author = {Effland, Alexander and Rumpf, Martin and Simon, Stefan and Stahn,
	Kirsten and Wirth, Benedikt},
  title = {B\'{e}zier curves in the space of images},
  booktitle = {Proc. of International Conference on Scale Space and Variational
	Methods in Computer Vision},
  publisher = {Springer, Cham},
  year = {2015},
  volume = {9087},
  series = {Lecture Notes in Computer Science},
  pages = {372--384},
  abstract = {B\'ezier curves are a widespread tool for the design of curves in
	Euclidian space. This paper generalizes the notion of B\'ezier curves
	to the infinite-dimensional space of images. To this end the space
	of images is equipped with a Riemannian metric which measures the
	cost of image transport and intensity variation in the sense of the
	metamorphosis model by Miller and Younes. B\'ezier curves are then
	computed via the Riemannian version of de Casteljau's algorithm,
	which is based on a hierarchical scheme of convex combination along
	geodesic curves. Geodesics are approximated using a variational discretization
	of the Riemannian path energy. This leads to a generalized de Casteljau
	method to compute suitable discrete B\'ezier curves in image space.
	Selected test cases demonstrate qualitative properties of the approach.
	Furthermore, a B\'ezier approach for the modulation of face interpolation
	and shape animation via image sketches is presented.},
  arxiv = {}