Paper ID sheet UCL-INMA-2018.04
- Title
-
Data fitting on manifolds with composite Bézier-like curves and blended cubic splines
- Authors
- Pierre-Yves Gousenbourger, Estelle Massart, P.-A. Absil
- Abstract
-
We propose several methods that address
the problem of fitting a $C^1$ curve $\gamma$ to time-labeled data
points on a manifold. The methods have a parameter, $\lambda$,
to adjust the relative importance of the two goals that
the curve should meet: being "straight enough" while
fitting the data "closely enough". The methods are designed for ease of use: they only require to compute
Riemannian exponentials and logarithms, they repre-
sent the curve by means of a number of tangent vectors
that grows linearly with the number of data points, and,
once the representation is computed, evaluating $\gamma(t)$ at
any $t$ requires a small number of exponentials and log-
arithms (independent of the number of data points).
Among the proposed methods, the blended cubic spline
technique combines the additional properties of inter-
polating the data when $\lambda \to \infty$ and reducing to the
well-known cubic smoothing spline when the manifold
is Euclidean. The methods are illustrated on synthetic
and real data.
- Key words
- Riemannian manifold; data fitting; curve
fitting; interpolation; smoothing; blended cubic spline
- Status
- Journal of Mathematical Imaging and Vision volume 61, pages 645–671 (2019)
- Download
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