Research projects

My research interests lie at the intersection of automatic control, robotics and computer vision. I am particularly interested in applications of Riemannian geometry and in distributed problems involving teams of multiple agents.

Distributed semantic processing in camera networks

By Roberto Tron
May 23rd, 2017 in Research.

Overview

In many applications, sensor networks can be used to monitor large geographical regions. This typically produces large quantities of data that need to be associated, summarized and classified in order to arrive to a semantically meaningful descriptions of the phenomena being monitored. The long-term guiding vision of this project is a distributed network that can perform this analysis autonomously, over long periods of times, and in a scalable way. As a concrete application, this research focuses on smart camera networks with nodes that are either static or part of robotic agents. The planned work will result in systems that are more efficient, accurate, and resilient. The algorithms developed will find wide applications, including in security (continuously detecting suspicious individuals in real time) and the Internet of Things. As part of the broader impacts, the project will produce educational material to explain the scientific results of the project to a K12 audience.

QuickMatch: Fast Multi-Image Matching via Density-Based Clustering

Illustration of the idea of finding multi-image correspondences by seeing each match as a cluster C_c (blue squares). This view automatically prevents inconsistent matches (red lines).

The first result of this project is an algorithm, QuickMatch, that performs consistent matching across multiple images. Quickmatch formulates the problem as a clustering problem (see figure) and then uses a modified density-based algorithm to separate the points in clusters that represents consistent matches across images.

In particular, with respect to previous work, QuickMatch 1) represents a novel application of density-based clustering; 2) directly outputs consistent multi-image matches without explicit pre-processing (e.g., initial pairwise decisions) or post-processing (e.g., thresholding of a matrix); 3) is non-iterative, deterministic, and initialization-free; 4) produces better results in a small fraction of the time (it is up to 62 times faster in some benchmarks); 5) can scale to large datasets that previous methods cannot handle (it has been tested with more than 20k+ features); 6) takes advantage of the distinctiveness of the descriptor as done in traditional matching to counteract the problem of repeated structures; 7) does not assume a one-to-one correspondence of features between images; 8) does not need a-priori knowledge of the number of entities (i.e., clusters) present in the images. Code is available under the Software page.

“NetMatch: the Game”, and educational board game

We  developed an alpha version of a board game, called NetMatch, that provides a tangible and fun way to explain the main research challenges in the project. This game is for two to four players, whose goal is to move their pawns across a network (one hop at a time) from the edges in order to match pawns with similar symbols. When all the pawns for a symbol are matched, a letter for a secret word is revealed. The player that discovers all the letters of his word is the winner.

To start playing, simply download, print, and cut the pieces from the PDF document.

The majority of the game’s components components (board, cards, pawns) are procedurally generated. The code is made freely available, so that it is possible to easily generate variations of the game. The code made available on a git repository (https://bitbucket.org/tronroberto/pythonnetmatchgame).

If you play the game, and have comments or suggestions, please email them to tron@bu.edu.

Publications

Funding and support

This project is supported by the National Science Foundation grant “III: Small: Distributed Semantic Information Processing Applied to Camera Sensor Networks” (Award number 1717656).
NSF Logo

Vision-based formation control

By Roberto Tron
August 22nd, 2016 in Research.

The goal of formation control is to move a group of agents in order to achieve and maintain a set of desired relative positions. This problem has a long history, and latest trends emphasize the use of vision-based solution. In this setting, the measurement of the relative direction (i.e., bearing) between two agents can be quite accurate, while the measurement of their distance is typically less reliable.

We propose a general solution which is based on pure bearing measurements, optionally augmented with the corresponding distances. As opposed to the state of the art, our control law does not require auxiliary distance measurements or estimators, it can be applied to leaderless or leader-based formations with arbitrary topologies. Our framework is based on distributed optimization, and it has global convergence guarantees.

We have experimentally validated our approach on a platform of three quadrotors.

A photograph of the formation of three quadrotors from our experimental setup

A photograph of the formation of three quadrotors from our experimental setup

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The space of essential matrices as a Riemannian manifold

By Roberto Tron
August 22nd, 2016 in Research.

The images of 3-D points in two views are related by the so-called _essential matrix_.
There have been attempts to characterize the space of valid essential matrices as a Riemannian manifold. These approaches either put an unnatural emphasis on one of the two cameras, or do not accurately take into account the geometric meaning of the representation.

We addressed these limitations[^1] by proposing a new parametrization which aligns the global reference frame with the baseline between the two cameras. This provides a symmetric, geometrically meaningful representation which can be naturally derived as a quotient manifold. This not only provides a principled way to define distances between essential matrices, but it also sheds new light on older results (such as the well-known twisted pair ambiguity).

A graphical representation of the quotient representation

A graphical representation of the quotient representation

We provide an implementation of the basic function for working with the essential manifold integrated with the Matlab toolbox MANOPT. Download link: Manopt 1.06b with essential manifold.

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Distributed localization algorithms

By Roberto Tron
August 22nd, 2016 in Research.

Imagine a wireless camera network, where each camera has a piece of local information, e.g., the pose of the object from a specific viewpoint or the relative poses with respect to the neighboring cameras.

Illustration of a camera network

Illustration of a camera network

It is natural to look for distributed algorithms which merge all these local measurements into a single, globally consistent estimate. I derived such algorithms by formulating a global optimization problem over the space of poses, and shown their convergence from a large set of initial conditions using the aforementioned theoretical tools.

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Consensus algorithms on Riemannian manifolds

By Roberto Tron
August 22nd, 2016 in Research.

Given a group of agents which move in Euclidean space and communicate according to a given communication graph, standard consensus algorithms provide a protocol which, as time passes, brings all the agents to a common location. The key aspect here is that only local communications are used. These algorithms, however, do not apply when the agents evolve on a manifold (for instance, imagine a group of satellites synchronizing their poses). Using my theoretical work, I proposed a natural extension for this case, and characterized its convergence for a large class of manifolds.
This work was awarded Best Student Paper and Best Student Paper Runner-up at the IEEE Conference for Decision and Control (CDC) in 2012 and 2011, respectively.

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Distributed optimization on Riemannian manifolds

By Roberto Tron
August 22nd, 2016 in Research.

I worked on distributed optimization problems involving variables lying on non-linear spaces (that is, Riemannian manifolds) using extensions of gradient descent algorithms with fixed step size. I developed novel theoretical tools which significantly broadened the state of the art for determining sufficient conditions for global behaviors (algorithm convergence) using only local information. These tools have been used in consensus algorithms, camera localization and formation control.

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Motion segmentation

By Roberto Tron
August 22nd, 2016 in Research.

My initial research included the comparison of different algorithms for segmenting multiple moving objects in a monocular video.  For this purpose,
I created the Hopkins 155 dataset, which, since its introduction, has been used in over 150 scholarly articles and is a de-facto standard benchmark in this field.
The following is a frame from the dataset, together with the manually labelled feature tracks.

 

A frame from the Hopkins dataset with superimposed tracks

A frame from the Hopkins dataset with superimposed tracks

 

Please refer to the dataset page on the JHU Vision Lab for more detailed information and download instructions.

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