Zeta and L-functions of elliptic curves

In questa tesi si studiano alcune proprietà fondamentali delle funzioni Zeta e L associate ad una curva ellittica. In particolare, si dimostra la razionalità della funzione Zeta e l'ipotesi di Riemann per due famiglie specifiche di curve ellittiche. Si studia poi il problema dell'esistenza di un prolungamento analitico al piano complesso della funzione L di una curva ellittica con moltiplicazione complessa, attraverso l'analisi diretta di due casi particolari.

Classificazione di oggetti in immagini attraverso il modello Bag of Visual Words

Generic object recognition is an important function of the human visual system and everybody finds it highly useful in their everyday life. For an artificial vision system it is a really hard, complex and challenging task because instances of the same object category can generate very different images, depending of different variables such as illumination conditions, the pose of an object, the viewpoint of the camera, partial occlusions, and unrelated background clutter. The purpose of this thesis is to develop a system that is able to classify objects in 2D images based on the context, and identify to which category the object belongs to. Given an image, the system can classify it and decide the correct categorie of the object. Furthermore the objective of this thesis is also to test the performance and the precision of different supervised Machine Learning algorithms in this specific task of object image categorization. Through different experiments the implemented application reveals good categorization performances despite the difficulty of the problem. However this project is open to future improvement; it is possible to implement new algorithms that has not been invented yet or using other techniques to extract features to make the system more reliable. This application can be installed inside an embedded system and after trained (performed outside the system), so it can become able to classify objects in a real-time. The information given from a 3D stereocamera, developed inside the department of Computer Engineering of the University of Bologna, can be used to improve the accuracy of the classification task. The idea is to segment a single object in a scene using the depth given from a stereocamera and in this way make the classification more accurate.