Anatomically-based skeleton kinetics and pose estimation in freely-moving rodents

Forming a complete picture of the relationship between neural activity and body kinetics requires quantification of skeletal joint biomechanics during behavior. However, without detailed knowledge of the underlying skeletal motion, inferring joint kinetics from surface tracking approaches is difficult, especially for animals where the relationship between surface anatomy and skeleton changes during motion. Here we developed a videography-based method enabling detailed three-dimensional kinetic quantification of an anatomically defined skeleton in untethered freely-behaving animals. This skeleton-based model has been constrained by anatomical principles and joint motion limits and provided skeletal pose estimates for a range of rodent sizes, even when limbs were occluded. Model-inferred joint kinetics for both gait and gap-crossing behaviors were verified by direct measurement of limb placement, showing that complex decision-making behaviors can be accurately reconstructed at the level of skeletal kinetics using our anatomically constrained model

The Estimation Methods for an Integrated INS/GPS UXO Geolocation System

This work was supported by a project funded by the US Army Corps of Engineers, Strategic Environment Research and Development Program, contract number W912HQ- 08-C-0044.This report was also submitted to the Graduate School of the Ohio State University in partial fulfillment of the PhD degree in Geodetic Science.Unexploded ordnance (UXO) is the explosive weapons such as mines, bombs, bullets, shells and grenades that failed to explode when they were employed. In North America, especially in the US, the UXO is the result of weapon system testing and troop training by the DOD. The traditional UXO detection method employs metal detectors which measure distorted signals of local magnetic fields. Based on detected magnetic signals, holes are dug to remove buried UXO. However, the detection and remediation of UXO contaminated sites using the traditional methods are extremely inefficient in that it is difficult to distinguish the buried UXO from the noise of geologic magnetic sources or anthropic clutter items. The reliable discrimination performance of UXO detection system depends on the employed sensor technology as well as on the data processing methods that invert the collected data to infer the UXO. The detection systems require very accurate positioning (or geolocation) of the detection units to detect and discriminate the candidate UXO from the non-hazardous clutter, greater position and orientation precision because the inversion of magnetic or EMI data relies on their precise relative locations, orientation, and depth. The requirements of position accuracy for MEC geolocation and characterization using typical state-of-the-art detection instrumentation are classified according to levels of accuracy outlined in: the screening level with position tolerance of 0.5 m (as standard deviation), area mapping (less than 0.05 m), and characterize and discriminate level of accuracy (less than 0.02m). The primary geolocation system is considered as a dual-frequency GPS integrated with a three dimensional inertial measurement unit (IMU); INS/GPS system. Selecting the appropriate estimation method has been the key problem to obtain highly precise geolocation of INS/GPS system for the UXO detection performance in dynamic environments. For this purpose, the Extended Kalman Filter (EKF) has been used as the conventional algorithm for the optimal integration of INS/GPS system. However, the newly introduced non-linear based filters can deal with the non-linear nature of the positioning dynamics as well as the non-Gaussian statistics for the instrument errors, and the non-linear based estimation methods (filtering/smoothing) have been developed and proposed. Therefore, this study focused on the optimal estimation methods for the highly precise geolocation of INS/GPS system using simulations and analyses of two Laboratory tests (cart-based and handheld geolocation system). First, the non-linear based filters (UKF and UKF) have been shown to yield superior performance than the EKF in various specific simulation tests which are designed similar to the UXO geolocation environment (highly dynamic and small area). The UKF yields 50% improvement in the position accuracy over the EKF particularly in the curved sections (medium-grade IMUs case). The UKF also performed significantly better than EKF and shows comparable improvement over the UKF when the IMU noise probability iii density function is symmetric and non-symmetric. Also, since the UXO detection survey does not require the real-time operations, each of the developed filters was modified to accommodate the standard Rauch-Tung-Striebel (RTS) smoothing algorithms. The smoothing methods are applied to the typical UXO detection trajectory; the position error was reduced significantly using a minimal number of control points. Finally, these simulation tests confirmed that tactical-grade IMUs (e.g. HG1700 or HG1900) are required to bridge gaps of high-accuracy ranging solution systems longer than 1 second. Second, these result of the simulation tests were validated from the laboratory tests using navigation-grade and medium-grade accuracy IMUs. To overcome inaccurate a priori knowledge of process noise of the system, the adaptive filtering methods have been applied to the EKF and UKF and they are called the AEKS and AUKS. The neural network aided adaptive nonlinear filtering/smoothing methods (NN-EKS and NN-UKS) which are augmented with RTS smoothing method were compared with the AEKS and AUKS. Each neural network-aided, adaptive filter/smoother improved the position accuracy in both straight and curved sections. The navigation grade IMU (H764G) can achieve the area mapping level of accuracy when the gap of control points is about 8 seconds. The medium grade IMUs (HG1700 and HG1900) with NN-AUKS can maintain less than 10cm under the same conditions as above. Also, the neural network aiding can decrease the difference of position error between the straight and the curved section. Third, in the previous simulation test, the UPF performed better than the other filters. However since the UPF needs a large number of samples to represent the a posteriori statistics in high-dimensional space, the RBPF can be used as an alternative to avoid the inefficiency of particle filter. The RBPF is tailored to precise geolocation for UXO detection using IMU/GPS system and yielded improved estimation results with a small number of samples. The handheld geolocation system using HG1900 with a nonlinear filter-based smoother can achieve the discrimination level of accuracy if the update rate of control points is less than 0.5Hz and 1Hz for the sweep and swing respectively. Also, the sweep operation is more preferred than the swing motion because the position accuracy of the sweep test was better than that of the swing test

Estimation of skeletal kinematics in freely moving rodents

Forming a complete picture of the relationship between neural activity and skeletal kinematics requires quantification of skeletal joint biomechanics during free behavior; however, without detailed knowledge of the underlying skeletal motion, inferring limb kinematics using surface-tracking approaches is difficult, especially for animals where the relationship between the surface and underlying skeleton changes during motion. Here we developed a videography-based method enabling detailed three-dimensional kinematic quantification of an anatomically defined skeleton in untethered freely behaving rats and mice. This skeleton-based model was constrained using anatomical principles and joint motion limits and provided skeletal pose estimates for a range of body sizes, even when limbs were occluded. Model-inferred limb positions and joint kinematics during gait and gap-crossing behaviors were verified by direct measurement of either limb placement or limb kinematics using inertial measurement units. Together we show that complex decision-making behaviors can be accurately reconstructed at the level of skeletal kinematics using our anatomically constrained model

Tracking Meteoroids in the Atmosphere: Fireball Trajectory Analysis

This thesis improves and develops algorithms for fireball trajectory analysis. Stochastic estimators outside the current field of fireball modelling have been applied, from Kalman filters to 3D particle filters. These techniques are fully automated and rigorously incorporate errors, providing a means to routinely analyse fireball data in an unbiased manner

Nonlinear Gaussian Filtering : Theory, Algorithms, and Applications

By restricting to Gaussian distributions, the optimal Bayesian filtering problem can be transformed into an algebraically simple form, which allows for computationally efficient algorithms. Three problem settings are discussed in this thesis: (1) filtering with Gaussians only, (2) Gaussian mixture filtering for strong nonlinearities, (3) Gaussian process filtering for purely data-driven scenarios. For each setting, efficient algorithms are derived and applied to real-world problems

Toward Constrained Animal Pose Estimation

Quantifying animal behavior is a crucial aspect of the ongoing neuroscientific endeavor to understand the brain, since it is a prerequisite for studying how neural computations relate to behavioral outputs. One method for obtaining an objective yet detailed description of an animal's unconstrained and therefore natural behavior is given by estimating its pose, i.e. the collective positions and orientations of all individual body parts in space at a given moment in time. While various approaches have been proposed for estimating the pose of a freely-moving animal, so far, studies relying on video cameras for recording the required behavioral data have neglected reconstructing the actual skeleton of an animal and only considered inferring the positions of anatomical landmarks located on its body surface. Additionally, many approaches lack incorporating mechanistic knowledge of an animal's anatomy, which leaves room for improving the resulting pose reconstruction accuracy. Consequently, methods for quantifying skeletal animal poses during free motion sequences are desirable tools for future neuroscientific studies. The work presented in this thesis tackles the problem of inferring skeletal poses from recorded video data of freely-moving animal subjects via a constrained animal pose estimation framework, which enables reconstructing underlying three-dimensional joint positions from observable surface markers while enforcing anatomical and temporal constraints. Anatomical constraints are implemented via a realistic skeleton model, which accounts for physiological joint angle limits, bone lengths and body symmetry. Besides, the realistic skeleton model allows for learning individual skeleton anatomies directly from recorded video data of behaving animals, taking into account subject-specific differences with respect to bone lengths and body-symmetry. Furthermore, to ensure that reconstructed joint positions follow smooth motion trajectories, the proposed animal pose estimation framework also enforces temporal constraints. Particularly, temporal constraints are implemented via an underlying state space model, which allows for deploying a Bayesian smoother for inferring bone rotations as well as an expectation-maximization algorithm for learning the unknown probabilistic hyper-parameters of the state space model. The proposed animal pose estimation framework is evaluated and tested with respect to its reconstruction accuracy and usability for quantifying a range of different behaviors. By comparing learned skeleton anatomies with ground truth data obtained via magnetic resonance imaging, it is shown that the framework offers the opportunity to learn three-dimensional joint positions and bone lengths solely from two-dimensional video data. Besides, to test whether poses of freely-moving animals are accurately inferred, independently measured paw positions are obtained using a frustrated total internal reflection imaging system and compared to their reconstructed counterparts, while the effects of the enforced anatomical and temporal constraints are analyzed. This analysis shows the advantages of constrained over unconstrained animal pose estimation, since enforcing constraints reduces errors with respect to reconstructed paw positions and orientations. Furthermore, to assess if the proposed pose estimation framework is capable of accurately quantifying common behaviors, periodic gait cycles are analyzed based on reconstructed skeletal poses, which shows that enforcing constraints is essential for successfully extracting characteristic movement patterns from recorded video data. Finally, the proposed pose estimation framework is also used to quantify complex gap-crossing behaviors, where animals jump over gaps of various distances. This analysis shows that reconstructing skeletal poses enables computing characteristic movement patterns during jumping and correlating skeletal kinematic quantities with each other as well as the jumped distances. In summary, this thesis proposes an animal pose estimation framework, which allows for reconstructing anatomically-plausible as well as time-consistent three-dimensional skeletal poses of freely-moving animals from two-dimensional video data. To achieve this, anatomical and temporal constraints are implemented into the proposed pose reconstruction framework, which transpired to be essential for obtaining accurate pose reconstruction results. Consequently, this thesis contains analyses, which demonstrate the importance of the implemented constraints in the context of animal pose estimation

Testing quantum mechanics: a statistical approach

As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited, how can we be sure that we are observing quantum behavior? This tutorial highlights some of the difficulties in such experimental tests of quantum mechanics, using optomechanics as the central example, and discusses how the issues can be resolved using techniques from statistics and insights from quantum information theory.Comment: v1: 2 pages; v2: invited tutorial for Quantum Measurements and Quantum Metrology, substantial expansion of v1, 19 pages; v3: accepted; v4: corrected some errors, publishe

Practical methods for Gaussian mixture filtering and smoothing

In many applications, there is an interest in systematically and sequentially estimating quantities of interest in a dynamical system, using indirect and inaccurate sensor observations. There are three important sub-problems of sequential estimation: prediction, filtering and smoothing. The objective in the prediction problem is to estimate the future states of the system, using the observations until the current point in time. In the filtering problem, we seek to estimate the current state of the system, using the same information and in the smoothing problem, the aim is to estimate a past state. The smoothing estimate has the advantage that it offers the best performance on average compared to filtering and prediction estimates. Often, the uncertainties regarding the system and the observations are modeled using Gaussian mixtures (GMs). The smoothing solutions to GMs are usually based on pruning approximations, which suffer from the degeneracy problem, resulting in inconsistent estimates. Solutions based on merging have not been explored well in the literature. We address the problem of GM smoothing using both pruning and merging approximations. We consider the two main smoothing strategies of forward-backward smoothing (FBS) and two-filter smoothing (TFS), and develop novel algorithms for GM smoothing which are specifically tailored for the two principles. The FBS strategy involves forward filtering followed by backward smoothing. The existing literature provides pruning-based solutions to the forward filtering and the backward smoothing steps involved. In this thesis, we present a novel solution to the backward smoothing step of FBS, when the forward filtering uses merging methods. The TFS method works by running two filtering steps: forward filtering and backward filtering. It is not possible to apply the pruning or merging strategies to the backward filtering, as it is not a density function. To the best of our knowledge, there does not exist practical approximation techniques to reduce the complexity of the backward filtering. Therefore, in this thesis we propose two novel techniques to approximate the output of the backward filtering, which we call intragroup approximation and smoothed posterior pruning. We also show that the smoothed posterior pruning technique is applicable to forward filtering as well. The FBS and TFS solutions based on the proposed ideas are implemented for a single target tracking scenario and are shown to have similar performance with respect to root mean squared error, normalized estimation error squared, computational complexity and track loss. Compared to the FBS based on N-scan pruning, both these algorithms provide estimates with high consistency and low complexity