## Nonnegative Matrix Factorization for Segmentation Analysis

By: Roman Sandler

The conducted research project is concerned with image segmentation — one of the central problems of image analysis. A new model of segmented image is proposed and used to develop tools for analysis of image segmentations: image specific evaluation of segmentation algorithms' performance, extraction of image segment descriptors, and extraction of image segments. Prevalent seg-mentation models are typically based on the assumption of smoothness in the chosen image representation within the segments and contrast between them. The proposed model, unlike them, describes segmentations using image adaptive properties, which makes it relatively robust to context factors such as image quality or the presence of texture. The image repre-sentation in the proposed terms may be obtained in a fully unsupervised process and it does not require learning from other images.

## Multi Agent Robotics in Dynamic Enviroments

By: Yaniv Altshuler

In this work we examine the use of a decentralized group of extremely simple robotic agents for cooperatively accomplishing missions of global properties. We show that using only local interactions, such simple robots can cope with the lack of a central supervisor, communication resources and large memory resources. Using redundancy, the systems also achieve fault tolerance (required as the robots' simplicity might also imply low hardware reliability, resulting in agents malfunctions).

## Biologically Motivated Modeling and Imitating the Chameleon's Vision System

By: Ofir Avni

This thesis takes the biologically motivated approach with regard to the visual system of the chameleon. The chameleon has a unique visual system, in which the two eyes scan independently the environment. In the rst part of this work, a complex and innovative computer vision system, which uses cameras and mirrors, is designed and implemented in order to track the direction of the eyes of chameleons. In this part the problem of pose estimation with multiple cameras and mirrors is formulated and solved. The problem is formulated as a minimization problem of the three-dimensional geometric errors given the location of features found in the image and their three-dimensional model. The direction of the eyes is found by founding the eyelid in the image, and based on a geometric model of the eye. Preliminary results from this part, which includes biological experiments, indicates that chameleons scan the environment using a "negative correlation" strategy. That is, when one eye scans forward, the other, with high probability, scans backwards.

## Mathematical Analysis of Emergent Behavior in Multi-Agent Systems

By: Yotam Elor

Swarm robotics is a new approach to the coordination of a large number of relatively simple mobile robotic agents. The approach takes its inspiration from the system-level functioning of social insects which demonstrate three desired characteristics for multi-robot systems: robustness, flexibility and scalability. By design, a single agent is cheap, simple and has low capabilities, hence, cannot accomplish the task by itself. Therefore, the agents must cooperate to achieve their goals. On the one hand, the tasks are of global nature, hence, require tight cooperation between all agents. On the other hand, the cheap agents have limited communication abilities. Clearly, achieving large scale cooperation between agents having very limited communication capabilities is challenging.

## Learning Methods for Modeling High-Dimensional Distributions

By: Assaf Glazer

A reliable density estimation is hard to obtain in problems of high-dimensional data, especially when the sample used for estimation is small. As a result, various studies have tried to find approximate solutions to this problem by reducing it to a less general, and hopefully solvable, form. One prominent approach in this direction is estimating the minimum-volume set (MV-set) of a distribution at level a instead of its density function. (An MV-set at level alpha is a subset of the input space with probability mass of at least alpha that has the smallest volume.) However, even a perfectly estimated MV-set reveals only partial information about the distribution. Can we define a problem whose solution is more informative than MV-set estimation, yet is easier to solve than density estimation? In this dissertation we introduce novel methods that do just that Our methods, which can also be regarded as generalized quantile functions, are based on the idea of estimating (or approximating) hierarchical MV-sets for distribution representation in high-dimensional data In most of our proposed methods, we use the one-class SVM (OCSVM) algorithm to estimate the hierarchical MV-sets. Note that a straightforward approach of training a set of OCSVMs, one for each MV-set, would not necessarily satisfy the hierarchy requirement We thus introduce novel variants of the OCSVM algorithm that find all estimated MV-sets such that the hierarchy constraint is fulfilled. We provide theoretical and empirical justifications for our methods in the general context of estimating hierarchical MV-sets. In addition, we apply our methods and show their superiority over competitors in various domains including concept drift detection, topic change detection in document streams, back-ground subtraction in image sequences, and hierarchical clustering.