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''-dimension ...

and statistical shape analysis, principal geodesic analysis is a generalization of

principal component analysis Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing. The data is linearly transformed onto a new coordinate system such that th ...

to a non-Euclidean, non-linear setting of manifolds suitable for use with shape descriptors such as medial representations.

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