will be provided. A universal just noticeable threshold is also derived by maximizing JSD constrained to the greatest Michelson contrast of an invisible distortion. Such a threshold is independent of both distortion parameters and the probability density function of the degraded image. It is then able to measure the bits budget to be spent for leaving the distortion invisible. Some tests on both synthetic and real distorted images validate the theoretical findings. They confirm that the proposed universal threshold is really able to get the lower bound of human perception and then it may be useful for many applications, such as bit allocation in coding procedures and automatic parameters setting in restoration algorithms.