Related papers: Efficient manifold evolution algorithm using adapt…
Point cloud registration is a task to estimate the rigid transformation between two unaligned scans, which plays an important role in many computer vision applications. Previous learning-based works commonly focus on supervised…
Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…
In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of…
In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…
Background and Objective. B-spline interpolation (BSI) is a popular technique in the context of medical imaging due to its adaptability and robustness in 3D object modeling. A field that utilizes BSI is Image Guided Surgery (IGS). IGS…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…
BSplines are one of the most promising curves in computer graphics. They are blessed with some superior geometric properties which make them an ideal candidate for several applications in computer aided design industry. In this article,…
This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial…
The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…
The increasing availability of geometric data has motivated the need for information processing over non-Euclidean domains modeled as manifolds. The building block for information processing architectures with desirable theoretical…
Local perturbations around contours strongly disturb the final result of computer vision tasks. It is common to introduce a priori information in the estimation process. Improvement can be achieved via a deformable model such as the snake…
In this paper, we propose binary sparse convolutional networks called BSC-Net for efficient point cloud analysis. We empirically observe that sparse convolution operation causes larger quantization errors than standard convolution. However,…
Point clouds are an increasingly relevant data type but they are often corrupted by noise. We propose a deep neural network based on graph-convolutional layers that can elegantly deal with the permutation-invariance problem encountered by…
Point cloud analysis is challenging due to its unique characteristics of unorderness, sparsity and irregularity. Prior works attempt to capture local relationships by convolution operations or attention mechanisms, exploiting geometric…
Point clouds, as a form of Lagrangian representation, allow for powerful and flexible applications in a large number of computational disciplines. We propose a novel deep-learning method to learn stable and temporally coherent feature…
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that…
We present a prior for manifold structured data, such as surfaces of 3D shapes, where deep neural networks are adopted to reconstruct a target shape using gradient descent starting from a random initialization. We show that surfaces…
We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class,…