Application and Evaluation of Lighthouse Technology for Precision Motion Capture

This thesis presents the development towards a system that can capture and quantify motion for applications in biomechanical and medical fields demanding precision motion tracking using the lighthouse technology. Commercially known as SteamVR tracking, the lighthouse technology is a motion tracking system developed for virtual reality applications that makes use of patterned infrared light sources to highlight trackers (objects embedded with photodiodes) to obtain their pose or spatial position and orientation. Current motion capture systems such as the camera-based motion capture are expensive and not readily available outside of research labs. This thesis provides a case for low-cost motion capture systems. The technology is applied to quantify motion to draw inferences about biomechanics capture and analysis, quantification of gait, and prosthetic alignment. Possible shortcomings for data acquisition using this system for the stated applications have been addressed. The repeatability of the system has been established by determining the standard deviation error for multiple trials based on a motion trajectory using a seven degree-of-freedom robot arm. The accuracy testing for the system is based on cross-validation between the lighthouse technology data and transformations derived using joint angles by developing a forward kinematics model for the robot’s end-effector pose. The underlying principle for motion capture using this system is that multiple trackers placed on limb segments allow to record the position and orientation of the segments in relation to a set global frame. Joint angles between the segments can then be calculated from the recorded positions and orientations of each tracker using inverse kinematics. In this work, inverse kinematics for rigid bodies was based on calculating homogeneous transforms to the individual trackers in the model’s reference frame to find the respective Euler angles as well as using the analytical approach to solve for joint variables in terms of known geometric parameters. This work was carried out on a phantom prosthetic limb. A custom application-specific motion tracker was also developed using a hardware development kit which would be further optimized for subsequent studies involving biomechanics motion capture

Classically Perfect Gauge Actions on Anisotropic Lattices

We present a method for constructing classically perfect anisotropic actions for SU(3) gauge theory based on an isotropic Fixed Point Action. The action is parametrised using smeared (``fat'') links. The construction is done explicitly for anisotropy $\xi=a_s/a_t=2$ and 4. The corresponding renormalised anisotropies are determined using the torelon dispersion relation. The renormalisation of the anisotropy is small and the parametrisation describes the true action well. Quantities such as the static quark-antiquark potential, the critical temperature of the deconfining phase transition and the low-lying glueball spectrum are measured on lattices with anisotropy $\xi=2$. The mass of the scalar $0^{++}$ glueball is determined to be 1580(60) MeV, while the tensor $2^{++}$ glueball is at 2430(60) MeV.Comment: 64 pages, 19 figures, LaTe

Fixed Point Gauge Actions with Fat Links: Scaling and Glueballs

A new parametrization is introduced for the fixed point (FP) action in SU(3) gauge theory using fat links. We investigate its scaling properties by means of the static quark-antiquark potential and the dimensionless quantities $r_0 T_c, T_c/\sqrt{\sigma}$ and $r_0 \sqrt{\sigma}$, where $T_c$ is the critical temperature of the deconfining phase transition, $r_0$ is the hadronic scale and $\sigma$ is the effective string tension. These quantities scale even on lattices as coarse as $a \approx 0.3$ fm. We also measure the glueball spectrum and obtain $m_{0^{++}}=1627(83)$ MeV and $m_{2^{++}}=2354(95)$ MeV for the masses of the scalar and tensor glueballs, respectively.Comment: 45 pages, 12 figures, Late

Classical Analog of Quantum Models in Synthetic Dimensions

We introduce a classical analog of quantum matter in ultracold molecule- or Rydberg atom- synthetic dimensions, extending the Potts model to include interactions J1 between atoms adjacent in both real and synthetic space and studying its finite temperature properties. For intermediate values of J1, the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high temperature disordered phase and the low temperature ferromagnetic phase. We also employ machine learning to uncover non-trivial features of the phase diagram using the learning by confusion approach.Comment: 12 pages, 10 figure

Computational Studies of Quantum Spin Systems

These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of Monte Carlo studies of classical spin systems, to illustrate finite-size scaling at continuous and first-order phase transitions. Exact diagonalization and quantum Monte Carlo (stochastic series expansion) algorithms and their computer implementations are then discussed in detail. Applications of the methods are illustrated by results for some of the most essential models in quantum magnetism, such as the S=1/2 Heisenberg antiferromagnet in one and two dimensions, as well as extended models useful for studying quantum phase transitions between antiferromagnetic and magnetically disordered states.Comment: 207 pages, 91 figures. Lecture notes for course given at the 14th Training Course in Physics of Strongly Correlated Systems, Salerno (Vietri sul Mare), Italy, in October 200

Convex Hulls: Complexity and Applications (a Survey)

Computational geometry is, in brief, the study of algorithms for geometric problems. Classical study of geometry and geometric objects, however, is not well-suited to efficient algorithms techniques. Thus, for the given geometric problems, it becomes necessary to identify properties and concepts that lend themselves to efficient computation. The primary focus of this paper will be on one such geometric problems, the Convex Hull problem

Localization and Optimization Problems for Camera Networks

In the framework of networked control systems, we focus on networks of autonomous PTZ cameras. A large set of cameras communicating each other through a network is a widely used architecture in application areas like video surveillance, tracking and motion. First, we consider relative localization in sensor networks, and we tackle the issue of investigating the error propagation, in terms of the mean error on each component of the optimal estimator of the position vector. The relative error is computed as a function of the eigenvalues of the network: using this formula and focusing on an exemplary class of networks (the Abelian Cayley networks), we study the role of the network topology and the dimension of the networks in the error characterization. Second, in a network of cameras one of the most crucial problems is calibration. For each camera this consists in understanding what is its position and orientation with respect to a global common reference frame. Well-known methods in computer vision permit to obtain relative positions and orientations of pairs of cameras whose sensing regions overlap. The aim is to propose an algorithm that, from these noisy input data makes the cameras complete the calibration task autonomously, in a distributed fashion. We focus on the planar case, formulating an optimization problem over the manifold SO(2). We propose synchronous deterministic and distributed algorithms that calibrate planar networks exploiting the cycle structure of the underlying communication graph. Performance analysis and numerical experiments are shown. Third, we propose a gossip-like randomized calibration algorithm, whose probabilistic convergence and numerical studies are provided. Forth and finally, we design surveillance trajectories for a network of calibrated autonomous cameras to detect intruders in an environment, through a continuous graph partitioning problem