Visual perception of an object depends on the discontinuity between the object and its background, which can be defined by a variety of visual features, such as luminance, colour and motion. While human object perception is largely cue invariant, the extent to which neural mechanisms in the primary visual cortex contribute to cue-invariant perception has not been examined extensively. Here we report that many V1 neurons in the awake monkey are sensitive to the stimulus discontinuity between their classical receptive field (CRF) and non-classical receptive field (nCRF) regardless of the visual feature that defines the discontinuity. The magnitude of this sensitivity is strongly dependent on the strength of nCRF suppression of the cell. These properties of V1 neurons may contribute significantly to cue-invariant object perception.