Optimal Spline Approximation via l0-Minimization

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dc.contributor.authorBrandt, Christopheren_US
dc.contributor.authorSeidel, Hans-Peteren_US
dc.contributor.authorHildebrandt, Klausen_US
dc.contributor.editorOlga Sorkine-Hornung and Michael Wimmeren_US
dc.date.accessioned2015-04-16T07:46:14Z
dc.date.available2015-04-16T07:46:14Z
dc.date.issued2015en_US
dc.description.abstractSplines are part of the standard toolbox for the approximation of functions and curves in Rd. Still, the problem of finding the spline that best approximates an input function or curve is ill-posed, since in general this yields a ''spline'' with an infinite number of segments. The problem can be regularized by adding a penalty term for the number of spline segments. We show how this idea can be formulated as an 0-regularized quadratic problem. This gives us a notion of optimal approximating splines that depend on one parameter, which weights the approximation error against the number of segments. We detail this concept for different types of splines including B-splines and composite Bézier curves. Based on the latest development in the field of sparse approximation, we devise a solver for the resulting minimization problems and show applications to spline approximation of planar and space curves and to spline conversion of motion capture data.en_US
dc.description.number2en_US
dc.description.sectionheadersSplines & Meshesen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume34en_US
dc.identifier.doi10.1111/cgf.12589en_US
dc.identifier.pages617-626en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12589en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectComputational Geometry and Object Modelingen_US
dc.subjectSplinesen_US
dc.titleOptimal Spline Approximation via l0-Minimizationen_US
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