GENIE: Gram-Eigenmode INR Editing with Closed-Form Geometry Updates

TL;DR

This paper introduces a method for editing implicit neural representations of geometry using deformation eigenmodes derived from the Gram operator, enabling efficient, optimization-free shape modifications.

Contribution

It reveals that deformation eigenmodes can parameterize realistic shape edits and provides a closed-form update for geometry editing without retraining.

Findings

Deformation modes are recoverable only with rich sampling distributions.

A closed-form update enables geometry edits without optimization.

Editing is well-posed within the span of deformation modes.

Abstract

Implicit Neural Representations (INRs) provide compact models of geometry, but it is unclear when their learned shapes can be edited without retraining. We show that the Gram operator induced by the INR's penultimate features admits deformation eigenmodes that parameterize a family of realizable edits of the SDF zero level set. A key finding is that these modes are not intrinsic to the geometry alone: they are reliably recoverable only when the Gram operator is estimated from sufficiently rich sampling distributions. We derive a single closed-form update that performs geometric edits to the INR without optimization by leveraging the deformation modes. We characterize theoretically the precise set of deformations that are feasible under this one-shot update, and show that editing is well-posed exactly within the span of these deformation modes.