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Chapitre D'ouvrage Année : 2011

The Kolmogorov Spline Network for Image Processing


In 1900, Hilbert stated that high order equations cannot be solved by sums and compositions of bivariate functions. In 1957, Kolmogorov proved this hypothesis wrong and presented his superposition theorem (KST) that allowed for writing every multivariate functions as sums and compositions of univariate functions. Sprecher has proposed in (Sprecher, 1996) and (Sprecher, 1997) an algorithm for exact univariate function reconstruction. Sprecher explicitly describes construction methods for univariate functions and introduces fundamental notions for the theorem comprehension (such as tilage). Köppen has presented applications of this algorithm to image processing in (Köppen, 2002) and (Köppen & Yoshida, 2005). The lack of flexibility of this scheme has been pointed out and another solution which approximates the univariate functions has been considered. More specifically, it has led us to consider Igelnik and Parikh's approach, known as the KSN which offers several perspectives of modification of the univariate functions as well as their construction. This chapter will focus on the presentation of Igelnik and Parikh's Kolmogorov Spline Network (KSN) for image processing and detail two applications: image compression and progressive transmission.
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Dates et versions

hal-00589887 , version 1 (02-05-2011)



Pierre-Emmanuel Leni, Yohan Fougerolle, Frederic Truchetet. The Kolmogorov Spline Network for Image Processing. B. Igelnik. Computational Modeling and Simulation of Intellect: Current State and Future Perspectives, IGI Global, pp.25-51, 2011, ⟨10.4018/978-1-60960-551-3⟩. ⟨hal-00589887⟩
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