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

Mots clés: Deformable models; Geometric variability; Principal component analysis; Mean pattern estimation; Fréchet mean; Curve and image registration; 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 images. 2012. ⟨hal-00665434v2⟩