SIAM Journal on Imaging Sciences, Volume 13, Issue 1, Page 265-290, January 2020.
We consider the problem of 3D shape reconstruction from multimodal data, given uncertain calibration parameters. Typically, 3D data modalities can come in diverse forms such as sparse point sets, volumetric slices, and 2D photos. To jointly process these data modalities, we exploit a parametric level set method that utilizes ellipsoidal radial basis functions. This method not only allows us to analytically and compactly represent the object; it also confers on us the ability to overcome calibration-related noise that originates from inaccurate acquisition parameters. This essentially implicit regularization leads to a highly robust and scalable reconstruction, surpassing other traditional methods. In our results we first demonstrate the ability of the method to compactly represent complex objects. We then show that our reconstruction method is robust both to a small number of measurements and to noise in the acquisition parameters. Finally, we demonstrate our reconstruction abilities from diverse modalities such as volume slices obtained from liquid displacement (similar to CT scans and X-rays) and visual measurements obtained from shape silhouettes as well as point clouds.

中文翻译：

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使用参数水平集方法在校准不确定性下进行多峰3D形状重建

SIAM影像科学杂志，第13卷，第1期，第265-290页，2020年1月。
在给定不确定的校准参数的情况下，我们考虑了从多峰数据重建3D形状的问题。通常，3D数据模态可以采用多种形式，例如稀疏点集，体积切片和2D照片。为了联合处理这些数据模态，我们利用了利用椭圆径向基函数的参数级集方法。这种方法不仅使我们能够分析和紧凑地表示对象；而且 它还使我们有能力克服由不准确的采集参数引起的与校准相关的噪声。这种本质上隐式的正则化导致高度健壮和可伸缩的重构，超越了其他传统方法。在我们的结果中，我们首先证明了该方法紧凑表示复杂对象的能力。然后，我们证明了我们的重建方法对于少量测量和采集参数中的噪声均具有鲁棒性。最后，我们通过多种方式展示了我们的重建能力，例如从液体位移获得的体积切片（类似于CT扫描和X射线）以及从形状轮廓以及点云获得的视觉测量结果。