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Daniel Abdul-Malak, Frank Durgin; Dividing the legs of sheep: Does Burr's Australian stockman strategy work?. Journal of Vision 2009;9(8):980. doi: https://doi.org/10.1167/9.8.980.
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Whereas Durgin (1995; 2008) has proposed that aftereffects of visual number are due to texture density aftereffects, Burr and Ross (20080 have responded that using texture density to estimate visual numerosity is like an “Australian stockman” enumerating a herd of cattle “by counting the legs and dividing by four”. To test this hypothesis (with sheep), subjects first compared collections of sheep legs (black and white lines) and collections of black and white sheep with splayed legs. For our naïve observers, approximately 165 legs corresponded to 100 sheep in apparent numerosity. Whereas fast numerosity judgments between collections of like items can compare total texture “energy,” those of unlike elements must construct some unit of division. Establishing apparent numerosity between the collections permitted exploring whether adaptation to subjectively similar quantities of legs and sheep could still produce an adaptation effect due to the differing densities of legs. To be safe, we adapted subjects to 100 sheep and 200 legs on opposite sides of fixation. The total texture energy of the sheep was still, of course, much greater. Test stimuli were either sheep or legs. In both cases adaptation was greater in the region adapted to sheep, consistent with Durgin and Huk's (1998) finding of greater transfer of adaptation from low to high spatial-frequency elements, rather than Burr and Ross (2008) who proposed that visual numerosity adaptation is immune to element type. Much as early vision has access to texture information that is no longer available to higher vision, the modified Australian Cattleman strategy of measuring something akin to global texture energy and normalizing by local element energy is among the simplest models of numerosity estimation in homogenous textures. It is almost certainly wrong in detail, but it is probably less wrong than theories that suppose vision represents large multitudes independently of magnitudes.
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