Precise attention filters for Weber contrast derived from centroid estimations.

How well can observers selectively attend only to dots that are lighter or darker than the background when all dot intensities are present? Observers estimated centroids of briefly flashed, sparse clouds of 8 or 16 dots, ranging in intensity from dark black to bright white on a gray background. Attention instructions were to equally weight: (i) dots brighter than the background, assigning zero weight to others; (ii) dots darker than the background, assigning zero weight to others; (iii) all dots. For each observer, a quantitative estimate of the operational attention filter (the weight exerted in the centroid estimates as a function of dot intensity) was derived for each attention instruction in each dot condition. Attended dots typically have 4× the weights of unattended dots. Whereas observers performed remarkably well in estimating centroids and achieving the three required attention filters, they achieved higher accuracy when equally weighing all dots than when selectively attending to dots of only one contrast polarity. Although their attention filters are similar, individual observers use significantly different parameters in their centroid computations. The complete model of performance enables perceptual measurements of observers' attention filters for shades of gray that are as accurate as physical measurements of color filters.