Iskra: A System for Inverse Geometry Processing

We propose a system for differentiating through solutions to geometry processing problems. Our system differentiates a broad class of geometric algorithms, exploiting existing fast problem-specific schemes common to geometry processing, including local-global and ADMM solvers. It is compatible with machine learning frameworks, opening doors to new classes of inverse geometry processing applications. We marry the scatter-gather approach to mesh processing with tensor-based workflows and rely on the adjoint method applied to user-specified imperative code to generate an efficient backward pass behind the scenes. We demonstrate our approach by differentiating through mean curvature flow, spectral conformal parameterization, geodesic distance computation, and as-rigid-as-possible deformation, examining usability and performance on these applications. Our system allows practitioners to differentiate through existing geometry processing algorithms without needing to reformulate them, resulting in low implementation effort, fast runtimes, and lower memory requirements than differentiable optimization tools not tailored to geometry processing.

Low-Rank Adaptation of Neural Fields

Processing visual data often involves small adjustments or sequences of changes, such as in image filtering, surface smoothing, and video storage. While established graphics techniques like normal mapping and video compression exploit redundancy to encode such small changes efficiently, the problem of encoding small changes to neural fields (NF) -- neural network parameterizations of visual or physical functions -- has received less attention. We propose a parameter-efficient strategy for updating neural fields using low-rank adaptations (LoRA). LoRA, a method from the parameter-efficient fine-tuning LLM community, encodes small updates to pre-trained models with minimal computational overhead. We adapt LoRA to instance-specific neural fields, avoiding the need for large pre-trained models yielding a pipeline suitable for low-compute hardware. We validate our approach with experiments in image filtering, video compression, and geometry editing, demonstrating its effectiveness and versatility for representing neural field updates.