  The "shape" of a planar curve and/or landmark configuration is considered its
equivalence class under translation, rotation and scaling, its "form" its
equivalence class under translation and rotation while scale is preserved. We
extend generalized additive regression to models for such shapes/forms as
responses respecting the resulting quotient geometry by employing the squared
geodesic distance as loss function and a geodesic response function to map the
additive predictor to the shape/form space. For fitting the model, we propose a
Riemannian $L_2$-Boosting algorithm well suited for a potentially large number
of possibly parameter-intensive model terms, which also yields automated model
selection. We provide novel intuitively interpretable visualizations for (even
non-linear) covariate effects in the shape/form space via suitable
tensor-product factorization. The usefulness of the proposed framework is
illustrated in an analysis of 1) astragalus shapes of wild and domesticated
sheep and 2) cell forms generated in a biophysical model, as well as 3) in a
realistic simulation study with response shapes and forms motivated from a
dataset on bottle outlines.
