Orthogonal Curve Analysis of Human Scalp Shape
Authors: Li Peng 
Published: June 2022

This paper presents a shape analysis on orthogonal feature curves of 3D bald head scans with the intention of predicting scalp shape under the hair. While there are currently a number of large scale 3D head data collections available around the world, they unfortunately all suffer from hair obstruction preventing an accurate description of true scalp shape. This study is aimed at exploring the relationship between a small set of head anthropometric measurements and the feature curves of the scalp shape based on a small set of 3D bald head scans. The feature curves include scalp profile along the sagittal plane, coronal plane and a cross-sectional curve at the level of glabella.Introduction: The ever increasing availability of 3D scans of the human head has been a valuable source of information for improving head shape related equipment design and engineering with the goal of improving overall fit, sizing and comfort. However the existence of the hair prevents the actual recording and analysis of true scalp shape, and thus the analysis of scalp shape remains an elusive work. For this reason, much of the data analysis based on 3D head scans is mostly limited on facial shape and some facial landmarks. To overcome this limitation, it is desirable to be able to reconstruct the cranium shape from a few easy to obtain anthropometric measurements. In order to achieve this goal we obtained three orthogonal feature curves from 83 bald head scans and build regression equation between principal component scores of these curves and a number of head measurements such as head length, head breadth and tragion-to-top of head distance. The prediction error of these equations are evaluated. The approach: A total of 83 bald head scans taken in the 2012 anthropometric survey of US Army personnel (ANSUR II) from male soldiers are available for the analysis. From these bald head scans we identified three feature curves that principally define the scalp shape. These curves are a profile along the sagittal plane, a profile curve along the coronal plane and a cross-sectional curve at glabella level. These curves are then sampled in an equal angular space and grouped by their respective plane. The collection of each feature curves forms a shape space. We applied Principal Component Analysis (PCA) to those shape curves and decomposed the shape variation of each curve group into its respective principal axes. After conducting the PCA each curve group has a reduced dimension of 4~5 principal components that account for 95% of total variance. It shows major shape variations within each feature curve group. Then we apply multiple linear regression to the above head measurements and PCA scores of each curve group (Principal component regression or PCR). The regression equations for each curve and each PC were evaluated for their predicting power. From these regression equations the constituent feature curves can be selected from respective shape space based on head anthropometric measurements. Then PCR was also applied to the shape space of combined three curves as compared to prediction power in individual curve spaces.The results and discussion: PCR results from all orthogonal curve spaces and combined three curve space have similar predicting power as their R-squared value falling between 0.6 ~ 0.7. With a set of feature curves it is possible to further derive a 3D shape of the scalp. Although the three head measurements used in this study are effectively correlated to the first and second principal component in each group, other principal components contribute to subtle shape variations. This is an area need further analysis. We will also investigate methods to predicting 3D scalp shape from three feature curves and accuracy of the reconstruction of 3D scalp from those curves.