# The Whole Is Greater Than the Sum of Its Nonrigid Parts

arXiv: https://arxiv.org/abs/2001.09650 · HTML: https://mlsanity.com/paper/2001.09650/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2020.

## Built on by (most cited first, 7 of 7)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface](https://mlsanity.com/paper/2105.01905/) (2021)
- [Neural Fields as Learnable Kernels for 3D Reconstruction](https://mlsanity.com/paper/2111.13674/) (2021)
- [Registered and Segmented Deformable Object Reconstruction from a Single View Point Cloud](https://mlsanity.com/paper/2311.07357/) (2023)
- [Learning Spectral Unions of Partial Deformable 3D Shapes](https://mlsanity.com/paper/2104.00514/) (2021)
- [Partial Matching in the Space of Varifolds](https://mlsanity.com/paper/2103.12441/) (2021)
- [How to Register a Live onto a Liver ? Partial Matching in the Space of Varifolds](https://mlsanity.com/paper/2204.05665/) (2022)

## Abstract (arXiv)

According to Aristotle, a philosopher in Ancient Greece, "the whole is greater than the sum of its parts". This observation was adopted to explain human perception by the Gestalt psychology school of thought in the twentieth century. Here, we claim that observing part of an object which was previously acquired as a whole, one could deal with both partial matching and shape completion in a holistic manner. More specifically, given the geometry of a full, articulated object in a given pose, as well as a partial scan of the same object in a different pose, we address the problem of matching the part to the whole while simultaneously reconstructing the new pose from its partial observation. Our approach is data-driven, and takes the form of a Siamese autoencoder without the requirement of a consistent vertex labeling at inference time; as such, it can be used on unorganized point clouds as well as on triangle meshes. We demonstrate the practical effectiveness of our model in the applications of single-view deformable shape completion and dense shape correspondence, both on synthetic and real-world geometric data, where we outperform prior work on these tasks by a large margin.