Name
Title | ||
|---|---|---|
Kolmogorov Superposition Theorem and Its Application to Multivariate Function Decompositions and Image Representation |
Abstract | ||
|---|---|---|
In this paper, we present the problem of multivariate function decompositions into sums and compositions of monovariate functions. We recall that such a decomposition exists in the Kolmogorov's superposition theorem, and we present two of the most recent constructive algorithms of these monovariate functions. We first present the algorithm proposed by Sprecher, then the algorithm proposed by Igelnik, and we present several results of decomposition for gray level images. Our goal is to adapt and apply the superposition theorem to image processing, \textit{i.e.} to decompose an image into simpler functions using Kolmogorov superpositions.We synthetise our observations, before presenting several research perspectives. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1109/SITIS.2008.16 | SITIS |
Keywords | Field | DocType |
image representation,gray level image,monovariate function,kolmogorov superpositions,recent constructive algorithm,multivariate function decompositions,superposition theorem,kolmogorov superposition theorem,image processing,research perspective,multivariate function decomposition,simpler function,neural network,approximation algorithms,oscillators,functional decomposition,hypercubes,spline,construction industry,signal processing,before present,image analysis,functional equations | Spline (mathematics),Signal processing,Applied mathematics,Image processing,Artificial intelligence,Kolmogorov structure function,Artificial neural network,Superposition theorem,Approximation algorithm,Discrete mathematics,Pattern recognition,Functional equation,Mathematics | Conference |
Citations | PageRank | References |
1 | 0.37 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pierre-Emmanuel Leni | 1 | 19 | 2.33 |
| Yohan D. Fougerolle | 2 | 32 | 7.06 |
| Frédéric Truchetet | 3 | 121 | 18.97 |