# Learning Fuzzy Set Representations of Partial Shapes on Dual Embedding Spaces

arXiv: https://arxiv.org/abs/1807.01519 · HTML: https://mlsanity.com/paper/1807.01519/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2018.

## Built on by (most cited first, 2 of 2)

- [Learning Spectral Unions of Partial Deformable 3D Shapes](https://mlsanity.com/paper/2104.00514/) (2021)
- [Diverse Part Synthesis for 3D Shape Creation](https://mlsanity.com/paper/2401.09384/) (2024)

## Abstract (arXiv)

Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of predefined semantic parts. We propose a novel framework based on neural networks that analyzes an uncurated collection of 3D models from the same category and learns two important types of semantic relations among full and partial shapes: complementarity and interchangeability. The former helps to identify which two partial shapes make a complete plausible object, and the latter indicates that interchanging two partial shapes from different objects preserves the object plausibility. Our key idea is to jointly encode both relations by embedding partial shapes as fuzzy sets in dual embedding spaces. We model these two relations as fuzzy set operations performed across the dual embedding spaces, and within each space, respectively. We demonstrate the utility of our method for various retrieval tasks that are commonly needed in geometric modeling interfaces.