My research involves the modeling, reconstruction and analysis of 2D and 3D phenomena. So far, it has focused on the modeling of fluid dynamical systems at micro and nano scales, and the study of distributed camera networks. Descriptions for some selected work can be found below.

Doctoral Dissertation

Occlusions in Camera Networks and Vision: The Bridge between Topological Recovery and Metric Reconstruction

by E.J. Lobaton

Camera networks are widely used for security and tracking. Knowledge of camera locations and geometric constraints in the environment are usually assumed in order to accomplish these tasks. However, many of these tasks do not require actual localization. Topological information about the network coverage is many times sufficient. In this work, a simplicial representation called the $CN$-Complex is presented which captures accurate topological information about the coverage of the network. The construction process of this representation relies on the detection of occlusion events. Occlusions are shown to occur when certain generalized topological invariants are violated. The use of these sparse events leads to algorithms which require the extraction of information from continuous observations. The $CN$-Complex is shown to be useful for navigation and path identification purposes. Augmenting this representation leads to the discovery of relations between camera pairs providing relative positions at different degrees of accuracy. These relations create a bridge between a purely topological model and a fully localized network. Several theoretical results are shown for occlusion detection and topology recovery, which are then validated by simulations and experiments.

[Thesis] - [Presentation]

Distributed Computer Vision

The goal of this study is the understanding of distributed camera networks as a whole. Applications include the recovery of metric and topological information of the environment (cameras and observed objects).

Algebraic Approach for Recovering Topology in Distributed Camera Networks

by E.J. Lobaton, P. Ahammad and S.S. Sastry

Camera networks are widely used for tasks such as surveillance, monitoring and tracking. In order to accomplish these tasks, knowledge of localization information such as camera locations and other geometric constraints about the environment (e.g. walls, rooms, and building layout) are typically considered to be essential. However, this information is not always required for many tasks such as estimating the topology of camera network coverage, or coordinate-free object tracking and navigation. In this paper, we propose a simplicial representation (called CN-Complex) that can be constructed from discrete local observations from cameras, and utilize this novel representation to recover the topological information of the network coverage. We prove that our representation captures the correct topological information from network coverage for 2.5D layouts, and demonstrate their utility in simulations as well as a real-world experimental set-up. Our proposed approach is particularly useful in the context of ad-hoc camera networks in indoor/outdoor urban environments with distributed but limited computational power and energy.

[Paper-IPSN'09] - [CITRIC Platform]

A Framework for Collaborative Real-Time 3D Teleimmersion in a Geographically Distributed Environment

by G. Kurillo, R. Vasudevan, E.J. Lobaton, and R. Bajcsy

In this paper, we present a framework for immersive 3D video conferencing and geographically distributed collaboration. Our multi-camera system performs a full-body 3D reconstruction of users in real time and renders their image in a virtual space allowing remote interaction between users and the virtual environment. The paper features an overview of the technology and algorithms used for calibration, capturing, and reconstruction. We introduce stereo mapping using adaptive triangulation which allows for fast (under 25 ms) and robust real-time 3D reconstruction. The chosen representation of the data provides high compression ratios for transfer to a remote site. The algorithm produces partial 3D meshes, instead of dense point clouds, which are combined on the renderer to create a unified model of the user. We have successfully demonstrated the use of our system in various applications such as remote dancing and immersive Tai Chi learning.

[Paper-ISM'08] - [Tele-Immersion Website]

Fluid Modeling and Analysis

This research involves a dynamics model for organisms at low Reynolds numbers, as well as the study of gas-liquid-solid interfaces at nanoscales.

Modeling and Optimization Analysis of a Single-Flagellum Micro-Structure Through the Method of Regularized Stokeslets

by E.J. Lobaton and A. Bayen

Bacteria such as Rhodobacter sphaeroides use a single flagellum for propulsion and change of orientation. These types of simple organisms have inspired microrobotic designs with potential applications in medicine, which motivates the present work. In this article, an elastic model for a single-flagellum micro-structure is presented and followed by an analysis of the system based on optimization. The model is based on the method of Regularized Stokeslets which allows for a discretization of the system into particles connected by spring forces. The optimization analysis leads to the design of an optimal elasticity distribution that maximizes the mean forward speed of the structure. These elasticity coefficients are obtained through the use of adjoint-based optimization. The results are illustrated through simulations showing improvement on the swimming pattern of the micro-structure.

[Paper-IEEE CST] - [Website]

A Study of Bacterial Flagellar Bundling

by H. Flores, E.J. Lobaton, S. Mendez-Diez, S. Tlupova, and R. Cortez

Certain bacteria, such as Escherichia coli (E. coli) and Salmonella typhimurium, use multiple flagella often concentrated at one end of their bodies to induce locomotion. Each flagellum is formed in a left-handed helix and has a motor at the base that rotates the flagellum in a corkscrew motion. We present a computational model of the flagellar motion and their hydrodynamic interaction. The model is based on the equations of Stokes flow to describe the fluid motion. The elasticity of the flagella is modeled with a network of springs of given resting length and stiffness while the motor is represented by a torque at the base of each flagellum. The fluid velocity due to the forces is described by regularized Stokeslets and the velocity due to the torques by the associated regularized rotlets. Their expressions are derived. The model is used to analyze the swimming motion of a single flagellum and of a group of three flagella in close proximity to one another. When all flagellar motors rotate counterclockwise, the hydrodynamic interaction can lead to bundling. We present an analysis of the flow surrounding the flagella. When one of the motors changes its direction of rotation, the same initial conditions lead to a tumbling behavior characterized by the separation of the flagella, changes in their orientation, and no net swimming motion. The analysis of the flow provides some intuition for these processes.

[Paper] - [Animation]

Computation of Constant Mean Curvature Surfaces: Application to the Gas–Liquid Interface of a Pressurized Fluid on a Superhydrophobic Surface

by E.J. Lobaton and T.R. Salamon

The interface shape separating a gas layer within a superhydrophobic surface consisting of a square lattice of posts from a pressurized liquid above the surface is computed numerically. The interface shape is described by a constant mean curvature surface that satisfies the Young–Laplace equation with the three-phase gas–liquid–solid contact line assumed pinned at the post outer edge. The numerical method predicts the existence of constant mean curvature solutions from the planar, zero curvature solution up to a maximum curvature that is dependent on the post shape, size and pitch. An overall force balance between surface tension and pressure forces acting on the interface yields predictions for the maximum curvature that agree with the numerical simulations to within one percent for convex shapes such as circular and square posts, but significantly over predicts the maximum curvature for non-convex shapes such as a circular post with a sinusoidal surface perturbation. Changing the post shape to increase the contact line length, while maintaining constant post area, results in increases of 2 to 12% in the maximum computable curvature for contact line length increases of 11 to 77%. Comparisons are made to several experimental studies for interface shape and pressure stability.

[Paper-Nanonails] - [Paper-Electrically Tunable Nanonails]