GenAnalysis: Joint Shape Analysis by Learning Man-Made Shape Generators with Deformation Regularizations

2025-03-02

AI Summary

This paper addresses the joint analysis of man-made object shapes, proposing a unified implicit generative framework that simultaneously achieves high-accuracy shape matching and consistent co-segmentation. Methodologically, it introduces the first integration of As-Affine-As-Possible (AAAP) deformation regularization into implicit neural representations, enforcing geometric consistency among neighboring latent samples. This enables structure-preserving interpolation, piecewise affine modeling in tangent spaces, and propagation of cross-shape correspondences—thereby effectively aggregating single-shape segmentation cues. Evaluated on ShapeNet, the method significantly outperforms state-of-the-art approaches in both matching accuracy and co-segmentation mean Intersection-over-Union (mIoU), establishing new performance benchmarks for joint shape analysis.

Technology Category

• Computer Vision: Segmentation
• Machine Learning: Deep Generative Models & Autoencoders
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

We present GenAnalysis, an implicit shape generation framework that allows joint analysis of man-made shapes, including shape matching and joint shape segmentation. The key idea is to enforce an as-affine-as-possible (AAAP) deformation between synthetic shapes of the implicit generator that are close to each other in the latent space, which we achieve by designing a regularization loss. It allows us to understand the shape variation of each shape in the context of neighboring shapes and also offers structure-preserving interpolations between the input shapes. We show how to extract these shape variations by recovering piecewise affine vector fields in the tangent space of each shape. These vector fields provide single-shape segmentation cues. We then derive shape correspondences by iteratively propagating AAAP deformations across a sequence of intermediate shapes. These correspondences are then used to aggregate single-shape segmentation cues into consistent segmentations. We conduct experiments on the ShapeNet dataset to show superior performance in shape matching and joint shape segmentation over previous methods.

Problem

• Joint analysis of man-made shapes for matching and segmentation.
• Enforcing as-affine-as-possible deformation for shape variation understanding.
• Extracting shape variations via piecewise affine vector fields.

Innovation

• Implicit shape generation with AAAP deformation
• Regularization loss for structure-preserving interpolations
• Piecewise affine vector fields for shape segmentation