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Generalized n-D C{sup}k B-Spline Scattered Data Approximation with Confidence Values

机译:广义N-D C {SUP} K B样条散射数据近似与置信度值

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The ability to reconstruct multivariate approximating or interpolating functions from sampled data finds many practical applications in medical image analysis. Parameterized reconstruction methods employing B-splines have typically utilized least-squares methodology for data fitting. For large sample sets, solving the resulting linear system is computationally demanding as well as susceptible to ill-conditioning. We present a generalization of a previously proposed fast surface fitting technique for cubic B-splines which avoids the pitfalls of the conventional fitting approach. Our proposed generalization consists of expanding the algorithm to n dimensions, allowing for arbitrary spline degree in the different parametric dimensions, permitting wrapping of the parametric domain, and the assignment of confidence values to the data points for more precise control over the fitting results. In addition, we implement our generalized B-spline approximation algorithm within the Insight Toolkit (ITK) for open source dissemination.
机译:从采样数据重建多变量近似或内插功能的能力在医学图像分析中找到了许多实际应用。采用B样条的参数化重建方法通常使用用于数据配件的最小二乘方法。对于大型样品集,解决所得到的线性系统是计算要求的要求,并且易于调节。我们展示了用于立方B样条的先前提出的快速表面拟合技术的概括,这避免了传统配件方法的缺陷。我们提出的泛化包括扩大算法n维,允许在不同的参数化尺寸任意样的程度,允许参数域的卷绕和信心值分配给数据点在拟合结果更精确的控制。此外,我们在Insight Toolkit(ITK)中实现了我们的广义B样条近似算法,以实现开源传播。

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