geometric data analysis Geometric data analysis comprises geometric aspects of image analysis, pattern analysis, and shape analysis, and the approach of multivariate statistics, which treat arbitrary data sets as ''clouds of points'' in a space that is ''n''-dimensional. ...

and

statistical shape analysis Statistical shape analysis is an analysis of the geometrical properties of some given set of shapes by statistical methods. For instance, it could be used to quantify differences between male and female gorilla skull shapes, normal and pathological ...

, principal geodesic analysis is a generalization of

principal component analysis Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and ...

to a

non-Euclidean In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean ge ...

, non-linear setting of

manifolds In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a ...

suitable for use with shape descriptors such as

medial representation The medial axis of an object is the set of all points having more than one closest point on the object's boundary. Originally referred to as the topological skeleton, it was introduced in 1967 by Harry Blum as a tool for biological shape recogn ...

References

Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape

Probabilistic Principal Geodesic Analysis

Kernel Principal Geodesic Analysis

Mixture Probabilistic Principal Geodesic Analysis
Image processing Digital geometry Differential geometry Topology Factor analysis {{geometry-stub