In this letter, we propose a PDE model for 3D smooth surfaces reconstruction from 2D parallel slices. One of the terms in the PDE model is derived from a magnitude penalization term, which enforces the gradient magnitude of the volume to the minimum point of a well-defined potential function. This gives us smooth reconstructed surfaces when assuming that the surfaces are given by the zero-isosurfaces of the volumes. The PDE model has a second term whose parameter controls the ability of the reconstructed surfaces to satisfy the slices constraint. At the end of this letter, we show experiments of employing the proposed reconstruction model to reconstruct surfaces. The numerical results demonstrate the utility of the model.

中文翻译：

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用于从 2D 平行切片重建平滑表面的 PDE 模型

在这封信中，我们提出了一个 PDE 模型，用于从 2D 平行切片重建 3D 光滑表面。PDE 模型中的一项源自幅度惩罚项，它将体积的梯度幅度强制到明确定义的势函数的最小值点。当假设曲面由体积的零等值面给出时，这为我们提供了平滑的重建曲面。PDE 模型有第二项，其参数控制重建表面满足切片约束的能力。在这封信的末尾，我们展示了使用所提出的重建模型来重建表面的实验。数值结果证明了该模型的实用性。