# Towards Learning Geometric Eigen-Lengths Crucial for Fitting Tasks

arXiv: https://arxiv.org/abs/2312.15610 · HTML: https://mlsanity.com/paper/2312.15610/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 34 references that are in the map.
- First posted on arXiv 25 Dec 2023.

## Builds on (most cited first, 25 of 25)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [AI2-THOR: An Interactive 3D Environment for Visual AI](https://mlsanity.com/paper/1712.05474/) (2017)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [SAPIEN: A SimulAted Part-based Interactive ENvironment](https://mlsanity.com/paper/2003.08515/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Where2Act: From Pixels to Actions for Articulated 3D Objects](https://mlsanity.com/paper/2101.02692/) (2021)
- [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)
- [kPAM: KeyPoint Affordances for Category-Level Robotic Manipulation](https://mlsanity.com/paper/1903.06684/) (2019)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Im2Vec: Synthesizing Vector Graphics without Vector Supervision](https://mlsanity.com/paper/2102.02798/) (2021)
- [3D AffordanceNet: A Benchmark for Visual Object Affordance Understanding](https://mlsanity.com/paper/2103.16397/) (2021)
- [Learning Disentangled Representations with Semi-Supervised Deep Generative Models](https://mlsanity.com/paper/1706.00400/) (2017)
- [Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single RGB Image](https://mlsanity.com/paper/2004.01176/) (2020)
- [KETO: Learning Keypoint Representations for Tool Manipulation](https://mlsanity.com/paper/1910.11977/) (2019)
- [KeypointDeformer: Unsupervised 3D Keypoint Discovery for Shape Control](https://mlsanity.com/paper/2104.11224/) (2021)
- [O2O-Afford: Annotation-Free Large-Scale Object-Object Affordance Learning](https://mlsanity.com/paper/2106.15087/) (2021)
- [Unsupervised Learning of Intrinsic Structural Representation Points](https://mlsanity.com/paper/2003.01661/) (2020)
- [Deep Parametric Shape Predictions using Distance Fields](https://mlsanity.com/paper/1904.08921/) (2019)
- [Unsupervised Learning of Visual 3D Keypoints for Control](https://mlsanity.com/paper/2106.07643/) (2021)
- [Learning to Manipulate Individual Objects in an Image](https://mlsanity.com/paper/2004.05495/) (2020)
- [GIFT: Generalizable Interaction-aware Functional Tool Affordances without Labels](https://mlsanity.com/paper/2106.14973/) (2021)
- [Early Visual Concept Learning with Unsupervised Deep Learning](https://mlsanity.com/paper/1606.05579/) (2016)

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

- [MaxMI: A Maximal Mutual Information Criterion for Manipulation Concept Discovery](https://mlsanity.com/paper/2407.15086/) (2024)
- [InfoCon: Concept Discovery with Generative and Discriminative Informativeness](https://mlsanity.com/paper/2404.10606/) (2024)
- [GOPLA: Generalizable Object Placement Learning via Synthetic Augmentation of Human Arrangement](https://mlsanity.com/paper/2510.14627/) (2025)

## Abstract (arXiv)

Some extremely low-dimensional yet crucial geometric eigen-lengths often determine the success of some geometric tasks. For example, the height of an object is important to measure to check if it can fit between the shelves of a cabinet, while the width of a couch is crucial when trying to move it through a doorway. Humans have materialized such crucial geometric eigen-lengths in common sense since they are very useful in serving as succinct yet effective, highly interpretable, and universal object representations. However, it remains obscure and underexplored if learning systems can be equipped with similar capabilities of automatically discovering such key geometric quantities from doing tasks. In this work, we therefore for the first time formulate and propose a novel learning problem on this question and set up a benchmark suite including tasks, data, and evaluation metrics for studying the problem. We focus on a family of common fitting tasks as the testbed for the proposed learning problem. We explore potential solutions and demonstrate the feasibility of learning eigen-lengths from simply observing successful and failed fitting trials. We also attempt geometric grounding for more accurate eigen-length measurement and study the reusability of the learned eigen-lengths across multiple tasks. Our work marks the first exploratory step toward learning crucial geometric eigen-lengths and we hope it can inspire future research in tackling this important yet underexplored problem.