Author ORCID Identifier

https://orcid.org/0009-0000-4319-1191

Date of Award

Spring 6-10-2025

Document Type

Thesis (Master's)

Department or Program

Computer Science

First Advisor

Lorie Loeb

Second Advisor

Adithya K Pediredla

Third Advisor

Bo Zhu

Abstract

Representing implicit geometry with intricate features has long been a challenge. Recent advances in Implicit Neural Representations (INRs) have shown great promise in applications such as 3D reconstruction, inverse rendering, and dynamic surface evolution. These methods leverage neural networks to model complex shapes continuously, offering advantages in resolution and flexibility over traditional discrete representations. Despite their success, efficiently handling fine geometric details and evolving dynamic scenes remains an open problem.

We introduce a differentiable moving particle representation based on the multi-level partition of unity (MPU) to model dynamic implicit geometries efficiently. Our approach employs two types of particles—feature particles and sample particles—that move in space and generate dynamic surfaces under external velocity fields or optimization gradients. These particles iteratively guide and refine each other by alternating roles as inputs and outputs. Feature particles encode local quadratic patches, which are assembled using partition-of-unity weights to construct a continuous implicit shape. Sample particles, carrying position and orientation, serve as dense surface samples for optimization. To enhance adaptability, we incorporate a multi-level background grid that adjusts particle distribution dynamically. Our fully differentiable framework enables high-fidelity implicit geometry inference and evolution across various inverse tasks. We validate its effectiveness through benchmark comparisons with state-of-the-art neural representations, demonstrating lower memory consumption, fewer training iterations, and orders-of-magnitude higher accuracy in handling complex topologies and dynamic tracking tasks.

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