# GenAnalysis: Joint Shape Analysis by Learning Man-Made Shape Generators with Deformation Regularizations

arXiv: https://arxiv.org/abs/2503.00807 · HTML: https://mlsanity.com/paper/2503.00807/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 110 references that are in the map.
- First posted on arXiv 2 Mar 2025.

## Builds on (most cited first, 30 of 50)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [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)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Efficient Test-Time Model Adaptation without Forgetting](https://mlsanity.com/paper/2204.02610/) (2022)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [SAM3D: Segment Anything in 3D Scenes](https://mlsanity.com/paper/2306.03908/) (2023)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [3D Point Capsule Networks](https://mlsanity.com/paper/1812.10775/) (2018)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [Learning elementary structures for 3D shape generation and matching](https://mlsanity.com/paper/1908.04725/) (2019)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [BAE-NET: Branched Autoencoder for Shape Co-Segmentation](https://mlsanity.com/paper/1903.11228/) (2019)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)

## Built on by (most cited first, 3 of 3)

- [Learning Convex Decomposition via Feature Fields](https://mlsanity.com/paper/2603.09285/) (2026)
- [Learning the Geometry of Data: A Mathematical Review of Shape Space Analysis](https://mlsanity.com/paper/2606.17022/) (2026)
- [GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models](https://mlsanity.com/paper/2607.00492/) (2026)

## Abstract (arXiv)

We present GenAnalysis, an implicit shape generation framework that allows joint analysis of man-made shapes, including shape matching and joint shape segmentation. The key idea is to enforce an as-affine-as-possible (AAAP) deformation between synthetic shapes of the implicit generator that are close to each other in the latent space, which we achieve by designing a regularization loss. It allows us to understand the shape variation of each shape in the context of neighboring shapes and also offers structure-preserving interpolations between the input shapes. We show how to extract these shape variations by recovering piecewise affine vector fields in the tangent space of each shape. These vector fields provide single-shape segmentation cues. We then derive shape correspondences by iteratively propagating AAAP deformations across a sequence of intermediate shapes. These correspondences are then used to aggregate single-shape segmentation cues into consistent segmentations. We conduct experiments on the ShapeNet dataset to show superior performance in shape matching and joint shape segmentation over previous methods.