The quantitative research on length and area perception: A guidance on shape encoding in visual interface

Abstract

Shape encoding is one of the most important ways to convey information in a visual interface. Length and area are two crucial visual design elements for shape encoding. By exploring the quantitative research of length and area perception, we hope to provide a basis for shape encoding in a visual interface. Three groups of visual estimation experiments were conducted to investigate the perceived quantitative difference in length and area. A total of 32 observers (12 men and 20 women, ages ranging from 20 to 26 years, Mean = 21.7, SD = 1.9) were asked to perform three visual estimation tasks. Observers' subjective estimation variation was measured as a function of the following independent variables: length estimation, absolute area, and relative area estimation. The results showed that there was no computational noise in length perception. The span of shape is the primary estimation element for area estimation; In addition, length estimations of solid and dashed lines obey Weber's law (R2 = 0.997), while for the relative area ratio, R2 = 0.636, indicating somewhat less linearity, and the perceptual sensitivity is square compared to a circle, which is more sensitive than triangle; Finally, the separation effect appeared in the estimation of relative area, and there is a specific logarithmic relationship between the length and the area perception bias. The findings of this study provide valuable guidelines for designing more efficient and user-friendly shape encoding and visual interfaces in the future.