Related papers: B-spline normal multi-scale transforms for planar …
In this work we apply commonly known methods of non-adaptive interpolation (nearest pixel, bilinear, B-spline, bicubic, Hermite spline) and sampling (point sampling, supersampling, mip-map pre-filtering, rip-map pre-filtering and FAST) to…
Based on the continuous interpretation of deep learning cast as an optimal control problem, this paper investigates the benefits of employing B-spline basis functions to parameterize neural network controls across the layers. Rather than…
We introduce B-splines on the line of quaternionic order $B_q$ ($q$ in the algebra of quaternions) for the purposes of multi-channel signal and image analysis. The functions $B_q$ are defined first by their Fourier transforms, then as the…
This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…
A fast algorithm for B-splines in mixed models is presented. B-splines have local support and are computational attractive, because the corresponding matrices are sparse. A key element of the new algorithm is that the local character of…
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…
A theorem of McCann shows that for any two absolutely continuous probability measures on R^d there exists a monotone transformation sending one probability measure to the other. A consequence of this theorem, relevant to statistics, is that…
Using a particle model of Physarum displaying emer- gent morphological adaptation behaviour we demonstrate how a minimal approach to collective material computation may be used to transform and summarise properties of spatially represented…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
Multiscale transforms for real-valued data, based on interpolatory subdivision operators have been studied in recent year. They are easy to define, and can be extended to other types of data, for example to manifold-valued data. In this…
In this paper, we develop approximation error estimates as well as corresponding inverse inequalities for B-splines of maximum smoothness, where both the function to be approximated and the approximation error are measured in standard…
A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them.…
In convolutional neural networks (CNNs), pooling operations play important roles such as dimensionality reduction and deformation compensation. In general, max pooling, which is the most widely used operation for local pooling, is performed…
In this paper we study scalar multivariate subdivision schemes with general integer expanding dilation matrix. Our main result yields simple algebraic conditions on the symbols of such schemes that characterize their polynomial…
This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…
Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of a simple base distribution. However, there are often applications that require more than invertibility. For instance,…
Today, three-dimensional reconstruction of objects has many applications in various fields, and therefore, choosing a suitable method for high resolution three-dimensional reconstruction is an important issue and displaying high-level…
We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…
In this paper subdivision schemes, which are used for functions approximation and curves generation, are considered. In classical case, for the functions defined on the real line, the theory of subdivision schemes is widely known due to…
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…