How do we know how far an object is? If an object's size is known, its retinal image size can be used to judge its distance. To some extent, the retinal image size of an unfamiliar object can also be used to judge its distance, because some object sizes are more likely than others. To examine whether assumptions about object size are used to judge distance, we had subjects indicate the distance of virtual cubes in complete darkness. In separate sessions, the simulated cube size either varied slightly or considerably across presentations. Most subjects indicated a further distance when the simulated cube was smaller, showing that they used retinal image size to judge distance. The cube size that was considered to be most likely depended on the simulated cubes on previous trials. Moreover, subjects relied twice as strongly on retinal image size when the range of simulated cube sizes was small. We conclude that the variability in the perceived cube sizes on previous trials influences the range of sizes that are considered to be likely.

*small sizes*condition, the cube could have one of two sizes: sides of 1.0 and 1.2 cm. In the

*large sizes*condition, the simulated cube sizes were three times as large: sides of 3.0 and 3.6 cm. Cubes of all four sizes were presented at the same 60 positions. In the

*mixed sizes*condition, the 240 cubes presented in the

*small sizes*and

*large sizes*conditions were interleaved with 60 other cubes. Of the other cubes, 20 had sides of 0.5 cm, 20 had random sizes between 2.0 and 2.5 cm, and 20 had random sizes between 4.5 and 5.0 cm (see Figure 2). The three conditions were presented in separate sessions on different days. The order of the conditions was counterbalanced across subjects. Within each condition, the sizes and positions were presented in random order.

*influence of cube size*separately for the matched 1.0- and 1.2-cm cubes in the

*small sizes*and

*mixed sizes*conditions and for the matched 3.0- and 3.6-cm cubes in the

*large sizes*and

*mixed sizes*conditions. For every subject, we averaged these influences for the

*small sizes*and

*large sizes*conditions and did so for the two sizes of the

*mixed sizes*condition. We tested whether the influence of cube size was consistently smaller (indicating that the size prior is wider) in the mixed condition with a paired

*t*-test.

*small sizes*and

*large sizes*conditions were averaged, as were the slopes for the same cube sizes in the

*mixed sizes*condition. We tested whether these average slopes were consistently shallower (again indicating a wider prior) in the

*mixed sizes*condition with a paired

*t*-test.

*small sizes*condition and for the

*large sizes*condition the measure (influence of cube size) was determined across conditions and, therefore, in different sessions. We used this third measure to find out whether the expected size differs between the sessions. We anticipate that the expected size (i.e., the mean of the prior) will be influenced by recent experience even if the confidence in the expected size (i.e., in the width of the prior) is not. Unless the expected size changes, the size effect will scale with the ratio between the sizes involved (assuming that the expected size can be considered as a straightforward prior). We evaluate such scaling for the influence of cube size for small and large differences in size. We do so both for the mixed sizes condition, where we assume that there is a single expected size, and for the other two conditions, where we predict that there will be different expected sizes. We express the above-mentioned ratio between the sizes as the difference divided by the sum, in analogy with Michelson contrast.

*small sizes*condition (blue lines and dots), where all cubes had about the same simulated size, than in the

*mixed sizes*condition (green lines and dots), where there were many simulated cube sizes. The change in pointed distance with simulated distance is also larger in the

*small sizes*condition than in the

*mixed sizes*condition (blue lines have a steeper slope).

*mixed*condition is plotted as a function of the influence of cube size in the

*small*and

*large*conditions. Each subject is represented by two dots: a bigger dot for the difference in pointing at the larger pair of cubes and a smaller dot for the difference in pointing at the smaller pair of cubes. The open dot represents the data shown in Figure 3. When many cube sizes were simulated (

*mixed*condition), the influence of cube size was significantly smaller than it was when the simulated cube sizes never differed by more than 20% (

*small*and

*large*conditions;

*t*

_{11}= 6.4;

*p*< 0.001). The difference in pointed distance halved when there were many simulated cube sizes; the best linear fit is a line with a slope of 0.49 and an intercept of −0.1 cm.

*small sizes*and

*large sizes*conditions than for the

*mixed sizes*condition (

*t*

_{11}= 3.3;

*p*< 0.01). This is consistent with subjects relying more on retinal image size to judge distance (for identical targets) in the

*small sizes*and

*large sizes*conditions than in the

*mixed sizes*condition. For some subjects, the difference in slope between the conditions was larger than for others (larger deviation from the unity line in Figure 4B). Subjects for whom the average slope in the

*small sizes*and

*large sizes*conditions was clearly larger than the average slope in the

*mixed sizes*condition tended to have large differences between these conditions in the effect of retinal image size on pointing distance (larger deviation from the unity line in Figure 4A). The correlation across subjects between these two measures of the weight given to retinal image size as a cue to distance was 0.69.

*influence of cube size*when the difference in size was small (20%; always within conditions) with the

*influence of cube size*when the difference in size was large (determined across conditions when considering the

*small sizes*and

*large sizes*conditions). In all cases, the influence of cube size was determined for matched positions. If subjects use the same prior (the same size expectation, assigned the same weight), the two measures of size effect should only differ to the extent that the size ratio differs (line with a slope of 5.5). For the

*mixed sizes*condition, the points are close to the line, indicating that subjects use the same size prior for all cubes. This is not true for the

*small sizes*and

*large sizes*conditions, presumably because subjects learn to expect different sizes for the cubes in the

*large sizes*condition than in the

*small sizes*condition (which reduces the influence of retinal image size when comparing across sessions).

*object size prior*. Consistency in the perceived cube size increases the confidence in the judgment of the cube's distance from its retinal image size and therefore decreases the width (increases the height) of the

*object size prior*.

*small sizes*and

*large sizes*conditions, which corresponds to a weight of 25% being given to retinal image size. The average weight was reduced to 12% in the

*mixed sizes*condition.

*small sizes*and

*large sizes*conditions (solid symbols in Figure 5). Since size was not the only distance cue, the set of presented sizes became clearer during each session, and this affected further judgments within that session.

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