Stanislav Katina, Vojtěch Šindlář

Masaryk University, Czech Republic

Keywords: Shape analysis, human face, functional data analysis, statistical modelling

Location: ZOOM

Meeting ID: 539 400 8430

Passcode: 431432

Date: Wednesday 30 September 2020

Time: 14:00 CET

Background: Spatial interpolation and smoothing is usually done for one surface. In our case, we have random samples of such surfaces represented by human faces captured by stereo-photogrammetry and characterised by about 150,000 points. These points are triangulated by about 300,000 triangles. The number of points is extremely high for the purpose of statistical analyses, therefore the 3D coordinates of (semi)landmarks on curves or surface patches sufficiently characterising the shape have to be automatically identified and this simplified model comprising about 1000 points is then used in further statistical modelling in functional data analysis setting. The identification of (semi)landmarks is a complex process during which B-splines, P-splines and thin-plate splines are used together with the measures of local surface topology, including principal curvatures and shape index [1].

Methods: Shape index is calculated in R using different linear statistical models of z coordinates on x and y coordinates, i.e. quadratic with interaction without/with intercept, cubic with interaction of x and y without/with intercept (without/with other interactions), and similar models of higher order. The estimates of regression coefficients related to the quadratic terms and their interaction are elements of Weingarten matrix from which the principal curvatures are calculated. These models are applied on sufficiently large neighbourhood of all points in local 3D coordinate system.

Objectives: Since the measures of local surface topology represent principal guide in estimating locations of ridge and valley curves across the face [2], we aim to compare different linear models used in shape index calculation on faces of patients with facial palsy and healthy controls.

Results: Problems related to the surface imperfections could be solved by trimming unimportant surface regions around face and by winsorisation of outliers of principal curvatures. It could also lead to spatial smoothing of these characteristics or shape index.

Conclusions: We suggest to use quadratic or cubic model with interaction of the first order without intercept.

Acknowledgment: Project No. MUNI/A/1418/2019.

References:

1. Vittert L, AW Bowman, S Katina. A hierarchical curve-based approach to the analysis of manifold data. The Annals of Applied Statistics 13,4 (2019): 2539–2563.

2. Katina S, et al. The definitions of three-dimensional landmarks on the human face: an interdisciplinary view. Journal of anatomy 228,3 (2016): 355–365.