STATISTICAL SHAPE ANALYSIS USING DEFORMETRICA : ESTIMATING MEAN SHAPE AND GEODESIC SHAPE TRAJECTORY
Open Access
- Author:
- Acharjee, Mithun
- Graduate Program:
- Statistics
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- June 22, 2021
- Committee Members:
- Matthew Logan Reimherr, Thesis Advisor/Co-Advisor
Jia Li, Committee Member
Ephraim Mont Hanks, Program Head/Chair - Keywords:
- Statistical Shape Analysis
Atlas Model
Geodesic Regression
Shape Trajectory
Mean Shape
Deformetrica
Facebase - Abstract:
- Statistical shape analysis is an emerging field of research that analyzes the geometrical properties of a given set of shapes or objects using different statistical methods. Two important aspects of the shape analysis are to estimate the mean shape from a given set of shapes and to estimate a shape trajectory as close as to the observed shapes in order to determine the continuous evaluation of shapes over time. A deterministic Atlas model is used to compute the mean shape (also referred to as atlas construction) from a set of shapes which builds a generalization of a typical representation by preserving the characteristics of the original shapes. Thus mean shape is useful in forecasting trends in form or pulling out stereotypes from a set of homologous shapes. The Geodesic regression is used to estimate the continuous shape evaluation at a certain time within its intervals where the mean face obtained from the deterministic atlas model can be used as baseline shape or initial template face to initiate the program. In this thesis, we are showing the application of the deterministic atlas model and geodesic regression model using a shape analysis software called Deformetrica. We collected data from the three Dimensional Facial Norm (3DFN) database which provides craniofacial anthropometric normative data deposited in the FaceBase consortium. Our data are 3D facial mesh where each facial mesh contains a high number of landmark points. We applied the deterministic atlas model using Deformetrica accessing the GPU allocation, which helps to estimate the mean facial object. We used this mean facial object as an initial template shape on geodesic regression which provides an estimated shape trajectory of the facial objects. This geodesic shape trajectory is a geodesic flow of diffeomorphisms acting on the above baseline template shape to estimate the continuous 3D facial evaluation with age varying continuously within its range. This thesis also describes the technical details of using Deformetrica in a high-performance computing environment while dealing a 3D geometric objects with a high number of landmark points.