How do we represent extent in our spatial world? Recent work has shown that even the simplest spatial judgments — estimates of 2D area — present challenges to our visual system. Indeed, area judgments are best accounted for by ‘additive area’ (the sum of objects' dimensions) rather than ‘true area’ (i.e., a pixel count). But is ‘additive area’ itself the right explanation — or might other models better explain the results? Here, we offer two direct and novel demonstrations that ‘additive area’ explains area judgments. First, using stimuli that are simultaneously equated for number and all other confounding dimensions, we show that area judgments are nevertheless explained by ‘additive area’. Next, we show how ‘scaling’ models of area fail to explain even basic illusions of area. By contrasting squares with diamonds (i.e., the same squares, but rotated), we show a robust tendency to perceive the diamonds as having more area — an effect that no other model of area perception would predict. These results not only confirm the fundamental role of ‘additive area’ in judgments of spatial extent, but they highlight the importance of accounting for this dimension in studies of other features (e.g., density, number) in visual perception.

我们如何表示空间世界中的范围？最近的工作表明，即使是最简单的空间判断（即2D面积的估计）也给我们的视觉系统带来了挑战。实际上，面积判断最好用“附加面积”（物体的尺寸之和）而不是“真实面积”（即像素数）来解释。但是“加法区域”本身是正确的解释吗？还是其他模型可以更好地解释结果？在这里，我们提供了两个直接且新颖的演示，它们“加法区域”解释了区域判断。首先，使用同时等于数量和所有其他混杂维度的刺激，我们表明，区域判断仍然由“加法区域”来解释。接下来，我们展示区域的“缩放”模型如何无法解释甚至是区域的基本错觉。通过将正方形与菱形进行对比（即，相同的正方形，但旋转），我们表现出强烈的趋势来感知钻石具有更大的面积-这种效果是其他区域感知模型无法预测的。这些结果不仅证实了“加法面积”在空间范围判断中的基本作用，而且突出了在研究视觉感知的其他特征（例如密度，数量）时考虑这一维度的重要性。