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Revision as of 14:45, 22 October 2009
Matteo Matteucci
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matteucc@elet.polimi.it
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warning.png"Soft Computing" is not in the list of possible values (Affective Computing, Agents - Multiagent Systems - Agencies, BioSignal Analysis, Computational Intelligence and Games, Computer Vision and Image Analysis, E-Science, Machine Learning, Philosophy of Artificial Intelligence, Robotics, Social Software and Semantic Web) for this property.
| Research Areas:
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This is my home page on the airwiki website. Here you can find projects and thesis proposals. You will not find here my research statements, my teaching material, my publications, and so on. If you are looking for something is not here you can try:
PhD Students I am currently tutoring
PhD Students I have tutored
Projects I am currently tutoring
List of project proposals
Bio Signal Analysis
Robotics & Computer Vision
Wiki Page: Accurate AR Marker Location
Title: C++ Library for accurate marker location based on subsequent pnp refinements
Description: ARTags, QR codes, Data Matrix, are visual landmark used for augmented reality, but they could be used for robotics as well. A thesis has already been done on using data matrix for robot localization and mapping, but improvements are required in terms generality, accuracy and robustness of the solution. The goal is thuss to:
- increase the number of markers supported by the system (ARTag + QR codes)
- increase the accuracy of the detection and localization of the marker
- test different algorithms for the solution of the perspective from n points problem
Material:
- papers on PnP algorithms, OpenCV,
- Matlab code with three PnP algorithms implementations
- C++ libraries for marker detection (to be found and evaluated)
Expected outcome:
- C++ library to the robust localization of artificial markers
- a ROS node performing accurate ARTag localization
- a comparison of Tags and algorithms in a real world scenario
- The use of this library in a SLAM framework (Thesis)
Required skills or skills to be acquired:
- background on computer vision and image processing
- C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 5 - 10 / Bachelor of Science, Master of Science / Thesis, Course
|
Wiki Page: Automatic Differentiation Techniques for Real Time Kalman Filtering
Title: Evaluation of Automatic Differentiation Techniques for Gauss-Newton based Simultaneous Localization and Mapping
Description: In Gauss-Newton non linear optimization one of the most tedious part is computing Jacobians. At the AIRLab we have developed a framework for non linear Simultaneous Localization and Mapping suitable for different motion models and measurement equations, but any time you need to change something you need to recompute the required Jacobian. Automatic differentiation is a tool for the automatic differentiation of source code either at compiling time or at runtime; we are interested in testing these techniques in the software we have developed and compare their performance with respect to (cumbersome) optimized computation.
Material
Expected outcome:
New modules implementations based on automatic differentiation
A comparison between the old stuff and new approach
Required skills or skills to be acquired:
- C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 10 - 20 / Master of Science / Thesis
|
Wiki Page: Comparison of State of the Art Visual Odometry Systems
Title: A Comparison of State of the Art Visual Odometry Systems (Monocular and Stereo)
Description: Visual odometry is the estimation of camera(s) movement from a sequence of images. In case we deal with a single camera system we have Monocular Visual Odometry; in case we have more cameras we have a Stero Visual Odometry. The goal of the thesis is to review the state of the art on in visual odometry, classify existing approaches and compare their implementations (many of the algorithms have online source code available).
Material
Expected outcome:
- a set of running algorithms performing visual odometry
Required skills or skills to be acquired:
- computer vision and 3D reconstruction
- C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 10 - 20 / Bachelor of Science, Master of Science / Thesis, Course
|
Wiki Page: MoonSLAM Reengineering
Title: Reengineering of a flexible framework for simultaneous localization and mapping
Description: In the last three years a general framework for the implementation of EKF-SLAM algorithm has been developed at the AIRLab. After several improvements it is now time to redesign it based on the experience cumulated. The goal is to have an international reference framework for the development of EKF based SLAM algorithms with multiple sensors (e.g., lasers, odometers, inertial measurement ) and different motion models (e.g., free 6DoF motion, planar motion, ackerman kinematic, and do on). The basic idea is to implement it by using C++ templates, numerically stable techniques for Kalman filtering and investigation the use of automatic differentiation. It should be possible to seamlessly exchange motion model and sensor model without having to write code beside the motion model and the measurement equation.
Material
- lots of theoretical background and material
- an existing (and working) C++ implementation of the framework
Expected outcome:
- a C++ library for the implementation of generic EKF-SLAM algorithms
Required skills:
- Experienced C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 20 - 20 / Master of Science / Thesis
|
Wiki Page: Poit cloud SLAM with Microsoft Kinect
Title: Point cloud SLAM with Microsoft Kinect
Description: Simultaneous Localization and Mapping (SLAM) is one of the basic functionalities required from an autonomous robot. In the past we have developed a framework for building SLAM algorithm based on the use of the Extended Kalman Filter and vision sensors. A recently available vision sensor which has tremendous potential for autonomous robots is the Microsoft Kinect RGB-D sensor. The thesis aims at the integration of the Kinect sensor in the framework developed for the development of a point cloud base system for SLAM.
Material:
- Kinect sensor and libraries
- A framework for multisensor SLAM
- PCL2.0 library for dealing with point clouds
Expected outcome:
- Algorithm able to build 3D point cloud representation of the observed scene
- Point clouds processing could be used to improve the accuracy of the filter as well
Required skills or skills to be acquired:
- Basic background in computer vision
- Basic background in Kalman filtering
- C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 10 - 20 / Master of Science / Thesis
|
Wiki Page: Unmanned Aerial Vehicles Visual Navigation
Title: A critical review on the state of the art in visual navigation for unmanned aerial vehicles
Description: Visual navigation is becoming more and more important in the development of unmanned aerial vehicles (UAV). The goal of this thesis/tesina is to review in a structured way the current state of art in the field from different perspective: research teams, projects, platforms, tasks, algorithms. The latter is the most important aspect obviously and the project should provide a clear view on what is done today, and obtaining which results. Two kind of operations are of most interest: tracking of fixed and mobile targets (and how this impact on the UAV path), navigation on a geo-referenced map. Implementing one of the standard approaches on a mini unmanned aerial vehicle would be the ideal ending of the work to turn it into a thesis.
Material:
- papers from major journals and conferences
- reports from research projects
Expected outcome:
- a report with a detailed review of the state of the art organized according to the main relevant aspects (to be identified during the work)
- an implementation of some state of the art algorithms for tracking or navigation
Required skills or skills to be acquired:
- proficiency in english
- basic understanding of computer vision
- basic understanding of filtering techniques
Tutor: MatteoMatteucci
Additional Info: CFU 10 - 20 / Bachelor of Science, Master of Science / Thesis
|
Machine Learning & Soft Computing
Wiki Page: Accurate AR Marker Location
Title: C++ Library for accurate marker location based on subsequent pnp refinements
Description: ARTags, QR codes, Data Matrix, are visual landmark used for augmented reality, but they could be used for robotics as well. A thesis has already been done on using data matrix for robot localization and mapping, but improvements are required in terms generality, accuracy and robustness of the solution. The goal is thuss to:
- increase the number of markers supported by the system (ARTag + QR codes)
- increase the accuracy of the detection and localization of the marker
- test different algorithms for the solution of the perspective from n points problem
Material:
- papers on PnP algorithms, OpenCV,
- Matlab code with three PnP algorithms implementations
- C++ libraries for marker detection (to be found and evaluated)
Expected outcome:
- C++ library to the robust localization of artificial markers
- a ROS node performing accurate ARTag localization
- a comparison of Tags and algorithms in a real world scenario
- The use of this library in a SLAM framework (Thesis)
Required skills or skills to be acquired:
- background on computer vision and image processing
- C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 5 - 10 / Bachelor of Science, Master of Science / Thesis, Course
|
Wiki Page: Automatic Differentiation Techniques for Real Time Kalman Filtering
Title: Evaluation of Automatic Differentiation Techniques for Gauss-Newton based Simultaneous Localization and Mapping
Description: In Gauss-Newton non linear optimization one of the most tedious part is computing Jacobians. At the AIRLab we have developed a framework for non linear Simultaneous Localization and Mapping suitable for different motion models and measurement equations, but any time you need to change something you need to recompute the required Jacobian. Automatic differentiation is a tool for the automatic differentiation of source code either at compiling time or at runtime; we are interested in testing these techniques in the software we have developed and compare their performance with respect to (cumbersome) optimized computation.
Material
Expected outcome:
New modules implementations based on automatic differentiation
A comparison between the old stuff and new approach
Required skills or skills to be acquired:
- C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 10 - 20 / Master of Science / Thesis
|
Wiki Page: Comparison of State of the Art Visual Odometry Systems
Title: A Comparison of State of the Art Visual Odometry Systems (Monocular and Stereo)
Description: Visual odometry is the estimation of camera(s) movement from a sequence of images. In case we deal with a single camera system we have Monocular Visual Odometry; in case we have more cameras we have a Stero Visual Odometry. The goal of the thesis is to review the state of the art on in visual odometry, classify existing approaches and compare their implementations (many of the algorithms have online source code available).
Material
Expected outcome:
- a set of running algorithms performing visual odometry
Required skills or skills to be acquired:
- computer vision and 3D reconstruction
- C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 10 - 20 / Bachelor of Science, Master of Science / Thesis, Course
|
Wiki Page: MoonSLAM Reengineering
Title: Reengineering of a flexible framework for simultaneous localization and mapping
Description: In the last three years a general framework for the implementation of EKF-SLAM algorithm has been developed at the AIRLab. After several improvements it is now time to redesign it based on the experience cumulated. The goal is to have an international reference framework for the development of EKF based SLAM algorithms with multiple sensors (e.g., lasers, odometers, inertial measurement ) and different motion models (e.g., free 6DoF motion, planar motion, ackerman kinematic, and do on). The basic idea is to implement it by using C++ templates, numerically stable techniques for Kalman filtering and investigation the use of automatic differentiation. It should be possible to seamlessly exchange motion model and sensor model without having to write code beside the motion model and the measurement equation.
Material
- lots of theoretical background and material
- an existing (and working) C++ implementation of the framework
Expected outcome:
- a C++ library for the implementation of generic EKF-SLAM algorithms
Required skills:
- Experienced C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 20 - 20 / Master of Science / Thesis
|
Wiki Page: Poit cloud SLAM with Microsoft Kinect
Title: Point cloud SLAM with Microsoft Kinect
Description: Simultaneous Localization and Mapping (SLAM) is one of the basic functionalities required from an autonomous robot. In the past we have developed a framework for building SLAM algorithm based on the use of the Extended Kalman Filter and vision sensors. A recently available vision sensor which has tremendous potential for autonomous robots is the Microsoft Kinect RGB-D sensor. The thesis aims at the integration of the Kinect sensor in the framework developed for the development of a point cloud base system for SLAM.
Material:
- Kinect sensor and libraries
- A framework for multisensor SLAM
- PCL2.0 library for dealing with point clouds
Expected outcome:
- Algorithm able to build 3D point cloud representation of the observed scene
- Point clouds processing could be used to improve the accuracy of the filter as well
Required skills or skills to be acquired:
- Basic background in computer vision
- Basic background in Kalman filtering
- C++ programming under Linux
Tutor: MatteoMatteucci
Additional Info: CFU 10 - 20 / Master of Science / Thesis
|
Wiki Page: Unmanned Aerial Vehicles Visual Navigation
Title: A critical review on the state of the art in visual navigation for unmanned aerial vehicles
Description: Visual navigation is becoming more and more important in the development of unmanned aerial vehicles (UAV). The goal of this thesis/tesina is to review in a structured way the current state of art in the field from different perspective: research teams, projects, platforms, tasks, algorithms. The latter is the most important aspect obviously and the project should provide a clear view on what is done today, and obtaining which results. Two kind of operations are of most interest: tracking of fixed and mobile targets (and how this impact on the UAV path), navigation on a geo-referenced map. Implementing one of the standard approaches on a mini unmanned aerial vehicle would be the ideal ending of the work to turn it into a thesis.
Material:
- papers from major journals and conferences
- reports from research projects
Expected outcome:
- a report with a detailed review of the state of the art organized according to the main relevant aspects (to be identified during the work)
- an implementation of some state of the art algorithms for tracking or navigation
Required skills or skills to be acquired:
- proficiency in english
- basic understanding of computer vision
- basic understanding of filtering techniques
Tutor: MatteoMatteucci
Additional Info: CFU 10 - 20 / Bachelor of Science, Master of Science / Thesis
|
warning.png"Soft Computing" is not in the list of possible values (Affective Computing, Agents - Multiagent Systems - Agencies, BioSignal Analysis, Computational Intelligence and Games, Computer Vision and Image Analysis, E-Science, Machine Learning, Philosophy of Artificial Intelligence, Robotics, Social Software and Semantic Web) for this property.
Past project proposals
- Aperiodic visual stimulation in a VEP-based BCI (Visual-evoked potentials (VEPs) are a possible way to drive the a Brain-Computer Interface (BCI). This projects aims at maximizing the discrimination between different stimuli by using numerical codes derived from techniques of digital telecommunications.
Automatic generation of domain ontologies (This thesis to be developed together with Noustat S.r.l. (see http://www.noustat.it), who are developing research activities directed toward the optimization of knowledge management services, in collaboration with another company operating in this field. This project is aimed at removing the ontology building bottleneck, long and expensive activity that usually requires the direct collaboration of a domain expert. The possibility of automatic building the ontology, starting from a set of textual documents related to a specific domain, is expected to improve the ability to provide the knowledge management service, both by reducing the time-to-application, and by increasing the number of domains that can be covered. For this project, unsupervised learning methods will be applied in sequence, exploiting the topological properties of the ultra-metric spaces that emerge from the taxonomic structure of the concepts present in the texts, and associative methods will extend the concept network to lateral, non-hierarchical relationships.)
Behavior recognition from visual data (In the literature several approaches have been used to model observed behaviors and these date back to early approaches in animal behavior analysis (Baum and Eagon, 1967)(Colgan, 1978). Nowadays several techniques are used and they can be roughly classified as: State space models, Automata (e.g., Finite State Machines, Agents, etc.), Grammars (e.g., strings, T-Patterns, etc.), Bayeasian models (e.g., Hidden Markov Models), and Dynamic State Variables. The work will leverage on a huge corpus of techniques to devise the most suitable for behavior recognition from visual data. We exclude from the very beginning any deterministic approach being the phenomenon under observation complex and affected by noisy observations. The focus will be mainly of the use of dynamic graphical models (Ghahramani, 1998) and the application of bottom up learning techniques (Stolcke and Omohundro, 1993)(Stolcke and Omohundro, 1994) for model induction.
- L. E. Baum and J. A. Eagon. An inequality with applications to statistical estimation for probabilistic functions of markov processes and to a model for ecology. Bull. Amer. Math. Soc, 73(73):360–363, 1967.
- P. W. Colgan. Quantitative Ethology. John Wiley & Sons, New York, 1978.
- A. Stolcke and S. M. Omohundro. Hidden markov model induction by bayesian model merging. In Stephen Jos é Hanson, Jack D. Cowan, and C. Lee Giles, editors, Advances in Neural Information Processing Systems, volume 5. Morgan Kaufmann, San Mateo, CA, 1993.
- Zoubin Ghahramani. Learning dynamic bayesian networks. Lecture Notes in Computer Science, 1387:168, 1998.
- A. Stolcke and S. M. Omohundro. Best-first model merging for hidden markov model induction. Technical Report TR-94-003, 1947 Center Street, Berkeley, CA, 1994.
Material:
- papers from major journals and conferences
- kinet SDK for the extraction of body poses
Expected outcome:
- general framework for the recognition of behaviors from time series
- toolkit for behavior segmentation and recognition from time series
- running prototype based on data coming from the Microsoft kinect sensor
Required skills or skills to be acquired:
- understanding of techniques for behavior recognition
- background on pattern recognition and stochastic models
- basic understanding of computer vision
- C++ programming under Linux or Matlab)
Combinatorial optimization based on stochastic relaxation (The project will focus on the study, implementation, comparison and
analysis of different algorithms for the optimization of pseudo-Boolean
functions, i.e., functions defined over binary variables with values in
R. These functions have been studied a lot in the mathematical
programming literature, and different algorithms have been proposed (1).
More recently, the same problems have been faced in evolutionary
computations, with the use of genetic algorithms, and in particular
estimation of distribution algorithms (2,3). Estimation of distribution
algorithms are a recent meta-heuristic, where classical crossover and
mutation operators used in genetic algorithms are replaced with
operators that come from statistics, such as sampling and estimation.
The focus will be on the implementation of a new algorithm able to
combine different approaches (estimation and sampling, from one side,
and exploitation of prior knowledge about the structure of problem, on
the other), together with the comparison of the results with existing
techniques that historically appear in different (and often separated)
communities. Good coding (C/C++) abilities are required. Since the
approach will be based on statistical models, the student is supposed to
be comfortable with notions that come from probability and statistics
courses. The project could require some extra effort in order to build
and consolidate some background in math, especially in Bayesian
statistics and MCMC techniques, such as Gibbs and Metropolis samplers (4).
The project can be extended to master thesis, according to interesting
and novel directions of research that will emerge in the first part of
the work. Possible ideas may concern the proposal of new algorithms able
to learn existing dependencies among the variables in the function to be
optimized, and exploit them in order to increase the probability to
converge to the global optimum.
Picture taken from http://www.ra.cs.uni-tuebingen.de/
Bibliography
- Boros, Endre and Boros, Endre and Hammer, Peter L. (2002) Pseudo-boolean optimization. Discrete Applied Mathematics.
- Pelikan, Martin; Goldberg, David; Lobo, Fernando (1999), A Survey of Optimization by Building and Using Probabilistic Models, Illinois: Illinois Genetic Algorithms Laboratory (IlliGAL), University of Illinois at Urbana-Champaign.
- Larrañga, Pedro; & Lozano, Jose A. (Eds.). Estimation of distribution algorithms: A new tool for evolutionary computation. Kluwer Academic Publishers, Boston, 2002.
- Image Analysis, Random Fields Markov Chain Monte Carlo Methods)
Combining Estimation of Distribution Algorithms and other Evolutionary techniques for combinatorial optimization (The project will focus on the study, implementation, comparison and analysis of different algorithms for combinatorial optimization using techniques and algorithms proposed in Evolutionary Computation. In particular we are interested in the study of Estimation of Distribution Algorithms (1,2,3,4), a recent meta-heuristic, often presented as an evolution of Genetic Algorithms, where classical crossover and mutation operators, used in genetic algorithms, are replaced with operators that come from statistics, such as sampling and
estimation.
The focus will be on the implementation of new hybrid algorithms able to combine estimation of distribution algorithms with different approaches available in the evolutionary computation literature, such as genetic algorithms and evolutionary strategies, together with other local search techniques. Good coding (C/C++) abilities are required. Some background in combinatorial optimization form the "Fondamenti di Ricerca Operativa" is desirable. The project could require some effort in order to build and consolidate some background in MCMC techniques, such as Gibbs and Metropolis samplers (4). The project could be extended to master thesis, according to interesting and novel directions of research that will emerge in the first part of the work.
Computer vision provides a large number of optimization problems, such as new-view synthesis, image segmentation, panorama stitching and texture restoration, among the others, (6). One common approach in this context is based on the use of binary Markov Random Fields and on the formalization of the optimization problem as the minimum of an energy function expressed as a square-free polynomial, (5). We are interested in the proposal, comparison and evaluation of different Estimation of Distribution Algorithms for solving real world problems that appear in computer vision.
Pictures taken from http://www.genetic-programming.org and (6)
Bibliography
- Pelikan, Martin; Goldberg, David; Lobo, Fernando (1999), A Survey of Optimization by Building and Using Probabilistic Models, Illinois: Illinois Genetic Algorithms Laboratory (IlliGAL), University of Illinois at Urbana-Champaign.
- Larrañga, Pedro; & Lozano, Jose A. (Eds.). Estimation of distribution algorithms: A new tool for evolutionary computation. Kluwer Academic Publishers, Boston, 2002.
- Lozano, J. A.; Larrañga, P.; Inza, I.; & Bengoetxea, E. (Eds.). Towards a new evolutionary computation. Advances in estimation of distribution algorithms. Springer, 2006.
- Pelikan, Martin; Sastry, Kumara; & Cantu-Paz, Erick (Eds.). Scalable optimization via probabilistic modeling: From algorithms to applications. Springer, 2006.
- Image Analysis, Random Fields Markov Chain Monte Carlo Methods
- Carsten Rother, Vladimir Kolmogorov, Victor Lempitsky, Martin Szummer. Optimizing Binary MRFs via Extended Roof Duality, CVPR 2007)
Creation of new EEG training by introduction of noise (A Brain-Computer Interface (BCI) must be trained on the individual user in order to be effective. This training phase require recording data in long sessions, which is time consuming and boring for the user. The aim of this project is to develop algorithm to create new training EEG (electroencephalography) data from existing ones, so as to speed up the training phase.
Driving an autonomous wheelchair with a P300-based BCI (This project pulls together different Airlab projects with the aim to drive an autonomous wheelchair (LURCH) with a BCI, through the development of key software modules. Depending on the effort the student is willing to put into it, the project can grow to a full experimental thesis.)
Exploratory data analysis by genetic feature extraction (Understanding the waves in EEG signals is an hard task and psicologists often need automatic tools to perform this task. In this project we are interested in using a genetic algorithm developed for P300 feature extraction in order to extract useful informations from Error Potentials. The project is a collaboration with the psicology department od Padua University.
Extended Kalman Filtering on Manifolds (Extended Kalman filtering is a well known technique for the estimation of the state of a dynamical system also used in robotics for localization and mapping. However in the basic formulation it assumes all variables to live in an Euclidean space while some components may span over the non-Euclidean 2D or 3D rotation group SO(2) or SO(3). It is thus possible to write tha Extended Kalman filter to operate on Lie Groups to take into account the presence of manifolds (http://www.ethaneade.org/latex2html/lie/lie.html). We are interestend in investigation this further applying it to the EKF-SLAM framework we have developed.
Material:
- papers about Manifold based optimization and space representations
- C++ framework for EKF-SLAM
Expected outcome:
- An extended Kalman filter which uses this new representation
Required skills or skills to be acquired:
- Good mathematical background
- C++ programming under Linux)
Information geometry and machine learning (In machine learning, we often introduce probabilistic models to handle uncertainty in the data, and most of the times due to the computational cost, we end up selecting (a priori, or even at run time) a subset of all possible statistical models for the variables that appear in the problem. From a geometrical point of view, we work with a subset (of points) of all possible statistical models, and the choice of the fittest model in out subset can be interpreted as a the point (distribution) minimizing some distance or divergence function w.r.t. the true distribution from which the observed data are sampled. From this perspective, for instance, estimation procedures can be considered as projections on the statistical model and other statistical properties of the model can be understood in geometrical terms. Information Geometry (1,2) can be described as the study of statistical properties of families of probability distributions, i.e., statistical models, by means of differential and Riemannian geometry.
Information Geometry has been recently applied in different fields, both to provide a geometrical interpretation of existing algorithms, and more recently, in some contexts, to propose new techniques to generalize or improve existing approaches. Once the student is familiar with the theory of Information Geometry, the aim of the project is to apply these notions to existing machine learning algorithms.
Possible ideas are the study of a particular model from the point of view of Information Geometry, for example as Hidden Markov Models, Dynamic Bayesian Networks, or Gaussian Processes, to understand if Information Geometry can give useful insights with such models. Other possible direction of research include the use of notions and ideas from Information Geometry, such as the mixed parametrization based on natural and expectation parameters (3) and/or families of divergence functions (2), in order to study model selection from a geometric perspective. For example by exploiting projections and other geometric quantities with "statistical meaning" in a statistical manifold in order to chose/build the model to use for inference purposes.
Since the project has a theoretical flavor, mathematical inclined students are encouraged to apply. The project requires some extra effort in order to build and consolidate some background in math, partially in differential geometry, and especially in probability and statistics.
Bibliography
- Shun-ichi Amari, Hiroshi Nagaoka, Methods of Information Geometry, 2000
- Shun-ichi Amari, Information geometry of its applications: Convex function and dually flat manifold, Emerging Trends in Visual Computing (Frank Nielsen, ed.), Lecture Notes in Computer Science, vol. 5416, Springer, 2009, pp. 75–102
- Shun-ichi Amari, Information geometry on hierarchy of probability distributions, IEEE Transactions on Information Theory 47 (2001), no. 5, 1701–1711.)
LARS and LASSO in non Euclidean Spaces (LASSO (1) and more recently LARS (2) are two algorithms proposed for linear regression tasks. In particular LASSO solves a least-squares (quadratic) optimization problem with a constrain that limits the sum of the absolute value of the coefficients of the regression, while LARS can be considered as a generalization of LASSO, that provides a more computational efficient way to obtain the solution of the regression problem simultaneously for all values of the constraint introduced by LASSO.
One of the common hypothesis in regression analysis is that the noise introduced in order to model the linear relationship between regressors and dependent variable has a Gaussian distribution. A generalization of this hypothesis leads to a more general framework, where the geometry of the regression task is no more Euclidean. In this context different estimation criteria, such as maximum likelihood estimation and other canonical divergence functions do not coincide anymore. The target of the project is to compare the different solutions associated to different criteria, for example in terms of robustness, and propose generalization of LASSO and LARS in non Euclidean contexts.
The project will focus on the understanding of the problem and on the implementation of different algorithms, so (C/C++ or Matlab or R) coding will be required. Since the project has also a theoretical flavor, mathematical inclined students are encouraged to apply. The project may require some extra effort in order to build and consolidate some background in math, especially in probability and statistics.
Picture taken from (2)
Bibliography
- Tibshirani, R. (1996), Regression shrinkage and selection via the lasso. J. Royal. Statist. Soc B., Vol. 58, No. 1, pages 267-288
- Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani, Least Angle Regression, 2003)
Multimodal GUI for driving an autonomous wheelchair (This project pulls together different Airlab projects with the aim to drive an autonomous wheelchair (LURCH - The autonomous wheelchair) with a multi modal interface (Speech Recognition, Brain-Computer Interface, etc.), through the development of key software modules. The work will be validated with live experiments.
Odometric system for robots based on laser mice (We developed an odometric system for robots by combining the reading of several laser mice. The system consists of a master PIC-based board and several slave boards where the sensors employed in optical mice are located. The readings are collected on the PIC and sent on the serial port to a PC which elaborates and combines the x and y readings in order to obtain a x,y,theta estimation of the movement of the robot.
The aim of the project is first to improve the current design of the PIC-based board, and realize a new working prototype, and then to implement and evaluate different algorithms able to estimate more precisely the x,y and theta odometric data from the mice readings. Experience with PIC-based systems and some experience with electronics circuits is a plus. Students are supposed to redesign the electronic board, improve the firmware of the PIC, and work on the algorithm that estimates the robot position on the PC. It would be also interesting to evaluate the possibility to embed the optimization and estimation
algorithms in the firmware of the PIC in order to produce a stand-alone device.
Ask the tutors of the project for extra material, such as data-sheets and other documentation.)
P300 BCI (Recovery, integration and adaptation of P300 BCI (hardware and software) stubs to generate a working interface for a speller. The aim is to develop a working prototype for an ALS affected patient.)
R2P IMU firmware development (We have developed the electronics of an Inertial Measurement Unit based on an ARM microcontroller to be integrated on an autonomous embedded aerial platform. The IMU has already some attitude heading reference system (AHRS) code implemented, but we are interested in:
- implementing embedded algorithms for the estimation of the IMU attitude to be compared with the actual one (e.g., Kalman filter, DCM, Madgwick, etc.)
- developing a, easy to use, procedure for the calibration of IMU parameters
- making a comparison with commercial units using a robot arm as testbed
- validate the accuracy of the IMU on a flying platform
- integrate the measurements from a GPS to reduce drift and provide accurate positiong (this will make it definitely a MS thesis)
Material
- electronic board and eclipse based C development toolkit for ARM processors
- papers describing the algorithms we are interested in implementing
Expected outcome:
- few different AHRS algorithms with comparative results
- user-friendly procedure to calibrate the IMU
- a sistem which integrated IMU and GPS to provide accurate positioning
Required skills or skills to be acquired:
- C programming on ARM microcontroller
- background on kalman filtering and attitude estimation)
Real-time removal of ocular artifact from EEG (In a Brain-Computer Interface (BCI) based on electroencephalogram (EEG), one of the most important sources of noise is related to ocular movements. Algorithms have been devised to cancel the effect of such artifacts. The project consists in the in the implementation in real time of an existing algorithm (or one newly developed) in order to improve the performance of a BCI.
Robocentric MoonSLAM (Simultaneous Localization and Mapping (SLAM) is one of the basic functionalities required from an autonomous robot. In the past we have developed a framework for building SLAM algorithm based on the use of the Extended Kalman Filter and vision sensors. The actual implementation of the EKF SLAM in the framework developed uses a world-centric approach, but from the literature it is known that a robocentric approach can provide higher performances on small maps. We would like to have both implementation to compare the results in two scenarios: pure visual odometry, conditional independent submapping.
Material
- A framework for multisensor SLAM using the world centric approach
- Papers and report about robocentric slam
Expected outcome:
- a fully functional robocentric version of the MoonSLAM framework
Required skills or skills to be acquired:
- Basic background in computer vision
- Background in Kalman filtering
- C++ programming under Linux)
Scan Matching Odometry and Multisensor SLAM (Starting from some C/C++ code for laser scan alignment and the covariance information associated to the matching, we are interested in the development of a library for the matching and fusion of laser scans under the ROS (www.ros.org) environment. From this we are interested in the development of an odometric system based on laser scan matching and in a Simultaneous Localization and Mapping system integrating scan matching with visual SLAM. The result is a complete navigation system that fuses laser and visual information to build consisten maps in an EKF-based environment.
Material:
- a MS thesis which describes the scan matching algorithms
- a BS thesis which implements a prototype of the system
Expected outcome:
- a complete system that build maps integrating laser scan and visual informtion
Required skills or skills to be acquired:
- Background on Kalman filtering
- C++ programming under Linux)
Self calibration of multiple odometric sensors (An odometric sensor measures the path followed by a robot in an incremental way (e.g., wheel mounted encoders, visual odometry, scan matching based odometry, etc.) . Having several odometry sensors mounted on the same platform can significantly improve the accuracy and robustness of the overall system but requires proper calibration of relative positioning and possible biases. We are interested in the development of techniques for the self calibration of a multi sensor based odometry sensor. These techniques could be inspired by classical non-linear optimization techniques used in the hand and eye problem but they could use techniques from Simultaneous Localization and Mapping. According to the setup, some information on the real position of the system may exists (i.e., external tracking system or GPS); the approach should be able to use this information as well.
Material:
- datasets with real data
- a few odometric system implementations
- C++ libraries for non linear optimization
Expected outcome:
- software for the self calibration of a set of odometry systems mounted on the same robot
Required skills or skills to be acquired:
- C++ programming under Linux)
Statistical inference for phylogenetic trees (The project will focus on the study, implementation, comparison, and analysis of different statistical inference techniques for phylogenetic trees. Phylogenetic trees (1, 2, 3) are evolutionary trees used to represent the relationships between different species with a common ancestor. Typical inference tasks concern the construction of a tree starting from DNA sequences, involving both the choice of the topology of the tree (i.e., model selection) and the values of the parameters (i.e., model fitting). The focus will be a probabilistic description of the tree, given by the introduction of stochastic
variables associated to both internal nodes and leaves of the tree.
The project will focus on the understanding of the problem and on the implementation of different algorithms, so (C/C++ or Matlab or R) coding will be required. Since the approach will be based on statistical models, the student is supposed to be comfortable with notions that come from probability and statistics courses.
The project is thought to be extended to master thesis, according to interesting and novel directions of research that will emerge in the first part of the work. Possible ideas may concern the proposal and implementation of new algorithms, based on recent approaches to phylogenetic inference available in the literature, as in (3) and (4). In this case the thesis requires some extra effort in order to build and consolidate some background in math in oder to understand some recent literature, especially in (mathematical) statistics and, for example, in the emerging field of algebraic statistics (5).
Other possible novel applications of phylogenetic trees have been proposed in contexts different from biology, as in (6). Malware (malicious software) is software designed to infiltrate a computer without the owner's informed consent. Often malwares are related to previous programs thought evolutionary relationships, i.e., new malwares appear as small mutations of previous softwares. We are interested in the use of techniques from phylogenetic trees to create a taxonomy of real world malwares.
Picture taken from http://www.tolweb.org/tree/ and http://www.blogscienze.com
Bibliography
- Felsenstein 2003: Inferring Phylogenies
- Semple and Steel 2003: Phylogenetics: The mathematics of phylogenetics
- Louis J. Billera, Susan P. Holmes and and Karen Vogtmann Geometry of the space of phylogenetic trees. Advances in Applied Math 27, 733-767 (2001)
- Evans, S.N. and Speed, T.P. (1993). Invariants of some probability models used in phylogenetic inference. Annals of Statistics 21, 355-377.
- Lior Pachter, Bernd Sturmfels 2005, Algebraic Statistics for Computational Biology.
- A. Walenstein, E-Md. Karim, A. Lakhotia, and L. Parida. Malware Phylogeny Generation Using Permutations of Code, Journal in Computer Virology, v1.1, 2005.)
… further results
Past tutored projects
Past tutored students
