Point-set manifold processing for computational mechanics: thin shells, reduced order modeling, cell motility and molecular conformations

In many applications, one would like to perform calculations on smooth manifolds of dimension d embedded in a high-dimensional space of dimension D. Often, a continuous description of such manifold is not known, and instead it is sampled by a set of scattered points in high dimensions. This poses a serious challenge. In this thesis, we approximate the point-set manifold as an overlapping set of smooth parametric descriptions, whose geometric structure is revealed by statistical learning methods, and then parametrized by meshfree methods. This approach avoids any global parameterization, and hence is applicable to manifolds of any genus and complex geometry. It combines four ingredients: (1) partitioning of the point set into subregions of trivial topology, (2) the automatic detection of the local geometric structure of the manifold by nonlinear dimensionality reduction techniques, (3) the local parameterization of the manifold using smooth meshfree (here local maximum-entropy) approximants, and (4) patching together the local representations by means of a partition of unity. In this thesis we show the generality, flexibility, and accuracy of the method in four different problems. First, we exercise it in the context of Kirchhoff-Love thin shells, (d=2, D=3). We test our methodology against classical linear and non linear benchmarks in thin-shell analysis, and highlight its ability to handle point-set surfaces of complex topology and geometry. We then tackle problems of much higher dimensionality. We perform reduced order modeling in the context of finite deformation elastodynamics, considering a nonlinear reduced configuration space, in contrast with classical linear approaches based on Principal Component Analysis (d=2, D=10000's). We further quantitatively unveil the geometric structure of the motility strategy of a family of micro-organisms called Euglenids from experimental videos (d=1, D~30000's). Finally, in the context of enhanced sampling in molecular dynamics, we automatically construct collective variables for the molecular conformational dynamics (d=1...6, D~30,1000's)

Joint optimization of manifold learning and sparse representations for face and gesture analysis

Face and gesture understanding algorithms are powerful enablers in intelligent vision systems for surveillance, security, entertainment, and smart spaces. In the future, complex networks of sensors and cameras may disperse directions to lost tourists, perform directory lookups in the office lobby, or contact the proper authorities in case of an emergency. To be effective, these systems will need to embrace human subtleties while interacting with people in their natural conditions. Computer vision and machine learning techniques have recently become adept at solving face and gesture tasks using posed datasets in controlled conditions. However, spontaneous human behavior under unconstrained conditions, or in the wild, is more complex and is subject to considerable variability from one person to the next. Uncontrolled conditions such as lighting, resolution, noise, occlusions, pose, and temporal variations complicate the matter further. This thesis advances the field of face and gesture analysis by introducing a new machine learning framework based upon dimensionality reduction and sparse representations that is shown to be robust in posed as well as natural conditions. Dimensionality reduction methods take complex objects, such as facial images, and attempt to learn lower dimensional representations embedded in the higher dimensional data. These alternate feature spaces are computationally more efficient and often more discriminative. The performance of various dimensionality reduction methods on geometric and appearance based facial attributes are studied leading to robust facial pose and expression recognition models. The parsimonious nature of sparse representations (SR) has successfully been exploited for the development of highly accurate classifiers for various applications. Despite the successes of SR techniques, large dictionaries and high dimensional data can make these classifiers computationally demanding. Further, sparse classifiers are subject to the adverse effects of a phenomenon known as coefficient contamination, where for example variations in pose may affect identity and expression recognition. This thesis analyzes the interaction between dimensionality reduction and sparse representations to present a unified sparse representation classification framework that addresses both issues of computational complexity and coefficient contamination. Semi-supervised dimensionality reduction is shown to mitigate the coefficient contamination problems associated with SR classifiers. The combination of semi-supervised dimensionality reduction with SR systems forms the cornerstone for a new face and gesture framework called Manifold based Sparse Representations (MSR). MSR is shown to deliver state-of-the-art facial understanding capabilities. To demonstrate the applicability of MSR to new domains, MSR is expanded to include temporal dynamics. The joint optimization of dimensionality reduction and SRs for classification purposes is a relatively new field. The combination of both concepts into a single objective function produce a relation that is neither convex, nor directly solvable. This thesis studies this problem to introduce a new jointly optimized framework. This framework, termed LGE-KSVD, utilizes variants of Linear extension of Graph Embedding (LGE) along with modified K-SVD dictionary learning to jointly learn the dimensionality reduction matrix, sparse representation dictionary, sparse coefficients, and sparsity-based classifier. By injecting LGE concepts directly into the K-SVD learning procedure, this research removes the support constraints K-SVD imparts on dictionary element discovery. Results are shown for facial recognition, facial expression recognition, human activity analysis, and with the addition of a concept called active difference signatures, delivers robust gesture recognition from Kinect or similar depth cameras

Compressed Sensing in Multi-Signal Environments.

Technological advances and the ability to build cheap high performance sensors make it possible to deploy tens or even hundreds of sensors to acquire information about a common phenomenon of interest. The increasing number of sensors allows us to acquire ever more detailed information about the underlying scene that was not possible before. This, however, directly translates to increasing amounts of data that needs to be acquired, transmitted, and processed. The amount of data can be overwhelming, especially in applications that involve high-resolution signals such as images or videos. Compressed sensing (CS) is a novel acquisition and reconstruction scheme that is particularly useful in scenarios when high resolution signals are difficult or expensive to encode. When applying CS in a multi-signal scenario, there are several aspects that need to be considered such as the sensing matrix, the joint signal model, and the reconstruction algorithm. The purpose of this dissertation is to provide a complete treatment of these aspects in various multi-signal environments. Specific applications include video, multi-view imaging, and structural health monitoring systems. For each application, we propose a novel joint signal model that accurately captures the joint signal structure, and we tailor the reconstruction algorithm to each signal model to successfully recover the signals of interest.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/98007/1/jaeypark_1.pd

Computational techniques to interpret the neural code underlying complex cognitive processes

Advances in large-scale neural recording technology have significantly improved the capacity to further elucidate the neural code underlying complex cognitive processes. This thesis aimed to investigate two research questions in rodent models. First, what is the role of the hippocampus in memory and specifically what is the underlying neural code that contributes to spatial memory and navigational decision-making. Second, how is social cognition represented in the medial prefrontal cortex at the level of individual neurons. To start, the thesis begins by investigating memory and social cognition in the context of healthy and diseased states that use non-invasive methods (i.e. fMRI and animal behavioural studies). The main body of the thesis then shifts to developing our fundamental understanding of the neural mechanisms underpinning these cognitive processes by applying computational techniques to ana lyse stable large-scale neural recordings. To achieve this, tailored calcium imaging and behaviour preprocessing computational pipelines were developed and optimised for use in social interaction and spatial navigation experimental analysis. In parallel, a review was conducted on methods for multivariate/neural population analysis. A comparison of multiple neural manifold learning (NML) algorithms identified that non linear algorithms such as UMAP are more adaptable across datasets of varying noise and behavioural complexity. Furthermore, the review visualises how NML can be applied to disease states in the brain and introduces the secondary analyses that can be used to enhance or characterise a neural manifold. Lastly, the preprocessing and analytical pipelines were combined to investigate the neural mechanisms in volved in social cognition and spatial memory. The social cognition study explored how neural firing in the medial Prefrontal cortex changed as a function of the social dominance paradigm, the "Tube Test". The univariate analysis identified an ensemble of behavioural-tuned neurons that fire preferentially during specific behaviours such as "pushing" or "retreating" for the animal’s own behaviour and/or the competitor’s behaviour. Furthermore, in dominant animals, the neural population exhibited greater average firing than that of subordinate animals. Next, to investigate spatial memory, a spatial recency task was used, where rats learnt to navigate towards one of three reward locations and then recall the rewarded location of the session. During the task, over 1000 neurons were recorded from the hippocampal CA1 region for five rats over multiple sessions. Multivariate analysis revealed that the sequence of neurons encoding an animal’s spatial position leading up to a rewarded location was also active in the decision period before the animal navigates to the rewarded location. The result posits that prospective replay of neural sequences in the hippocampal CA1 region could provide a mechanism by which decision-making is supported

Computational methods for percussion music analysis : the afro-uruguayan candombe drumming as a case study

Most of the research conducted on information technologies applied to music has been largely limited to a few mainstream styles of the so-called `Western' music. The resulting tools often do not generalize properly or cannot be easily extended to other music traditions. So, culture-specific approaches have been recently proposed as a way to build richer and more general computational models for music. This thesis work aims at contributing to the computer-aided study of rhythm, with the focus on percussion music and in the search of appropriate solutions from a culture specifc perspective by considering the Afro-Uruguayan candombe drumming as a case study. This is mainly motivated by its challenging rhythmic characteristics, troublesome for most of the existing analysis methods. In this way, it attempts to push ahead the boundaries of current music technologies. The thesis o ers an overview of the historical, social and cultural context in which candombe drumming is embedded, along with a description of the rhythm. One of the specific contributions of the thesis is the creation of annotated datasets of candombe drumming suitable for computational rhythm analysis. Performances were purposely recorded, and received annotations of metrical information, location of onsets, and sections. A dataset of annotated recordings for beat and downbeat tracking was publicly released, and an audio-visual dataset of performances was obtained, which serves both documentary and research purposes. Part of the dissertation focused on the discovery and analysis of rhythmic patterns from audio recordings. A representation in the form of a map of rhythmic patterns based on spectral features was devised. The type of analyses that can be conducted with the proposed methods is illustrated with some experiments. The dissertation also systematically approached (to the best of our knowledge, for the first time) the study and characterization of the micro-rhythmical properties of candombe drumming. The ndings suggest that micro-timing is a structural component of the rhythm, producing a sort of characteristic "swing". The rest of the dissertation was devoted to the automatic inference and tracking of the metric structure from audio recordings. A supervised Bayesian scheme for rhythmic pattern tracking was proposed, of which a software implementation was publicly released. The results give additional evidence of the generalizability of the Bayesian approach to complex rhythms from diferent music traditions. Finally, the downbeat detection task was formulated as a data compression problem. This resulted in a novel method that proved to be e ective for a large part of the dataset and opens up some interesting threads for future research.La mayoría de la investigación realizada en tecnologías de la información aplicadas a la música se ha limitado en gran medida a algunos estilos particulares de la así llamada música `occidental'. Las herramientas resultantes a menudo no generalizan adecuadamente o no se pueden extender fácilmente a otras tradiciones musicales. Por lo tanto, recientemente se han propuesto enfoques culturalmente específicos como forma de construir modelos computacionales más ricos y más generales. Esta tesis tiene como objetivo contribuir al estudio del ritmo asistido por computadora, desde una perspectiva cultural específica, considerando el candombe Afro-Uruguayo como caso de estudio. Esto está motivado principalmente por sus características rítmicas, problemáticas para la mayoría de los métodos de análisis existentes. Así , intenta superar los límites actuales de estas tecnologías. La tesis ofrece una visión general del contexto histórico, social y cultural en el que el candombe está integrado, junto con una descripción de su ritmo. Una de las contribuciones específicas de la tesis es la creación de conjuntos de datos adecuados para el análisis computacional del ritmo. Se llevaron adelante sesiones de grabación y se generaron anotaciones de información métrica, ubicación de eventos y secciones. Se disponibilizó públicamente un conjunto de grabaciones anotadas para el seguimiento de pulso e inicio de compás, y se generó un registro audiovisual que sirve tanto para fines documentales como de investigación. Parte de la tesis se centró en descubrir y analizar patrones rítmicos a partir de grabaciones de audio. Se diseñó una representación en forma de mapa de patrones rítmicos basada en características espectrales. El tipo de análisis que se puede realizar con los métodos propuestos se ilustra con algunos experimentos. La tesis también abordó de forma sistemática (y por primera vez) el estudio y la caracterización de las propiedades micro rítmicas del candombe. Los resultados sugieren que las micro desviaciones temporales son un componente estructural del ritmo, dando lugar a una especie de "swing" característico. El resto de la tesis se dedicó a la inferencia automática de la estructura métrica a partir de grabaciones de audio. Se propuso un esquema Bayesiano supervisado para el seguimiento de patrones rítmicos, del cual se disponibilizó públicamente una implementación de software. Los resultados dan evidencia adicional de la capacidad de generalización del enfoque Bayesiano a ritmos complejos. Por último, la detección de inicio de compás se formuló como un problema de compresión de datos. Esto resultó en un método novedoso que demostró ser efectivo para una buena parte de los datos y abre varias líneas de investigación

Object recognition in infrared imagery using appearance-based methods

Abstract unavailable please refer to PD

A psychophysical study of the neural representation of time by striatal populations

Time is a fundamental dimension of the environment. The ability to estimate the passage of time is essential for both learning and performance of adaptive behavior in natural situations. Yet, how this ability is implemented in the brain is poorly understoo