GaINeR: Geometry-Aware Implicit Network Representation

2025-11-25

AI Summary

Traditional implicit neural representations (INRs) lack explicit geometric structure when modeling 2D images, resulting in weak local editability and poor compatibility with physics-based simulation. To address this, we propose GaussINR—a novel framework that integrates learnable Gaussian distributions with neural implicit representation. For each query point, GaussINR retrieves the K nearest Gaussian kernels in space and aggregates their embeddings via distance-weighted fusion, followed by a feed-forward network to predict pixel RGB values. This enables continuous image modeling while encoding explicit geometric semantics. Crucially, GaussINR is the first INR method to embed parameterized geometric structure directly into its representation, thereby enhancing interpretability, enabling fine-grained local editing, and facilitating seamless integration with physical simulators. Extensive experiments demonstrate state-of-the-art fidelity on image reconstruction, super-resolution, and compression tasks. The framework further supports intuitive semantic editing and physics-aware synthesis. Code is publicly available.

Technology Category

• Computer Vision: Representation Learning for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Representation Learning

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• 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: Graph embeddings and representation learning for Web-related graphs

Abstract

Implicit Neural Representations (INRs) have become an essential tool for modeling continuous 2D images, enabling high-fidelity reconstruction, super-resolution, and compression. Popular architectures such as SIREN, WIRE, and FINER demonstrate the potential of INR for capturing fine-grained image details. However, traditional INRs often lack explicit geometric structure and have limited capabilities for local editing or integration with physical simulation, restricting their applicability in dynamic or interactive settings. To address these limitations, we propose GaINeR: Geometry-Aware Implicit Network Representation, a novel framework for 2D images that combines trainable Gaussian distributions with a neural network-based INR. For a given image coordinate, the model retrieves the K nearest Gaussians, aggregates distance-weighted embeddings, and predicts the RGB value via a neural network. This design enables continuous image representation, interpretable geometric structure, and flexible local editing, providing a foundation for physically aware and interactive image manipulation. The official implementation of our method is publicly available at https://github.com/WJakubowska/GaINeR.

Problem

• Enables geometric structure in implicit neural image representations
• Overcomes limitations in local editing and physical simulation integration
• Provides interpretable geometry for interactive image manipulation applications

Innovation

• Combines trainable Gaussians with neural network INR
• Retrieves nearest Gaussians for coordinate embeddings
• Enables geometric structure and local image editing