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Geometric shock-capturing ENO schemes for subpixel interpolation, computation, and curve evolution

机译:用于子像素插值,计算和曲线演化的几何震荡捕获ENO方案

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Subpixel interpolation methods often use local surface fits or structural models in a local neighborhood to obtain the interpolated curve. Whereas their performance is good in smooth regions of the curve, it is typically poor in the vicinity of singularities. Similarly, when geometric estimates are regularized, discontinuities are often blurred over, leading to poor estimates in their vicinity. We propose a geometric interpolation technique to overcome these limitations by: 1) not blurring across discontinuities, and 2) explicitly and accurately placing them. The essential idea is to prevent the propagation of information across singularities by explicitly placing a "shock"; information is only allowed to propagate from the smoother side. The placement of shocks is guided by geometric continuity constraints, resulting in subpixel interpolation with accurate geometric estimates. The interpolations are shown to be better than spline-like interpolations in smooth regions, and far better in discontinuous ones. We demonstrate the usefulness of the technique in capturing not only smooth evolving curves, but also discontinuous ones, even when multiple or entire curves are present in the same pixel.
机译:亚像素插值方法通常在局部邻域中使用局部表面拟合或结构模型来获得插值曲线。尽管它们在曲线的平滑区域中的性能很好,但是在奇异点附近的性能通常很差。同样,当对几何估计进行正则化时,不连续性通常会模糊不清,从而导致附近的估计不佳。我们提出了一种几何插值技术来克服这些限制,方法是:1)不使不连续性模糊不清,以及2)明确且准确地放置它们。基本思想是通过显式放置“冲击”来防止信息跨奇异点传播。信息仅允许从较平滑的一侧传播。震动的放置受几何连续性约束的指导,从而可以进行具有精确几何估计的子像素插值。所示插值在平滑区域比样条样插值要好,而在不连续区域则要好得多。我们证明了该技术不仅可以捕获平滑的演化曲线,而且还可以捕获不连续的曲线,即使在同一像素中存在多个或整个曲线时也很有用。

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