Radial frequency (RF) textures (created by applying a sinusoidal modulation of orientation to an otherwise circular texture) have been shown to be globally processed. RF textures differ from RF patterns (paths deformed from circular by a sinusoidal modulation in radius) in that the elements need not be constrained to a specific path. In the natural environment, objects differ from their background in texture, and a bounding contour can mark this textural change. This study examines the extent to which modulation of texture sums across space and whether the inclusion of a boundary between two areas provides a segmentation cue that limits the area over which summation occurs. RF textures were split into two annular regions and signal introduced to inner, outer, or both annuli Thresholds for the detection of RF modulation of orientation were not affected by the presence of a boundary. Further, it was found that the thresholds matched predictions for the independent contribution of the inner and outer areas to performance and that changing the relative phase of the modulation in the inner and outer annuli had no impact on performance, implying independent integration within the two annuli. Finally, integration of modulation information within the annuli was confirmed to ensure these results do apply to textures that are globally processed.