The ability to localize visual objects is a fundamental component of human behavior and requires the integration of position information from object components. The retinal eccentricity of a stimulus and the locus of spatial attention can affect object localization, but it is unclear whether these factors alter the global localization of the object, the localization of object components, or both. We used psychophysical methods in humans to quantify behavioral responses in a centroid estimation task. Subjects located the centroid of briefly presented random dot patterns (RDPs). A peripheral cue was used to bias attention toward one side of the display. We found that although subjects were able to localize centroid positions reliably, they typically had a bias toward the fovea and a shift toward the locus of attention. We compared quantitative models that explain these effects either as biased global localization of the RDPs or as anisotropic integration of weighted dot component positions. A model that allowed retinal eccentricity and spatial attention to alter the weights assigned to individual dot positions best explained subjects performance. These results show that global position perception depends on both the retinal eccentricity of stimulus components and their positions relative to the current locus of attention.