Analysis of Modulated Multivariate Oscillations

The concept of a common modulated oscillation spanning multiple time series is formalized, a method for the recovery of such a signal from potentially noisy observations is proposed, and the time-varying bias properties of the recovery method are derived. The method, an extension of wavelet ridge analysis to the multivariate case, identifies the common oscillation by seeking, at each point in time, a frequency for which a bandpassed version of the signal obtains a local maximum in power. The lowest-order bias is shown to involve a quantity, termed the instantaneous curvature, which measures the strength of local quadratic modulation of the signal after demodulation by the common oscillation frequency. The bias can be made to be small if the analysis filter, or wavelet, can be chosen such that the signal's instantaneous curvature changes little over the filter time scale. An application is presented to the detection of vortex motions in a set of freely-drifting oceanographic instruments tracking the ocean currents

Radon spectrogram-based approach for automatic IFs separation

The separation of overlapping components is a well-known and difficult problem in multicomponent signals analysis and it is shared by applications dealing with radar, biosonar, seismic, and audio signals. In order to estimate the instantaneous frequencies of a multicomponent signal, it is necessary to disentangle signal modes in a proper domain. Unfortunately, if signal modes supports overlap both in time and frequency, separation is only possible through a parametric approach whenever the signal class is a priori fixed. In this work, time-frequency analysis and Radon transform are jointly used for the unsupervised separation of modes of a generic frequency modulated signal in noisy environment. The proposed method takes advantage of the ability of the Radon transform of a proper time-frequency distribution in separating overlapping modes. It consists of a blind segmentation of signal components in Radon domain by means of a near-to-optimal threshold operation. The inversion of the Radon transform on each detected region allows us to isolate the instantaneous frequency curves of each single mode in the time-frequency domain. Experimental results performed on constant amplitudes chirp signals confirm the effectiveness of the proposed method, opening the way for its extension to more complex frequency modulated signals

Longitudinal tracking of physiological state with electromyographic signals.

Electrophysiological measurements have been used in recent history to classify instantaneous physiological configurations, e.g., hand gestures. This work investigates the feasibility of working with changes in physiological configurations over time (i.e., longitudinally) using a variety of algorithms from the machine learning domain. We demonstrate a high degree of classification accuracy for a binary classification problem derived from electromyography measurements before and after a 35-day bedrest. The problem difficulty is increased with a more dynamic experiment testing for changes in astronaut sensorimotor performance by taking electromyography and force plate measurements before, during, and after a jump from a small platform. A LASSO regularization is performed to observe changes in relationship between electromyography features and force plate outcomes. SVM classifiers are employed to correctly identify the times at which these experiments are performed, which is important as these indicate a trajectory of adaptation

Atmospheric blocking and intercomparison of objective detection methods: flow field characteristics.

Objective methods for identifying and quantifying atmospheric blocking have been developed over recent decades, primarily targeting North Atlantic blocks. Differences arise from these methods, leading to changes in the resultant blocking climatology. To understand these differences, and better inform future assessments built on quantitative detection of blocks, this paper examines blocking properties produced by three different objective detection algorithms over the global extratropics. Blocking criteria examined include 500 hPa geopotential height anomaly ( Z∗ ), column-averaged potential vorticity anomaly ( PV∗ ), and 500 hPa geopotential height gradient (AGP). Results are analyzed for blocking climatologies and for instantaneous blocking patterns, as well as distributions of block size, speed, duration, and distance traveled. The results emphasize physical characteristics of the flow field and the subsequent blocking regions that emerge; overall, PV∗ and Z∗ blocked regions often have higher pattern correlation and spatial similarity, though these two methods also display high agreement with AGP in some instances. Z∗ finds the largest (and greatest number of) blocked regions, while PV∗ -detected regions are smallest in all instances except Southern Hemisphere winter. In some cases, PV∗ tracks a nearby jet streak, leading to differences with height-based algorithms. All three algorithms detect some questionable low-latitude blocks that are stationary and persist but do not impair zonal flow, although at different times. Therefore, careful consideration of the algorithm biases is important in future blocking studies. For example, linking extreme weather to detected blocking could vary substantially depending on the algorithm used

A parallel hypothesis method of autonomous underwater vehicle navigation

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2009This research presents a parallel hypothesis method for autonomous underwater vehicle navigation that enables a vehicle to expand the operating envelope of existing long baseline acoustic navigation systems by incorporating information that is not normally used. The parallel hypothesis method allows the in-situ identification of acoustic multipath time-of-flight measurements between a vehicle and an external transponder and uses them in real-time to augment the navigation algorithm during periods when direct-path time-of-flight measurements are not available. A proof of concept was conducted using real-world data obtained by the Woods Hole Oceanographic Institution Deep Submergence Lab's Autonomous Benthic Explorer (ABE) and Sentry autonomous underwater vehicles during operations on the Juan de Fuca Ridge. This algorithm uses a nested architecture to break the navigation solution down into basic building blocks for each type of available external information. The algorithm classifies external information as either line of position or gridded observations. For any line of position observation, the algorithm generates a multi-modal block of parallel position estimate hypotheses. The multimodal hypotheses are input into an arbiter which produces a single unimodal output. If a priori maps of gridded information are available, they are used within the arbiter structure to aid in the elimination of false hypotheses. For the proof of concept, this research uses ranges from a single external acoustic transponder in the hypothesis generation process and grids of low-resolution bathymetric data from a ship-based multibeam sonar in the arbitration process. The major contributions of this research include the in-situ identification of acoustic multipath time-of-flight measurements, the multiscale utilization of a priori low-resolution bathymetric data in a high-resolution navigation algorithm, and the design of a navigation algorithm with a exible architecture. This flexible architecture allows the incorporation of multimodal beliefs without requiring a complex mechanism for real-time hypothesis generation and culling, and it allows the real-time incorporation of multiple types of external information as they become available in situ into the overall navigation solution

Analysis and decomposition of frequency modulated multicomponent signals

Frequency modulated (FM) signals are studied in many research fields, including seismology, astrophysics, biology, acoustics, animal echolocation, radar and sonar. They are referred as multicomponent signals (MCS), as they are generally composed of multiple waveforms, with specific time-dependent frequencies, known as instantaneous frequencies (IFs). Many applications require the extraction of signal characteristics (i.e. amplitudes and IFs). that is why MCS decomposition is an important topic in signal processing. It consists of the recovery of each individual mode and it is often performed by IFs separation. The task becomes very challenging if the signal modes overlap in the TF domain, i.e. they interfere with each other, at the so-called non-separability region. For this reason, a general solution to MCS decomposition is not available yet. As a matter of fact, the existing methods addressing overlapping modes share the same limitations: they are parametric, therefore they adapt only to the assumed signal class, or they rely on signal-dependent and parametric TF representations; otherwise, they are interpolation techniques, i.e. they almost ignore the information corrupted by interference and they recover IF curve by some fitting procedures, resulting in high computational cost and bad performances against noise. This thesis aims at overcoming these drawbacks, providing efficient tools for dealing with MCS with interfering modes. An extended state-of-the-art revision is provided, as well as the mathematical tools and the main definitions needed to introduce the topic. Then, the problem is addressed following two main strategies: the former is an iterative approach that aims at enhancing MCS' resolution in the TF domain; the latter is a transform-based approach, that combines TF analysis and Radon Transform for separating individual modes. As main advantage, the methods derived from both the iterative and the transform-based approaches are non-parametric, as they do not require specific assumptions on the signal class. As confirmed by the experimental results and the comparative studies, the proposed approach contributes to the current state of the-art improvement

The 2D Continuous Wavelet Transform: Applications in Fringe Pattern Processing for Optical Measurement Techniques

Optical metrology and interferometry are widely known disciplines that study and develop techniques to measure physical quantities such as dimensions, force, temperature, stress, etc. A key part of these disciplines is the processing of interferograms, also called fringe patterns. Owing that this kind of images contains the information of interest in a codified form, processing them is of main relevance and has been a widely studied topic for many years. Several mathematical tools have been used to analyze fringe patterns, from the classic Fourier analysis to regularization methods. Some methods based on wavelet theory have been proposed for this purpose in the last years and have evidenced virtues to consider them as a good alternative for fringe pattern analysis. In this chapter, we resume the theoretical basis of fringe pattern image formation and processing, and some of the most relevant applications of the 2D continuous wavelet transform (CWT) in fringe pattern analysis

Visual Analysis of Extremely Dense Crowded Scenes

Visual analysis of dense crowds is particularly challenging due to large number of individuals, occlusions, clutter, and fewer pixels per person which rarely occur in ordinary surveillance scenarios. This dissertation aims to address these challenges in images and videos of extremely dense crowds containing hundreds to thousands of humans. The goal is to tackle the fundamental problems of counting, detecting and tracking people in such images and videos using visual and contextual cues that are automatically derived from the crowded scenes. For counting in an image of extremely dense crowd, we propose to leverage multiple sources of information to compute an estimate of the number of individuals present in the image. Our approach relies on sources such as low confidence head detections, repetition of texture elements (using SIFT), and frequency-domain analysis to estimate counts, along with confidence associated with observing individuals, in an image region. Furthermore, we employ a global consistency constraint on counts using Markov Random Field which caters for disparity in counts in local neighborhoods and across scales. We tested this approach on crowd images with the head counts ranging from 94 to 4543 and obtained encouraging results. Through this approach, we are able to count people in images of high-density crowds unlike previous methods which are only applicable to videos of low to medium density crowded scenes. However, the counting procedure just outputs a single number for a large patch or an entire image. With just the counts, it becomes difficult to measure the counting error for a query image with unknown number of people. For this, we propose to localize humans by finding repetitive patterns in the crowd image. Starting with detections from an underlying head detector, we correlate them within the image after their selection through several criteria: in a pre-defined grid, locally, or at multiple scales by automatically finding the patches that are most representative of recurring patterns in the crowd image. Finally, the set of generated hypotheses is selected using binary integer quadratic programming with Special Ordered Set (SOS) Type 1 constraints. Human Detection is another important problem in the analysis of crowded scenes where the goal is to place a bounding box on visible parts of individuals. Primarily applicable to images depicting medium to high density crowds containing several hundred humans, it is a crucial pre-requisite for many other visual tasks, such as tracking, action recognition or detection of anomalous behaviors, exhibited by individuals in a dense crowd. For detecting humans, we explore context in dense crowds in the form of locally-consistent scale prior which captures the similarity in scale in local neighborhoods with smooth variation over the image. Using the scale and confidence of detections obtained from an underlying human detector, we infer scale and confidence priors using Markov Random Field. In an iterative mechanism, the confidences of detections are modified to reflect consistency with the inferred priors, and the priors are updated based on the new detections. The final set of detections obtained are then reasoned for occlusion using Binary Integer Programming where overlaps and relations between parts of individuals are encoded as linear constraints. Both human detection and occlusion reasoning in this approach are solved with local neighbor-dependent constraints, thereby respecting the inter-dependence between individuals characteristic to dense crowd analysis. In addition, we propose a mechanism to detect different combinations of body parts without requiring annotations for individual combinations. Once human detection and localization is performed, we then use it for tracking people in dense crowds. Similar to the use of context as scale prior for human detection, we exploit it in the form of motion concurrence for tracking individuals in dense crowds. The proposed method for tracking provides an alternative and complementary approach to methods that require modeling of crowd flow. Simultaneously, it is less likely to fail in the case of dynamic crowd flows and anomalies by minimally relying on previous frames. The approach begins with the automatic identification of prominent individuals from the crowd that are easy to track. Then, we use Neighborhood Motion Concurrence to model the behavior of individuals in a dense crowd, this predicts the position of an individual based on the motion of its neighbors. When the individual moves with the crowd flow, we use Neighborhood Motion Concurrence to predict motion while leveraging five-frame instantaneous flow in case of dynamically changing flow and anomalies. All these aspects are then embedded in a framework which imposes hierarchy on the order in which positions of individuals are updated. The results are reported on eight sequences of medium to high density crowds and our approach performs on par with existing approaches without learning or modeling patterns of crowd flow. We experimentally demonstrate the efficacy and reliability of our algorithms by quantifying the performance of counting, localization, as well as human detection and tracking on new and challenging datasets containing hundreds to thousands of humans in a given scene

A contribution to unobtrusive video-based measurement of respiratory signals

Due to the growing popularity of video-based methods for physiological signal measurement, and taking into account the technological advancements of these type of devices, this work proposes a series of new novel methods to obtain the respiratory signal from a distance, based on video analysis. This thesis aims to improve the state of the art video methods for respiratory measurement, more specifically, by presenting methods that can be used to obtain respiratory variability or perform respiratory rhythm measurements. Moreover, this thesis also aims to present a new implementation of a time-frequency signal processing technique, to improve its computational efficiency when applied to the respiratory signals. In this document a first approach to video-based methods for respiratory signal measurement is performed, to assert the feasibility of using a consumer-grade camera, not only to measure the mean respiratory rate or frequency, but to assert if this hardware could be used to acquire the raw respiratory signal and the respiratory rhythm as well. In this regard a new video-based method was introduced that measures the respiratory signal of a subject at a distance, with the aid of a custom pattern placed on the thorax of the subject. Given the results from the first video-based method, a more broad approach was taken by comparing three different types of video hardware, with the aim to characterise if they could be used for respiratory signal acquisition and respiratory variability measurements. The comparative analysis was performed in terms of instantaneous frequency, as it allowed to characterise the methods in terms of respiratory variability and to compare them in the same terms with the reference method. Subsequently, and due to the previous obtained results, a new method was proposed using a stereo depth camera with the aim to tackle the limitations of the previous study. The proposed method uses an hybrid architecture were the synchronized infrared frame and depth point-cloud from the same camera are acquired. The infrared frame is used to detect the movements of the subject inside the scene, and to recompute on demand a region of interest to obtain the respiratory signal from the depth point-cloud. Furthermore, in this study an opportunistic approach is taken in order to process all the obtained data, as it is also the aim of this study to verify if using a more realistic approach to respiratory signal analysis in real-life conditions, would influence the respiratory rhythm measurement. Even though the depth camera method proved reliable in terms of respiratory rhythm measurement, the opportunistic approach relied on visual inspection of the obtained respiratory signal to properly define each piece. For this reason, a quality indicator had to be proposed that could objectively identify whenever a respiratory signal contained errors. Furthermore, from the idea to characterise the movements of a subject, and by changing the measuring point from a frontal to a lateral perspective to avoid most of the occlusions, a new method based on obtaining the movement of the thoraco-abdominal region using dense optical flow was proposed. This method makes us of the phase of the optical flow to obtain the respiratory signal of the subject, while using the modulus to compute a quality index. Finally, regarding the different signal processing methods used in this thesis to obtain the instantaneous frequency, there were none that could perform in real-time, making the analysis of the respiratory variability not possible in real-life systems where the signals have to be processed in a sample by sample basis. For this reason, as a final chapter a new implementation of the synchrosqueezing transform for time-frequency analysis in real-time is proposed, with the aim to provide a new tool for non-contact methods to obtain the variability of the respiratory signal in real-time.A causa de la creixent popularitat en la mesura de senyals fisiològics amb mètodes de vídeo, i tenint en compte els avenços tecnològics d'aquests dispositius, aquesta tesi proposa una sèrie de nous mètodes per tal d'obtenir la respiració a distància mitjançant l'anàlisi de vídeo. Aquesta tesi té com a objectiu millorar l'estat de l'art referent a la mesura de senyal respiratòria mitjançant els mètodes que en ella es descriuen, així com presentar mètodes que puguin ser usats per obtenir la variabilitat o el ritme respiratori. A més, aquesta tesi té com a objectiu presentar una nova implementació d'un mètode de processat de senyal temps-freqüencial, per tal de millorar-ne l'eficiència computacional quant s’aplica a senyals respiratoris. En aquest document, es realitza una primera aproximació a la mesura de senyal respiratòria mitjançant mètodes de vídeo per tal de verificar si és factible utilitzar una càmera de consum, no només per mesurar el senyal respiratori, sinó verificar si aquest tipus de hardware també pot ser emprat per obtenir el ritme respiratori. En aquest sentit, es presenta en aquest document un nou mètode d'adquisició de senyal respiratòria a distància basat en vídeo, el qual fa ús d'un patró ubicat al tòrax del subjecte per tal d'obtenir-ne la respiració. Un cop obtinguts els resultats del primers resultats, s'han analitzat tres tipus diferents de càmeres, amb la finalitat de caracteritzar-ne la viabilitat d'obtenir el senyal respiratori i la seva variabilitat. L'estudi comparatiu s'ha realitzat en termes de freqüència instantània, donat que permet caracteritzar els mètodes en termes de variabilitat respiratòria i comparar-los, en les mateixes condicions, amb el mètode de referencia. A continuació, s'ha presentat un nou mètode basat en una càmera de profunditat estèreo amb la finalitat de millorar i corregir les limitacions anteriors. El nou mètode proposat es basa en una arquitectura hibrida la qual utilitza els canals de vídeo infraroig i de profunditat de forma sincronitzada. El canal infraroig s'utilitza per detectar els moviments del subjecte dins l'escena i calcular, sota demanda, una regió d'interès que s'utilitza posteriorment en el canal de profunditat per extreure el senyal respiratori. A més a més, en aquest estudi s'ha utilitzat una aproximació oportunista en el processat del senyal respiratori, donat que també és un dels objectius d'aquest estudi, verificar si el fet d'utilitzar una aproximació més realista en l'adquisició de senyal, pot influir en la mesura del ritme respiratori. Tot i que el mètode anterior es mostra fiable en termes de mesura del ritme respiratori, la selecció oportunista del senyal necessita d’inspecció visual per tal de definir correctament cada fragment. Per aquest motiu, era necessari definir un índex de qualitat el qual permetés identificar de forma objectiva cada tram de senyal, així com detectar si el senyal conté errors. Partint de la idea de caracteritzar el moviment del subjecte de l'estudi anterior, i modificant el punt de mesura frontal cap a un de lateral per tal d'evitar oclusions, es proposa un nou mètode basat en l'obtenció del moviment toràcic-abdominal a partir del flux òptic del senyal de vídeo. Aquest mètode recupera el senyal respiratori del subjecte a partir de la fase del flux òptic, tot calculant un índex de qualitat a partir del mòdul. Finalment, i tenint en compte els diferents mètodes de processat utilitzats en aquesta tesi per tal de obtenir la freqüència instantània, es pot apreciar que cap d'ells és capaç de funcionar en temps real, fent inviable l'anàlisi de la variabilitat respiratòria en sistemes reals amb processat mostra a mostra. Per aquest motiu, en el capítol final d'aquesta tesi, s'ha proposat una nova implementació de la transformació "synchrosqueezing" per tal de realitzar l’anàlisi temporal-freqüencial en temps real, i proveir d'una nova eina per tal d'obtenir la variabilitat respiratòria en temps real, amb mètodes sense contacte