Glass patterns are visual textures composed of a field of dot pairs (dipoles) whose orientations are determined by a simple geometrical transformation, such as a rotation. Detection of structure in these patterns requires the observer to perform local grouping (to find dipoles) and global grouping to combine their orientations into a percept of overall shape. We estimated the spatial frequency tuning of these grouping processes by measuring signal-to-noise detection thresholds for Glass patterns composed of spatially narrow-band elements. Local tuning was probed by varying the spatial frequency difference between the two elements comprising each dipole. Global tuning was estimated using dipoles containing one spatial frequency and then estimating masking as a function of the spatial frequency of randomly positioned noise elements. We report that the tuning of local grouping is band-pass (ie, it is responsive to a narrow range of spatial frequencies), but that tuning of global grouping is broad and low-pass (ie, it integrates across a broader range of lower spatial frequencies). Control experiments examined how the contrast and visibility of elements might contribute to these findings. Local grouping proved to be more resistant to local contrast variation than global grouping. We conclude that local grouping is consistent with the use of simple-oriented filtering mechanisms. Global grouping seems to depend more on the visibility of elements that can be affected by both spatial frequency and contrast.