In models of complex motion processing of expanding, contracting or rotating patterns, localization of the center of motion is regarded as an implicit function of the system, used for heading determination and achieved by coarse population encoding. The situation modeled contains an optic flow pattern that is modified by including translational motion, as occurs when the observer is not looking directly at their heading, and relies on global processing of the entire optic flow field. Our psychophysics experiments show that accurately localizing the center of a symmetrical complex motion pattern, or an analogous complex radial or concentric form pattern, relies on local processing near the center of the pattern. This contrasts with detection of the same patterns, which involves considerable spatial summation, relies on global processing, and is very tolerant of noisy stimuli. Coarse localization uses both central and peripheral information, involving some spatial summation. Some differences are seen between different pattern types. The low level of spatial summation seen in position discrimination is surprising if position discrimination is seen as an implicit function of the global processing system, and suggests modifications may be needed to models of heading determination.