# Implicit Modeling of Non-rigid Objects with Cross-Category Signals

arXiv: https://arxiv.org/abs/2312.10246 · HTML: https://mlsanity.com/paper/2312.10246/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 15 Dec 2023.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Predicting Semantic Map Representations from Images using Pyramid Occupancy Networks](https://mlsanity.com/paper/2003.13402/) (2020)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Deep Implicit Templates for 3D Shape Representation](https://mlsanity.com/paper/2011.14565/) (2020)
- [DualSDF: Semantic Shape Manipulation using a Two-Level Representation](https://mlsanity.com/paper/2004.02869/) (2020)
- [Curriculum DeepSDF](https://mlsanity.com/paper/2003.08593/) (2020)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Dynamic Plane Convolutional Occupancy Networks](https://mlsanity.com/paper/2011.05813/) (2020)
- [An Implicit Parametric Morphable Dental Model](https://mlsanity.com/paper/2211.11402/) (2022)

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

- [VecHeart: Holistic Four-Chamber Cardiac Anatomy Modeling via Hybrid VecSets](https://mlsanity.com/paper/2604.19403/) (2026)
- [S2MDF: A Plug-And-Play Layer for Intersection-Free Multi-Object Signed Distance Fields](https://mlsanity.com/paper/2605.29761/) (2026)
- [Automating Catheterization Labs with Real-Time Perception](https://mlsanity.com/paper/2403.05758/) (2024)

## Abstract (arXiv)

Deep implicit functions (DIFs) have emerged as a potent and articulate means of representing 3D shapes. However, methods modeling object categories or non-rigid entities have mainly focused on single-object scenarios. In this work, we propose MODIF, a multi-object deep implicit function that jointly learns the deformation fields and instance-specific latent codes for multiple objects at once. Our emphasis is on non-rigid, non-interpenetrating entities such as organs. To effectively capture the interrelation between these entities and ensure precise, collision-free representations, our approach facilitates signaling between category-specific fields to adequately rectify shapes. We also introduce novel inter-object supervision: an attraction-repulsion loss is formulated to refine contact regions between objects. Our approach is demonstrated on various medical benchmarks, involving modeling different groups of intricate anatomical entities. Experimental results illustrate that our model can proficiently learn the shape representation of each organ and their relations to others, to the point that shapes missing from unseen instances can be consistently recovered by our method. Finally, MODIF can also propagate semantic information throughout the population via accurate point correspondences