Spherical averages and applications to spherical splines and interpolation

By S. Buss, Jay P. Fillmore. TOGS, 2001

346 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/c6925a1a863542fa9280ee05f3be0902048aedc5

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Barycentric subspace analysis on manifolds (2016, background): “We retrieve here the results of (Buss and Fillmore, 2001, lemma 2) expressed in a more general coordinate system.”
Geodesic finite elements on simplicial grids (2012, background): “Its usefulness for data interpolation on manifolds has been recognized by Buss and Fillmore [12] for M D S and by Moakher [13] for M D SO(3).”
Riemannian Lp center of mass: existence, uniqueness, and convexity (2011, methodology): “Buss and Fillmore show that for a discrete probability measure with finite support on the unit sphere in Rn, if the support is within a closed hemisphere and not contained entirely in the boundary, the global L2 center of mass is unique and belongs to the hemisphere.”
Medians and Means in Riemannian Geometry: Existence, Uniqueness and Computation (2011, background): “Fillmore showed in [17] that if the support of μ is not totally contained in the equator then μ has a unique Karcher mean which lies in the open hemisphere and equals to the Fréchet mean.”
Lie-algebraic averaging for globally consistent motion estimation (2004, background): “Following arguments in [1] it can be seen that this iteration is similar in spirit to a gradient-descent algorithm and always converges to a local minima.”
Geodesic Finite Elements of Higher Order (2015, methodology): “The idea to use shape functions as the weight functions in a Riemannian center of mass to obtain higher order interpolation also appeared in the work of Buss and Fillmore [5], who used it to construct spline curves on the sphere.”
Principal geodesic analysis for the study of nonlinear statistics of shape (2004, background): “Buss and Fillmore [28] prove for data on spheres, a value of is sufficient.”
Skinning with dual quaternions (2007, methodology): “Firstly, it is clear that DLB always returns a rigid transformation, because DLB computes a unit dual quaternion which can be subsequently converted to a rigid transformation matrix.”
Population Shape Regression from Random Design Data (2007, methodology): “Following the approach in [6], we solve the weighted averaging problem in (8) by a gradient descent algorithm.”
Skinning mesh animations (2005, background): “Finally, we note that averages of spherical quantities, such as quaternions, have been discussed in the graphics community for some time (see [Buss and Fillmore 2001]).”
Riemannian geometry for the statistical analysis of diffusion tensor data (2007, methodology): “Weighted averaging of data on an sphere S n has been studied by Buss and Fillmore [7].”