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Visual thresholds play an important role in the process of incorporating properties of the human visual system in encoding picture signals. They tell us how much the picture signal can be perturbed without the perturbations being visible to human observers. We describe psychovisual experiments to determine the amplitude thresholds at a single edge having a given slope and then present methods to incorporate the visual threshold data directly into the design of quantizers for use in Differential Pulse Code Modulation (DPCM) systems. In the first class of methods, quantizer characteristics are obtained such that the quantization error is kept below the visual threshold as determined by the slope at a picture element and either (a) the number of quantizer levels, or (b) the entropy of the quantized output is minimized. In the second class of methods, different measures of the suprathreshold quantization error are minimized for a fixed number of levels, or for a given constraint on the entropy of the quantized signal. We present empirical relationships between the various distortion measures and the subjective quality of the pictures rated on a five point impairment scale. We then discuss the structure of the quantizers obtained by the above mentioned optimization methods, evaluate their performance on real pictures, and compare them with the ones described in the literature.