Related Experiment Video
Updated: Jul 31, 2026

Trajectory Data Analyses for Pedestrian Space-time Activity Study
Published on: February 25, 2013
Estimating average growth trajectories in shape-space using kernel smoothing
Tim J Hutton1, Bernard F Buxton, Peter Hammond
1Biomedical Informatics Unit, Eastman Dental Institute for Oral Health Care Sciences, University College London, 256 Gray's Inn Road, London WC1X 8LD, UK. T.Hutton@eastman.ucl.ac.uk
This study models human face shape changes during growth and aging using 3D scans. It reveals average facial development trajectories without needing long-term patient data, aiding in understanding facial morphology.
Area of Science:
- Biomedical Engineering
- Anthropometry
- Computer Vision
Background:
- Understanding human facial morphology changes over time is crucial for various applications.
- Existing methods often require extensive longitudinal data, which is difficult to obtain.
- High-dimensional shape-space analysis offers a novel approach to model complex biological structures.
Purpose of the Study:
- To compute a dense surface point distribution model of the human face.
- To demonstrate the utility of high-dimensional shape-space for analyzing facial growth and aging.
- To derive average human face growth trajectories using cross-sectional data.
Main Methods:
- Utilized a training dataset of 3D surface scans from 400 subjects (199 male, 201 female) aged 0-50 years.
- Developed a dense surface point distribution model for comprehensive facial shape representation.
- Applied kernel smoothing techniques to estimate average growth trajectories from population data.
Main Results:
- Successfully computed a detailed 3D facial shape model.
- Demonstrated that the high-dimensional shape-space effectively captures shape variations due to growth and aging.
- Generated average facial growth trajectories by analyzing the population's shape-space.
Conclusions:
- The developed facial shape model and high-dimensional shape-space are effective tools for studying human facial development.
- The method allows for the computation of average growth trajectories without longitudinal data, offering a valuable alternative.
- This research provides insights into facial morphology changes across the lifespan, with potential applications in medicine and computer graphics.
Related Concept Videos
Curvilinear Motion: Rectangular Components
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...
Curvilinear Motion: Normal and Tangential Components
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...
First Derivatives and the Shape of a Graph
Second Derivatives and the Shape of a Graph
Exponential Equations for Modeling Growth
Orthogonal Trajectories

