scholarly journals User-guided Image Editing using Radial Basis Functions

2021 ◽  
Author(s):  
◽  
Evgeny Patrikeev
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Image Point ◽  
Image Editing ◽  
Image Region ◽  
Image Deformation ◽  
User Input ◽  
Advantages And Disadvantages ◽  
Edit Propagation ◽  
Radial Basis

<p>Good image editing tools that modify colors of specified image regions or deform the depicted objects have always been an important part of graphics editors. Manual approaches to this task are too time-consuming, while fully automatic methods are not robust enough. Thus, the ideal editing method should include a combination of manual and automated components. This thesis shows that radial basis functions provide a suitable “engine” for two common image editing problems, where interactivity requires both reasonable performance and fast training.  There are many freeform image deformation methods to be used, each having advantages and disadvantages. This thesis explores the use of radial basis functions for freeform image deformation and compares it to a standard approach that uses B-spline warping.  Edit propagation is a promising user-guided color editing technique, which, instead of requiring precise selection of the region being edited, accepts color edits as a few brush strokes over an image region and then propagates these edits to the regions with similar appearance. This thesis focuses on an approach to edit propagation, which considers user input as an incomplete set of values of an intended edit function. The approach interpolates between the user input values using radial basis functions to find the edit function for the whole image.  While the existing approach applies the user-specified edits to all the regions with similar colors, this thesis presents an extension that propagates the edits more selectively. In addition to color information of each image point, it also takes the surrounding texture into account and better distinguishes different objects, giving the algorithm more information about the user-specified region and making the edit propagation more precise.</p>

scholarly journals User-guided Image Editing using Radial Basis Functions

2021 ◽  
Author(s):  
◽  
Evgeny Patrikeev
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Image Point ◽  
Image Editing ◽  
Image Region ◽  
Image Deformation ◽  
User Input ◽  
Advantages And Disadvantages ◽  
Edit Propagation ◽  
Radial Basis

<p>Good image editing tools that modify colors of specified image regions or deform the depicted objects have always been an important part of graphics editors. Manual approaches to this task are too time-consuming, while fully automatic methods are not robust enough. Thus, the ideal editing method should include a combination of manual and automated components. This thesis shows that radial basis functions provide a suitable “engine” for two common image editing problems, where interactivity requires both reasonable performance and fast training.  There are many freeform image deformation methods to be used, each having advantages and disadvantages. This thesis explores the use of radial basis functions for freeform image deformation and compares it to a standard approach that uses B-spline warping.  Edit propagation is a promising user-guided color editing technique, which, instead of requiring precise selection of the region being edited, accepts color edits as a few brush strokes over an image region and then propagates these edits to the regions with similar appearance. This thesis focuses on an approach to edit propagation, which considers user input as an incomplete set of values of an intended edit function. The approach interpolates between the user input values using radial basis functions to find the edit function for the whole image.  While the existing approach applies the user-specified edits to all the regions with similar colors, this thesis presents an extension that propagates the edits more selectively. In addition to color information of each image point, it also takes the surrounding texture into account and better distinguishes different objects, giving the algorithm more information about the user-specified region and making the edit propagation more precise.</p>

scholarly journals Use of Multiquadric Functions for Multivariable Representation of the Aerodynamic Coefficients of Airfoils

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Filipe Ribeiro ◽  
Pedro Albuquerque ◽  
Pedro Gamboa ◽  
Kouamana Bousson
Keyword(s):  
Radial Basis Functions ◽  
Piecewise Linear ◽  
Research Work ◽  
Computational Cost ◽  
Basis Functions ◽  
Aerodynamic Coefficients ◽  
Independent Variables ◽  
Advantages And Disadvantages ◽  
Radial Basis ◽  
Multivariable Interpolation

Given an array (or matrix) of values for a function of one or more variables, it is often desired to find a value between two given points. Multivariable interpolation and approximation by radial basis functions are important subjects in approximation theory that have many applications in Science and Engineering fields. During the last decades, radial basis functions (RBFs) have found increasingly widespread use for functional approximation of scattered data. This research work aims at benchmarking two different approaches: an approximation by radial basis functions and a piecewise linear multivariable interpolation in terms of their effectiveness and efficiency in order to conclude about the advantages and disadvantages of each approach in approximating the aerodynamic coefficients of airfoils. The main focus of this article is to study the main factors that affect the accuracy of the multiquadric functions, including the location and quantity of centers and the choice of the form factor. It also benchmarks them against piecewise linear multivariable interpolation regarding their precision throughout the selected domain and the computational cost required to accomplish a given amount of solutions associated with the aerodynamic coefficients of lift, drag and pitching moment. The approximation functions are applied to two different multidimensional cases: two independent variables, where the aerodynamic coefficients depend on the Reynolds number (Re) and the angle-of-attack (α), and four independent variables, where the aerodynamic coefficients depend on Re, α, flap chord ratio (cflap), and flap deflection (δflap).

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

Sign in / Sign up

Export Citation Format

Share Document