Problem
Research questions and friction points this paper is trying to address.
Implicit Surfaces
As-Rigid-As-Possible
Regularization
Neural Shape Processing
As-Rigid-As-Possible Regularization for Implicit Surfaces
🤖 AI Summary
This study addresses the absence of efficient and precise As-Rigid-As-Possible (ARAP) regularization in implicit surface optimization by extending ARAP energy to implicit representations for the first time. By integrating point sampling with implicit differentiation, we establish a gradient-based framework that enables accurate evaluation and efficient optimization of ARAP energy. This approach effectively resolves geometric fidelity challenges in neural shape processing. Extensive experiments across diverse tasks demonstrate the method's versatility and superiority, establishing it as a novel regularization paradigm for implicit geometry optimization.
📝 Abstract
Implicit surface representations have regained popularity because of their use in machine learning. A common component in optimization is regularization, penalizing the deviation of the surface from its original shape. The popular as-rigid-aspossible (ARAP) energy strikes a good compromise between realistic deformation behavior and efficient computation, at least for piecewise linear meshes. We develop an approach for computing the ARAP energy of a deformation function based on point sampling of the surface. The implicit representation is exploited to provide differentials in each sample. The evaluation is efficient and exact in each sample (up to numerical precision). We demonstrate the general applicability of the method to neural shape processing in several applications and contrast its properties with alternatives from the literature.
Innovation
Methods, ideas, or system contributions that make the work stand out.
As-Rigid-As-Possible
Implicit Surfaces
Regularization
Neural Shape Processing
Point Sampling
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2024-02-13Citations: 1
