arXiv subjects

Julia Schulte

Publications and source records attributed to Julia Schulte.

2 recordsLinked to original sources

arXiv2020

Reconstruction of convex bodies from moments

We investigate how much information about a convex body can be retrieved from a finite number of its geometric moments. We give a sufficient condition for a convex body to be uniquely determined by a finite number of its geometric moments, and we show that among all convex bodies, those which are uniquely determined by a finite number of moments form a dense set. Further, we derive a stability result for convex bodies based on geometric moments. It turns out that the stability result is improved considerably by using another set of moments, namely Legendre moments. We present a reconstruction algorithm that approximates a convex body using a finite number of its Legendre moments. The consistency of the algorithm is established using the stability result for Legendre moments. When only noisy measurements of Legendre moments are available, the consistency of the algorithm is established under certain assumptions on the variance of the noise variables.

math.MG↗

arXiv2019

A feasibility study of deep neural networks for the recognition of banknotes regarding central bank requirements

This paper contains a feasibility study of deep neural networks for the classification of Euro banknotes with respect to requirements of central banks on the ATM and high speed sorting industry. Instead of concentrating on the accuracy for a large number of classes as in the famous ImageNet Challenge we focus thus on conditions with few classes and the requirement of rejection of images belonging clearly to neither of the trained classes (i.e. classification in a so-called 0-class). These special requirements are part of frameworks defined by central banks as the European Central Bank and are met by current ATMs and high speed sorting machines. We also consider training and classification time on state of the art GPU hardware. The study concentrates on the banknote recognition whereas banknote class dependent authenticity and fitness checks are a topic of its own which is not considered in this work.

cs.CV↗