Differentiable Topology Estimating from Curvatures for 3D Shapes
In the field of data-driven 3D shape analysis and generation, the estimation of global topological features from localized representations such as point clouds, voxels, and neural implicit fields is a longstanding challenge. This paper introduces a novel, differentiable algorithm tailored to accurately estimate the global topology of 3D shapes, overcoming the limitations of traditional methods rooted in mesh reconstruction and topological data analysis. The proposed method ensures high accuracy, efficiency, and instant computation with GPU compatibility. It begins with an efficient calculation of the self-adjoint Weingarten map for point clouds and its adaptations for other modalities. The curvatures are then extracted, and their integration over tangent differentiable Voronoi elements is utilized to estimate key topological invariants, including the Euler number and Genus. Additionally, an auto-optimization mechanism is implemented to refine the local moving frames and area elements based on the integrity of topological invariants. Experimental results demonstrate the method's superior performance across various datasets. The robustness and differentiability of the algorithm ensure its seamless integration into deep learning frameworks, offering vast potential for downstream tasks in 3D shape analysis.
Code (0)
등록된 구현이 없습니다.
Tasks
GPUTopological Data AnalysisSimilar Papers 제목 키워드 기반
SDFDiff: Differentiable Rendering of Signed Distance Fields for 3D Shape Optimization
We propose SDFDiff, a novel approach for image-based shape optimization using differentiable rendering of 3D shapes represented by signed distance functions (SDFs). Compared to other representations, SDFs have the advant…
3D ReconstructionMulti-View 3D ReconstructionSingle-View 3D ReconstructionHierarchical Part-based Generative Model for Realistic 3D Blood Vessel
Advancements in 3D vision have increased the impact of blood vessel modeling on medical applications. However, accurately representing the complex geometry and topology of blood vessels remains a challenge due to their i…
Graph GenerationRepresenting 3D Shapes with Probabilistic Directed Distance Fields
Differentiable rendering is an essential operation in modern vision, allowing inverse graphics approaches to 3D understanding to be utilized in modern machine learning frameworks. Explicit shape representations (voxels, …
3D ReconstructionNeurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains
We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3…
3D ReconstructionNumerical IntegrationShape from Projections via Differentiable Forward Projector for Computed Tomography
In computed tomography, the reconstruction is typically obtained on a voxel grid. In this work, however, we propose a mesh-based reconstruction method. For tomographic problems, 3D meshes have mostly been studied to simu…
Electron Tomography