Geometric PCA of curves and images

Jérémie Bigot (1) , Raul Gouet (2) , Alfredo Lopez (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

We describe a new method for analyzing the shape variability of images, called geometric PCA. Our approach is based on the use of random deformation operators to model the geometric variability of images around the same mean pattern. This leads to a new algorithm for estimating shape variability, and the consistency of this procedure is analyzed in statistical deformable models. Some numerical experiments on real and simulated data sets are proposed to highlight the benefits of this approach.

Mots clés: Geometric variability; Principal component analysis; Mean pattern estimation; Fréchet mean; Curve and image registration; Deformable models.; Deformable models

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Jérémie Bigot, Raul Gouet, Alfredo Lopez. Geometric PCA of curves and images. 2012. ⟨hal-00665434v1⟩