Related papers: The Depth of a Hypersubstitution
We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…
Image deblurring is a notoriously challenging ill-posed inverse problem. In recent years, a wide variety of approaches have been proposed based upon regularization at the level of the image or on techniques from machine learning. We propose…
The regression depth of a hyperplane with respect to a set of n points in R^d is the minimum number of points the hyperplane must pass through in a rotation to vertical. We generalize hyperplane regression depth to k-flats for any k between…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
An accurate method for warping images is presented. Differently from most commonly used techniques, this method guarantees the conservation of the intensity of the transformed image, evaluated as the sum of its pixel values over the whole…
Accurate monocular depth estimation is crucial for 3D scene understanding, but existing methods often blur depth at object boundaries, introducing spurious intermediate 3D points. While achieving sharp edges usually requires very…
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
This article provides an overview of our joint work on binary polynomial optimization over the past decade. We define the multilinear polytope as the convex hull of the feasible region of a linearized binary polynomial optimization problem.…
Special scattered subwords, in which the gaps are of length from a given set, are defined. The scattered subword complexity, which is the number of such scattered subwords, is computed for rainbow words.
We derive an exact formula for the volume fraction of an inclusion in a body when the inclusion and the body are linearly elastic materials with the same shear modulus. Our formula depends on an appropriate measurement of the displacement…
The aim of this paper is to introduce a method for computing Hilbert decompositions (and consequently the Hilbert depth) of a finitely generated multigraded module $M$ over the polynomial ring $K[X_1,..., X_n]$ by reducing the problem to…
The notion of analyticity is studied in the context of hypercomplex numbers. A critical review of the problems arising from the conventional approach is given. We describe a local analyticity condition which yields the desired type of…
This paper surveys hyperinterpolation, a quadrature-based approximation scheme. We cover classical results, provide examples on several domains, review recent progress on relaxed quadrature exactness, introduce methodological variants, and…
Though there exists a reasonable forward model for blur based on optical physics, recovering depth from a collection of defocused images remains a computationally challenging optimization problem. In this paper, we show that with…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
We describe a method that predicts, from a single RGB image, a depth map that describes the scene when a masked object is removed - we call this "counterfactual depth" that models hidden scene geometry together with the observations. Our…
Stereo depth estimation relies on optimal correspondence matching between pixels on epipolar lines in the left and right images to infer depth. In this work, we revisit the problem from a sequence-to-sequence correspondence perspective to…
This paper collects some important formulas on hyperbolic volume. To determine concrete values of volume function is a very hard question requiring the knowledge of various methods. Our goal to give a non-elementary integral on the volume…
We introduce the concept of relational depth of a finite semigroup $S$ whose $J$-classes form a chain. It captures how far down in the ideal structure one is obliged to go in order to define the semigroup by generators and defining…
The halfspace depth is a prominent tool of nonparametric multivariate analysis. The upper level sets of the depth, termed the trimmed regions of a measure, serve as a natural generalization of the quantiles and inter-quantile regions to…