We generalize the notion of Bézier surfaces and surface splines to Riemannian manifolds.
To this end we put forward and compare three possible alternative definitions of Bézier …

We introduce techniques for the processing of motion and animations of non‐rigid shapes.
The idea is to regard animations of deformable objects as curves in shape space. Then, we …

Cubic splines in Euclidean space minimize the mean squared acceleration among all
curves interpolating a given set of data points. We extend this observation to the …

For decades, de Casteljau's algorithm has been used as a fundamental building block in
curve and surface design and has found a wide range of applications in fields such as …

Splines and subdivision curves are flexible tools in the design and manipulation of curves in
Euclidean space. In this paper we study generalizations of interpolating splines and …

The main contribution of this thesis concerns two larger mathematical topics. As a first topic,
we study the geodesic and spline interpolation of images in the framework of the …

Continuous image morphing is a classical task in image processing. The metamorphosis
model proposed by Trouvé, Younes, and coworkers [MI Miller and L. Younes, Int. J. Comput …

The space of images can be equipped with a Riemannian metric measuring both the cost of
transport of image intensities and the variation of image intensities along motion lines. The …

We describe a new de Casteljau–type algorithm for complex rational Bézier curves. After
proving that these curves exhibit the maximal possible circularity, we construct their points …

This paper investigates a variational model for splines in the image metamorphosis model
for the smooth interpolation of key frames in the space of images. The Riemannian manifold …