This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages)
This article needs attention from an expert in Mathematics or Computing. The specific problem is: The explanation is incomplete and the math contains inconsistencies. WikiProject Mathematics or WikiProject Computing may be able to help recruit an expert.(September 2020)
This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details.(October 2020) (Learn how and when to remove this message)
(Learn how and when to remove this message)
In computer graphics, a hierarchical RBF is an interpolation method based on Radial basis functions (RBF). Hierarchical RBF interpolation has applications in the construction of shape models in 3D computer graphics (see Stanford Bunny image below), treatment of results from a 3D scanner, terrain reconstruction, and others.
This problem is informally named as "large scattered data point set interpolation."
The steps of the method (for example in 3D) consist of the following:
Let the scattered points be presented as set
Let there exist a set of values of some function in scattered points
Find a function that will meet the condition for points lying on the shape and for points not lying on the shape
As J. C. Carr et al. showed,[1] this function looks like where:
— is RBF;
— is coefficients that are the solution of the system shown in the picture:
For determination of surface, it is necessary to estimate the value of function in interesting points x.
A lack of such method is a considerable complication [2] to calculate RBF, solve system, and determine surface.
^Carr, J.C.; Beatson, R.K.; Cherrie, J.B.; Mitchell, T.J.; Fright, W.R.; McCallum B.C.; Evans, T.R. (2001), “Reconstruction and Representation of 3D Objects with Radial Basis Functions” ACM SIGGRAPH 2001, Los Angeles, CA, P. 67–76.
^Bashkov, E.A.; Babkov, V.S. (2008) “Research of RBF-algorithm and his modifications apply
possibilities for the construction of shape computer models in medical practice”. Proc Int.
Conference "Simulation-2008", Pukhov Institute for Modelling in Energy Engineering, [1] Archived 2011-07-22 at the Wayback Machine (in Russian)
In computer graphics, a hierarchicalRBF is an interpolation method based on Radial basis functions (RBF). HierarchicalRBF interpolation has applications...
In mathematics a radial basis function (RBF) is a real-valued function φ {\textstyle \varphi } whose value depends only on the distance between the input...
especially useful when combined with LSTM. Hierarchical RNN connects elements in various ways to decompose hierarchical behavior into useful subprograms. A district...
function Thin plate spline — a specific polyharmonic spline: r2 log r HierarchicalRBF Subdivision surface — constructed by recursively subdividing a piecewise...
trees (IDE4, ID5R and gaenari), decision rules, artificial neural networks (RBF networks, Learn++, Fuzzy ARTMAP, TopoART, and IGNG) or the incremental SVM...
class of activation functions known as radial basis functions (RBFs) are used in RBF networks, which are extremely efficient as universal function approximators...
through a radial basis function (a technique that has been used to train RBF networks). Coates and Ng note that certain variants of k-means behave similarly...
vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions. Different types of similarity...
neural networks (SLFNs), including but not limited to sigmoid networks, RBF networks, threshold networks, trigonometric networks, fuzzy inference systems...
inverse of the covariance matrix. Hierarchical: algorithms which approximate the covariance matrix with a hierarchical matrix. These columns are about the...
matrix. Naive constructions of the graph adjacency matrix, e.g., using the RBF kernel, make it dense, thus requiring n 2 {\displaystyle n^{2}} memory and...
increases preglomerular vasoconstriction, thus decreasing both renal blood flow (RBF) and GFR. Accurate determination of core temperature often requires a special...
(2015). "Computational Identification of MoRFs in Protein Sequences Using Hierarchical Application of Bayes Rule". PLOS ONE. 10 (10): e0141603. Bibcode:2015PLoSO...
Global Information
