0000000000976358
AUTHOR
Yohan Fougerolle
The Kolmogorov superposition theorem and its application to image processing
Best student paper award; International audience
Numérisation 3D intelligente : deux algorithmes automatiques et progressifs
This paper presents two methods for the digitization of 3D objects without prior knowledge on their shape. The first method is based on the bounding box of the object during the acquisition steps. The second method is a combination of two concepts : the Mass Vector Chains (MVC) to define the orientation of the scanned part and the Mesurability Matrix to determine the coverage rate for each view point. Tests with simulated objects were performed and results of digitization are provided.
A novel approach for image sweeping functions using approximating scheme
International audience; Using Kolmogorov's superposition theorem, complex N-dimensional signal can be expressed by simpler 1D functions. Precisely, Kolmogorov has demonstrated that any multivariate function can be decomposed into sums and compositions of monovariate functions, that are called inner and external functions. We present one of the most recent method of monovariate functions construction. The algorithm proposed by Igelnik approximates the monovariate functions. Different layers are constructed and superposed. A layer is constituted by a couple of internal and external functions, that realizes an approximation of the multivariate function with a given precision, which corresponds…