Shared Latent Membership Enables Joint Shape Abstraction and Segmentation With Deformable Superquadrics

Area of Science:

• Computer Vision
• Artificial Intelligence
• Computational Geometry

Background:

• Part-level 3D shape representation is vital for shape reasoning.
• Existing methods for shape abstraction and segmentation often rely on task-specific priors, leading to semantically inaccurate parts.
• 3D object point cloud analysis requires robust methods for part identification.

Purpose of the Study:

• To develop a unified, unsupervised framework for joint shape abstraction and shape segmentation.
• To overcome limitations of prior-dependent methods in 3D part analysis.
• To enable autonomous identification of common object parts without human supervision.

Main Methods:

• Formalized joint shape abstraction and segmentation as linear transformations in a shared latent space.
• Derived transformations based on k-means, Non-negative Matrix Factorization (NMF), and attention mechanisms.
• Introduced Latent Membership Pursuit (LMP) for joint optimization, utilizing deformable superquadrics (DSQs) for primitive representation.

Main Results:

• LMP successfully performs joint shape abstraction and segmentation in a fully unsupervised manner.
• The method autonomously identifies common object parts, linking points and parts for mutual reinforcement.
• Experiments demonstrate consistent 3D shape interpretations across instances and categories.

Conclusions:

• Latent Membership Pursuit (LMP) offers a novel, unsupervised approach to 3D shape analysis.
• The joint optimization framework enhances the accuracy and semantic relevance of identified object parts.
• This method advances 3D shape understanding by enabling consistent part discovery without reliance on predefined rules or data labels.