CvxNet: Learnable Convex Decomposition
Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This decomposition is fundamental in computer graphics, where it provides one of the most common ways to approximate geometry, for example, in real-time physics simulation. A convex object also has the property of being simultaneously an explicit and implicit representation: one can interpret it explicitly as a mesh derived by computing the vertices of a convex hull, or implicitly as the collection of half-space constraints or support functions. Their implicit representation makes them particularly well suited for neural network training, as they abstract away from the topology of the geometry they need to represent. However, at testing time, convexes can also generate explicit representations -- polygonal meshes -- which can then be used in any downstream application. We introduce a network architecture to represent a low dimensional family of convexes. This family is automatically derived via an auto-encoding process. We investigate the applications of this architecture including automatic convex decomposition, image to 3D reconstruction, and part-based shape retrieval.
Code (0)
등록된 구현이 없습니다.
Tasks
3D ReconstructionImage to 3DRetrievalSimilar Papers 제목 키워드 기반
ATD: Augmenting CP Tensor Decomposition by Self Supervision
Tensor decompositions are powerful tools for dimensionality reduction and feature interpretation of multidimensional data such as signals. Existing tensor decomposition objectives (e.g., Frobenius norm) are designed for …
Data AugmentationDimensionality ReductionSelf-Supervised LearningStochastic Optimization+1Novel convex decomposition of piecewise affine functions
In this paper, we present a novel approach to decompose a given piecewise affine (PWA) function into two convex PWA functions. Convex decompositions are useful to speed up or distribute evaluations of PWA functions. Diff…
Learning Convex Decomposition via Feature Fields
This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces hi…
Self-Supervised LearningConvex Decomposition And Efficient Shape Representation Using Deformable Convex Polytopes
Decomposition of shapes into (approximate) convex parts is essential for applications such as part-based shape representation, shape matching, and collision detection. In this paper, we propose a novel convex decompositi…
A non-convex approach to low-rank and sparse matrix decomposition
In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fr…