Vernier acuity for opposite-contrast polarity stimuli clearly poses problems for local contrast models of relative position processing. In Expt 1 we show that vernier thresholds for abutting, or closely separated features of opposite-contrast polarity, are degraded across a wide range of stimulus strengths and configurations; but for widely separated stimuli they are more or less independent of contrast polarity (confirming and extending previous work). In Expts 2 and 3 we use a one-dimensional spatial noise masking paradigm to investigate to what extent the same mechanisms masked by this noise contribute to the relative position processing of same and opposite polarity stimuli. The orientation tuning functions determined using this paradigm are quite different for same and opposite polarity targets, for both line vernier acuity, and closely spaced two-dot alignment. However, for widely separated targets (24 min arc or more), they are similar. Over a range of separations from 3 to 30 min arc, for same and opposite polarity dots, masking is strongest at a spatial frequency of about 10 c/deg. Our results are consistent with the notion that signals from early (and relatively high spatial frequency) linear filters are collected in a second-stage nonlinear mechanism, which collates information along an orientation trajectory. We suggest that different properties of the mechanisms at each level of processing, can constrain positional acuity at small and large separations.