Estimating Physical Parameters from a Single Video using Neural Implicit Representations

Core Concepts

Our method can identify physical parameters like length, damping, and friction directly from a single video by combining neural implicit representations for appearance modeling with neural ordinary differential equations for dynamics modeling.

Abstract

The paper proposes a method that combines neural implicit representations for appearance modeling with neural ordinary differential equations (ODEs) for modeling planar physical phenomena. This allows estimating the unknown physical parameters and initial conditions of the ODE, as well as the parameters of the appearance representations, directly from a single input video. The key highlights are: The method can identify physical parameters like length, damping, and friction from a single video, without requiring large training datasets. It uses a parametric dynamics model in the form of an ODE, which enables interpretable physical parameters and long-term prediction in state space. The combination of the neural implicit representations and the ODE-based dynamics allows for photo-realistic rendering of novel scenes with modified physical parameters. Contrary to existing learning-based approaches, the proposed method is a per-scene model that does not suffer from generalization issues to out-of-distribution data. The paper evaluates the method on synthetic and real-world datasets, including a pendulum, a sliding block, and a thrown ball. The results show that the method can accurately recover the physical parameters and produce high-quality predictions, outperforming baseline approaches that require large training datasets.

Stats

The length of the pendulum is recovered with a relative error of less than 4.1%. The angle of the inclined plane for the sliding block is recovered with a relative error of 3.6%.

Quotes

"Contrary to existing learning-based approaches that require large corpora of training data, we propose a per-scene model, so that only a single short video clip that depicts the physical phenomenon is necessary." "The unique combination of powerful neural implicit representations with rich physical models allows to synthesize high-resolution and photo-realistic imagery. Moreover, it enables physical editing by rendering novel scenes with modified physical parameters."

Key Insights Distilled From

Neural Implicit Representations for Physical Parameter Inference from a Single Video

by Florian Hofh... at arxiv.org 04-03-2024

https://arxiv.org/pdf/2204.14030.pdf

Deeper Inquiries

How could the proposed method be extended to handle more complex 3D physical phenomena?

The proposed method could be extended to handle more complex 3D physical phenomena by incorporating volumetric representations and dynamics models. Currently, the method focuses on planar dynamics and 2D implicit representations. To handle 3D scenarios, the neural implicit representations could be extended to volumetric representations, such as 3D occupancy grids or signed distance functions. This would allow for the modeling of complex shapes and interactions in three dimensions. Additionally, the dynamics model based on ODEs could be extended to handle 3D motion and interactions, enabling the modeling of more intricate physical systems in three-dimensional space. By combining 3D implicit representations with 3D dynamics models, the method could effectively capture and analyze a wider range of complex 3D physical phenomena.

What are the limitations of the current ODE-based dynamics model, and how could it be further improved to handle a wider range of physical systems?

The current ODE-based dynamics model has limitations in terms of its expressiveness and flexibility to handle a wider range of physical systems. One limitation is that ODEs are limited in their ability to capture complex and nonlinear dynamics accurately. To improve the model's capability to handle a wider range of physical systems, more sophisticated differential equation models could be explored, such as partial differential equations (PDEs) or stochastic differential equations (SDEs). These models can better capture the dynamics of systems with spatial variations, randomness, or more intricate interactions. Additionally, the current ODE-based model may struggle with systems that exhibit chaotic behavior or discontinuities. To address this, advanced numerical methods for solving ODEs, such as adaptive step size control or higher-order integrators, could be implemented. These techniques can improve the accuracy and stability of the model when simulating complex and chaotic systems. Furthermore, incorporating domain knowledge and physical constraints into the ODE model can enhance its ability to represent a wider range of physical systems accurately. By integrating domain-specific information and constraints into the dynamics model, the ODE-based approach can be tailored to handle specific types of physical phenomena more effectively.

What other applications beyond physical parameter estimation could benefit from the combination of neural implicit representations and physics-based modeling?

The combination of neural implicit representations and physics-based modeling has a wide range of applications beyond physical parameter estimation. Some potential applications include: Computer Graphics and Animation: The integration of neural implicit representations with physics-based modeling can revolutionize computer graphics and animation. By accurately simulating physical interactions and dynamics, realistic and interactive virtual environments, characters, and effects can be created. Robotics and Autonomous Systems: The combination of neural implicit representations and physics-based modeling can enhance the perception and control capabilities of robots and autonomous systems. By incorporating physical constraints and dynamics into the models, robots can navigate complex environments, manipulate objects, and perform tasks more effectively. Medical Imaging and Simulation: In the field of medical imaging and simulation, the integration of neural implicit representations with physics-based modeling can improve the accuracy of diagnostic imaging, patient-specific simulations, and treatment planning. By simulating physiological processes and interactions, more realistic and personalized medical simulations can be developed. Virtual Reality and Augmented Reality: The combination of neural implicit representations and physics-based modeling can enhance the realism and interactivity of virtual and augmented reality experiences. By simulating physical interactions and dynamics in virtual environments, immersive and engaging user experiences can be created. Material Science and Engineering: In material science and engineering, the integration of neural implicit representations with physics-based modeling can facilitate the design and optimization of materials and structures. By simulating material properties, behaviors, and interactions, novel materials with specific characteristics can be developed. Overall, the combination of neural implicit representations and physics-based modeling has the potential to revolutionize various fields by enabling more accurate simulations, predictions, and analyses of complex systems and phenomena.