vision Res. Vol. 30, No. 7, pp. 102~~1031, 1990 0042-6989/W $3.00 + 0.00 Printed in Great Britain. All rights nscrvcd Copyright 0 1990 Pergamon Press plc REGIONAL DISTRIBUTION OF THE MECHANISTS THAT UNDERLIE SPATIAL LOCALIZATION R. F. HESS’ and R. J. WAX-~ ‘The Physiological Laboratory, Downing Street, Cambridge, CB2 3EG, England and 2Department of Psychology, University of Stirling, Stirling, Scotland, U.K. (Received 6 April 1988; in &al revised fomt 20 December 1989) Abstract-In order to understand the regional distribution of the mechanisms which underlie localization accuracy we (1) chose a task which is known to involve localization accuracy (2) optimized stimulus parameters for eccentric loci and (3) determined how two key spatial factors which affect localization accuracy vary as a function of eccentricity. These involve Gaussian blur and Gaussian jitter. These results suggest that there are three different functions with eccentricity for the mechanisms underlying this task which we mlate to the spatial properties of the retina, namely mean cone density, receptoral convergence and regularity. Localization Hyperacuity Eccentricity Filters Cones. zyxwvutsrqponmlkjihgfedcbaZYXWVUTS INTRODUCTION Over the long history of vision research a lim- ited number of basic visual measures have emerged from which we have obtained most insight into the visual process. High up on this list are acuity, contrast sensitivity and localiz- ation accuracy. Each has given a rather different insight into visual processing, however their interrelationship is still obscure. This lack of understanding of the relationship between the mechanisms underlying these three basic visual measures is particularly evident whenever fovea1 and peripheral visual processing is compared. This has in turn impeded our understanding of one of the most important properties of functional organization, namely how the visual system processes information at different eccentricities. The question of how the mechanisms which underlie our vision vary with eccentricity has long been recognized as an important issue. Acuity measurements have traditionally been applied to answer this question since this measure tells us how the smallest visual filter varies as a function of eccentricity (Wertheim, 1894). Since there is evidence for a range of different sized filters subserving vision (Campbell & Robson, 1968; Blakemore & Campbell, 1969; Stromeyer & Julesz, 1972) it was seen to be important to know how their individual sensitivity varied with eccentricity. Robson and Graham (1981) and more recently Pointer and Hess (1989) showed that for stimuli above 1 c/leg, the fall-off in sensitivity is equiva- lent when eccentricity is considered in units of the spatial wavelength of the stimulus. Thus there is a linear scaling that relates how the ~nsiti~ty falls-off across eccentricity (in de- grees) for stimuli of different spatial frequency. One interpretation of this scaling is that filters of different size might have scaled distributions across the visual field. Another potentially important piece to the puzzle of how visual function varies with eccen- tricity involves the measure localization accu- racy. However, to date the approaches that have been adopted to provide this information have been disappointing. Most studies have used stimuli that provide several different cues for the subject to use. For example, Vernier acuity (Levi, Klein & Aitsebaomo, 1985) has orien- tation, spatial offset, phase and shape cues, and perhaps others. There is no reason to suppose that these all co-vary with eccentricity, or all relate to the same determining factors in per- formance. This means that it is difficult to reach conclusions about anything except how per- formance itself on the specific task varies with eccentricity. If we are to understand how the rn~~~~~~ that underlie localization accuracy vary with eccentricity then it is important to determine not how localization accuracy itself varies with eccentricity but how the most relevant factors that affect it vary as a function of eccentricity. For example, it is just as 1021