A Functional Linear Regression for High-Resolution 3D Faces

Many scientific disciplines are faced with the challenge of extracting meaningful information from large, complex and highly structured datasets. A significant portion of contemporary statistical research is dedicated to developing tools for handling such data. This paper introduces a functional linear regression model specifically designed for 3D facial shapes, which are viewed as manifolds. We propose a comprehensive framework that includes converting 3D facial data into functional objects, employing a functional principal component analysis method and utilising a function-on-scalar regression model. This framework facilitates computation for high-dimensional data and is employed to investigate how individual traits, such as age and genetic ancestry, impact the diversity of human facial features.