Learning Fuzzy Set Representations of Partial Shapes on Dual Embedding Spaces

TL;DR

This paper introduces a neural network framework that learns fuzzy set representations of partial 3D shapes to model their complementarity and interchangeability, enabling improved geometric retrieval tasks.

Contribution

It proposes a novel dual embedding space approach to jointly encode shape relations as fuzzy set operations, reducing reliance on labeled components.

Findings

Effective in modeling shape relations without labeled parts

Improves retrieval tasks in geometric modeling interfaces

Demonstrates the utility of fuzzy set embeddings for 3D shape analysis

Abstract

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.