Stanislav Katina

Masaryk University | Faculty of Science
, Institute of Mathematics and Statistics


Kotlářská 267/2, 611 37 Brno, Czech Republic


Keywords: Human face, curves, surfaces, automatic identification, penalised regression models, functional registration, functional principal component analysis, functional regression.

Location: Institute of Computer Science, Pod Vodárenskou věží 2, 180 00 Prague, Czechia

   Room 318

Date:   Thursday 19 October 2023

Time: 14:00 CET

Background: The advent of high-resolution imaging has made surface shape data widespread. Methods for the analysis of shapes based on points (landmarks) are well established, but high-resolution data require a functional approach.

Methods: First, a systematic and consistent description of each surface shape (using landmarks, curves (semi-landmarks), and surface patches (semi-landmarks)) and a method of automatic identification of this using penalised regression models with constraints and conditions are described. Second, the registration of curves and surfaces in functional form is discussed. Then the functional principal component (PC) analysis (PCA) of curves and surfaces and PC subspaces where interesting behaviour, such as population differences, is exhibited (rather than on individual PCs), are presented. Finally, functional regression models of curves and surfaces are defined.

Objectives: The aims is to set functional data analysis framework across whole process of facial data analysis.

Results: All these ideas are developed and illustrated in the important context of the human facial shape of healthy individuals, patients before and after orthognathic surgery, or patients with psychotic or other disorders and controls, with a strong emphasis on effective visual communication of effects of interest. All the methods presented here are implemented in R as part of the development of the face3d package.

Conclusions: We suggest using functional data analysis principles across whole facial data analysis, starting with automatic identification of semi-landmarks across human face, following by the registration (superimposition) of curves and surfaces, PCA of curves and surfaces, and regression models.

Acknowledgment: Project No. MUNI/A/1132/2022.

References: 

1. Katina, S., L. Vittert, and A. W. Bowman (2021). Data Analysis and Visualisation of Three-dimensional Surface Shape. Journal of Royal Statistical Society, Series C 70, 3, 691–713.

2. Vittert L., A. W. Bowman, and S. Katina (2020). A hierarchical curve-based approach to the analysis of manifold data. Annals of Applied Statistics 13, 4, 2539–2563.

3. Bowman, A. W., S. Katina, J. Smith, and D. Brown (2015). Anatomical curve identification. Computational Statistics and Data Analysis 86, 6, 52–64.