# Neural Implicit Shape Editing using Boundary Sensitivity

arXiv: https://arxiv.org/abs/2304.12951 · HTML: https://mlsanity.com/paper/2304.12951/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 24 Apr 2023.

## Builds on (most cited first, 21 of 21)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020)
- [Controlling Neural Level Sets](https://mlsanity.com/paper/1905.11911/) (2019)
- [Sketch2Mesh: Reconstructing and Editing 3D Shapes from Sketches](https://mlsanity.com/paper/2104.00482/) (2021)
- [3D Shape Generation with Grid-based Implicit Functions](https://mlsanity.com/paper/2107.10607/) (2021)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [Exploring Differential Geometry in Neural Implicits](https://mlsanity.com/paper/2201.09263/) (2022)
- [Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields](https://mlsanity.com/paper/2108.08931/) (2021)
- [Intuitive Shape Editing in Latent Space](https://mlsanity.com/paper/2111.12488/) (2021)
- [Local Distance Preserving Auto-encoders using Continuous k-Nearest Neighbours Graphs](https://mlsanity.com/paper/2206.05909/) (2022)

## Built on by (most cited first, 4 of 4)

- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing](https://mlsanity.com/paper/2405.12895/) (2024)
- [Diverse Topology Optimization using Modulated Neural Fields](https://mlsanity.com/paper/2502.13174/) (2025)
- [Refining 3D Medical Segmentation with Verbal Instruction](https://mlsanity.com/paper/2603.14496/) (2026)

## Abstract (arXiv)

Neural fields are receiving increased attention as a geometric representation due to their ability to compactly store detailed and smooth shapes and easily undergo topological changes. Compared to classic geometry representations, however, neural representations do not allow the user to exert intuitive control over the shape. Motivated by this, we leverage boundary sensitivity to express how perturbations in parameters move the shape boundary. This allows to interpret the effect of each learnable parameter and study achievable deformations. With this, we perform geometric editing: finding a parameter update that best approximates a globally prescribed deformation. Prescribing the deformation only locally allows the rest of the shape to change according to some prior, such as semantics or deformation rigidity. Our method is agnostic to the model its training and updates the NN in-place. Furthermore, we show how boundary sensitivity helps to optimize and constrain objectives (such as surface area and volume), which are difficult to compute without first converting to another representation, such as a mesh.