Search results for "Function representation"
showing 4 items of 4 documents
Representation and estimation of spectral reflectances using projection on PCA and wavelet bases
2008
In this article, we deal with the problem of spectral reflectance function representation and estimation in the context of multispectral imaging. Because the reconstruction of such functions is an inverse problem, slight variations in input data completely skew the expected results. Therefore, stabilizing the reconstruction process is necessary. To do this, we propose to use wavelets as basis functions, and we compare those with Fourier and PCA bases. We present the idea and compare these three methods, which belong to the class of linear models. The PCA method is training-set dependent and confirms its robustness when applied to reflectance estimation of the training sets. Fourier and wave…
The Kolmogorov Spline Network for Image Processing
2011
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 &…
New Representations for Multidimensional Functions Based on Kolmogorov Superposition Theorem. Applications on Image Processing
2012
Mastering the sorting of the data in signal (nD) can lead to multiple applications like new compression, transmission, watermarking, encryption methods and even new processing methods for image. Some authors in the past decades have proposed to use these approaches for image compression, indexing, median filtering, mathematical morphology, encryption. A mathematical rigorous way for doing such a study has been introduced by Andrei Nikolaievitch Kolmogorov (1903-1987) in 1957 and recent results have provided constructive ways and practical algorithms for implementing the Kolmogorov theorem. We propose in this paper to present those algorithms and some preliminary results obtained by our team…
Loop-free Gray code algorithm for the e-restricted growth functions
2011
The subject of Gray codes algorithms for the set partitions of {1,2,...,n} had been covered in several works. The first Gray code for that set was introduced by Knuth (1975) [5], later, Ruskey presented a modified version of [email protected]?s algorithm with distance two, Ehrlich (1973) [3] introduced a loop-free algorithm for the set of partitions of {1,2,...,n}, Ruskey and Savage (1994) [9] generalized [email protected]?s results and give two Gray codes for the set of partitions of {1,2,...,n}, and recently, Mansour et al. (2008) [7] gave another Gray code and loop-free generating algorithm for that set by adopting plane tree techniques. In this paper, we introduce the set of e-restricte…