Kanizsa’s square may be the best known example of perceptual surface completion: a whole shape is perceived where only fragments of its bounding contour are present. But surface completion also plays a major role in perceiving whole objects from binarized pictures (‘two-tone’ images) such as Mooney faces. The binarization often causes lighter facets of the objects to merge with the background (or darker facets, for dark backgrounds), yet perceptually those regions appear figural, distinctly segregated from the background. For Kanizsa surfaces, it has been long known that perceptual completion is greatly reduced when the inducers are placed on a patterned background (e.g., a checkerboard). Here we show that patterned backgrounds produce detrimental effects on perceptual completion also in the case of two-tone images. Although this effect has not been previously described in the perception literature, analysis of a large corpus of work by the graffiti artist Banksy suggests that the type and condition of the background wall significantly affected his artistic choices. To minimize on-site production time, Banksy renders his famous subjects (e.g., the rat) by applying single-color paint over pre-fabricated stencils. When the wall is smooth, Banksy leaves the regions previously covered by the stencil unpainted, relying on observers’ perception to segregate figural regions from the (identically colored) background. But when the wall is patterned with large-scale luminance edges — e.g., due to bricks — Banksy takes the extra time to fill in unpainted figural regions with another color. This reveals the artist’s insight into perceptual processing, although it remains unknown whether the knowledge of the crucial effect of background patterns on perceptual completion is explicit or implicit.