According to numerous studies observers can rapidly and precisely evaluate mean or range of the set. Recent studies have shown that the mean size estimated based on sizes of objects rescaled to their distances (Tiurina & Utochkin, 2019). In the current study, we directly tested this rescaling mechanism on the perception of range using binocular and monocular cues.

In Experiment 1, a sample set of circles with different angular sizes and in different apparent distances were stereoscopically presented. Participants had to adjust the range of the test set to match the range of the sample set. The main manipulation was the size-distance correlation for sample and test sets: in negative size-distance correlation, the apparent range had to decrease, while in positive correlation - increase. We found the highest underestimation in the condition with the negative sample correlation and positive test correlation, which could be explained only if ensemble summary statistics were estimated after the item's rescaling.

In Experiment 2, we used Ponzo-like illusion and spatial positions as a depth cue. Sets were presented with positive, negative or without size-distance correlation on a grey background or the background with Ponzo-like illusion. We found that the range was underestimated in negative correlation and overestimated in positive correlation.

Thus, items of ensemble could be automatically rescaled according to their distance, based on both binocular and monocular cues, and ensemble summary statistics estimation is based on perceived sizes.

根据大量研究，观察者可以快速，准确地评估集合的均值或范围。最近的研究表明，根据物体的大小估计的平均大小会重新调整为它们的距离（Tiurina＆Utochkin，2019）。在当前的研究中，我们使用双目和单眼线索直接在距离感知方面测试了这种缩放机制。

在实验1中，以立体方式展示了一组具有不同角度大小和不同视距的圆形样本集。参与者必须调整测试集的范围以匹配样本集的范围。主要操作是样本和测试集的大小-距离相关：在负的大小-距离相关中，表观范围必须减小，而在正相关-中增大。我们发现在负样本相关性和正测试相关性的情况下，低估率最高，只有在对项目进行重新缩放后估计总体汇总统计量的情况下，这才可以得到解释。

在实验2中，我们使用了类似庞佐的幻觉和空间位置作为深度提示。在灰色背景或具有庞氏样错觉的背景下，呈现的集具有正，负或无大小距离相关性。我们发现该范围在负相关中被低估，而在正相关中被高估。

因此，基于双目和单眼线索，可以根据集合的距离自动调整集合项，并且集合摘要统计估计基于感知的大小。