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We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
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…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
Mobile devices equipped with a multi-camera system and an inertial measurement unit (IMU) are widely used nowadays, such as self-driving cars. The task of relative pose estimation using visual and inertial information has important…
To achieve visual consistency in composite images, recent image harmonization methods typically summarize the appearance pattern of global background and apply it to the global foreground without location discrepancy. However, for a real…
The image restoration problem is one of the popular topics in image processing studied by many authors on account of its applications in various areas. The aim of this paper is to present a new algorithm by using viscosity approximation…
Common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating radial…
Nonlinear lens distortion rectification is a common first step in image processing applications where the assumption of a linear camera model is essential. For rectifying the lens distortion, forward distortion model needs to be known.…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
Recovering the missing regions of an image is a task that is called image inpainting. Depending on the shape of missing areas, different methods are presented in the literature. One of the challenges of this problem is extracting features…
Finding suitable points for multivariate polynomial interpolation and approximation is a challenging task. Yet, despite this challenge, there has been tremendous research dedicated to this singular cause. In this paper, we begin by…
Copying an element from a photo and pasting it into a painting is a challenging task. Applying photo compositing techniques in this context yields subpar results that look like a collage --- and existing painterly stylization algorithms,…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
Determining the position and orientation of a calibrated camera from a single image with respect to a 3D model is an essential task for many applications. When 2D-3D correspondences can be obtained reliably, perspective-n-point solvers can…
Image matching is a key component of many tasks in computer vision and its main objective is to find correspondences between features extracted from different natural images. When images are represented as graphs, image matching boils down…
Image geolocalization is the task of identifying the location depicted in a photo based only on its visual information. This task is inherently challenging since many photos have only few, possibly ambiguous cues to their geolocation.…
This paper presents a practical method for finding the globally optimal solution to the sum-of-ratios problem arising in image processing, engineering and management. Unlike traditional methods which may get trapped in local minima due to…