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Geometry Reconstruction from Noisy Data using a Radial Basis Function Partition of Unity Method

Elisabeth Larsson 1 Pierre-Frédéric Villard 2 Igor Tominec 1 Nicola Cacciani 3
2 TANGRAM - Recalage visuel avec des modèles physiquement réalistes
Inria Nancy - Grand Est, UL - Université de Lorraine, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, CNRS - Centre National de la Recherche Scientifique
Abstract : Manual three-dimensional segmentation of medical images results in noisy data sets representing three-dimensional objects. Based on this data, we look at how to perform a smooth object reconstruction. In particular, we are interested in the diaphragm, which is a thin curved volume. We use a partition of unity method where local object representations in each patch are blended into a global reconstruction. We use principal component analysis of the local data to align the local approximations with the data. Patches are adaptively refined based on local curvature. Due to the independence of the local approximations, we can increase the resolution in the thin dimension locally in each patch. We use infinitely smooth radial basis functions (RBF) to form a level set function with the object surface as its zero level set. Least squares approximation of the location, gradients, and values outside the object is employed to handle the noise in the data set. We evaluate the resulting reconstruction in terms of residual with respect to the initial data, local curvature, and visual appearance. We present guidelines for how to choose the method parameters, and investigate how they affect the result.
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https://hal.inria.fr/hal-03147251
Contributor : Pierre-Frédéric Villard Connect in order to contact the contributor
Submitted on : Friday, February 19, 2021 - 4:58:36 PM
Last modification on : Saturday, October 16, 2021 - 11:26:10 AM

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Identifiers

  • HAL Id : hal-03147251, version 1

Citation

Elisabeth Larsson, Pierre-Frédéric Villard, Igor Tominec, Nicola Cacciani. Geometry Reconstruction from Noisy Data using a Radial Basis Function Partition of Unity Method. SIAM Conference on Computational Science and Engineering, Mar 2021, Fort Worth/Virtual, United States. ⟨hal-03147251⟩

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