Implicit and Nonparametric Shape Reconstruction from Unorganized Data Using a Variational Level Set Method

By Hongkai Zhao, Stanley J. Osher, Barry Merriman, Myung-joo Kang. 2000

320 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Yaron Lipman
2. Xavier Bresson
3. Matan Atzmon
4. Tom Goldstein
5. Lior Yariv
6. Stanley J. Osher
7. Vladimir G. Kim
8. Chohong Min

In Computer Graphics and Computer-Aided Design

1. Yaron Lipman
2. Xavier Bresson
3. Lior Yariv
4. Tom Goldstein
5. Matan Atzmon
6. Vladimir G. Kim
7. Amos Gropp
8. Niv Haim

In Computer Vision and Pattern Recognition

1. Xavier Bresson
2. Yaron Lipman
3. Tom Goldstein
4. Stanley J. Osher
5. Lior Yariv
6. Matan Atzmon
7. Luc Van Gool
8. Ming-Hsuan Yang

Citations in the corpus

• Deep Level Sets: Implicit Surface Representations for 3D Shape Inference (2019, background): “…of X = { x i } mi =1 and their corresponding normals N = { n i } mi =1 , and let d X ( x ) denote as the distance distance function to X , As in [36], we then define the following energy functional for the variational formulation, The above functional measures the deviation as the L p - norm of…”
• Local level set method in high dimension and codimension (2004, background): “Its successful applications include multiphase flows [17,19], surface reconstructions [6,7], and image processing [14,22].”
• Implicit Surface Representations As Layers in Neural Networks (2019, background): “As in [37], we then define the following energy functional for the variational formulation,”
• Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction (2010, methodology): “To build an implicit representation for these surfaces, an initial guess was first chosen using the initialization method of [52].”
• Implicit Geometric Regularization for Learning Shapes (2020, methodology): “Their work introduced a loss function inspired by the level set method (Osher et al., 2004) based surface reconstruction techniques (Zhao et al., 2000; 2001), operating directly on level sets of RGVF.”
• Convolutional neural networks on surfaces via seamless toric covers (2017, methodology): “We approximated the input with a genus-0 surface using a simple reconstruction algorithm [Zhao et al. 2000] and applied our method to it.”