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This thesis focuses on various aspects of community mobility and lifespace. Mobility is of particular interest to those working with the elderly population or patients affected by neurological diseases, such as Alzheimer's and Parkinson's diseases. One aspect of mobility is the number of “hotspots" in a person's daily (or weekly) trajectory, which represent the locations at which an individual remains for a minimum predetermined length of time. The individual demonstrates potential limited mobility if there is only one identified hotspot; the individual is more mobile if there are multiple identified hotspots. Based on GPS time series, we can use cluster analysis to identify hotspots. However, existing clustering algorithms such as k-means and trimmed k-means do not take into account the time dependencies between the location points in the series, and require knowing the number of clusters ahead of time. Thus, the resulting clusters do not represent the subjects' activity centres well. In this thesis we have developed a robust time-dependent clustering criterion that works very well to find clusters. Another aspect of mobility is the total distance travelled. The total distance computed from the original GPS data is inflated as there is noise in the data. Due to the particular characteristics of noise specific to GPS time series, we have investigated the identification of noisy segments of data as well as smoothing techniques. The average amplitude of acceleration is proposed as an appropriate method to identify the large noise that occurs in GPS data. A multi-level trimmed means smoother is proposed as an appropriate method to filter the identified large noise. Three methods were investigated to determine an ellipse that identifies the spatial area an individual purposely moves through in daily life. The classical and robust 95% ellipses contain 95% of the points, but do not necessarily capture the distinct shape of the data. The minimum spanning ellipse over the series with all points in each identified cluster reduced to each cluster's central value captures the shape of the data very well and is proposed as the most appropriate lifespace ellipse. Results are obtained and presented for the subjects available in the mobility study for the total distance travelled and a meaningful lower bound, the number of hotspots, the proportion of time spent in the hotspots, as well as the area of the classical 95% ellipse, robust 95% ellipse and minimum spanning ellipse. In the processing of the data, other problems that had to be addressed include obtaining appropriate estimates for the missing values and translating time series from degrees of longitude and latitude to metres in the Cartesian (x,y) plane. / Graduate / 0463 / lauramor@uvic.ca

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Thesis (M.S.)--University of Texas at El Paso, 2008. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 59-60). Also available via the Internet.

Thesis (M.S. in Astronautical Engineering)--Naval Postgraduate School, December 2003. / "December 2003". Thesis advisor(s): Cristi, Roberto ; Agrawal, Brij. Includes bibliographical references (p. 53). Also available online.

Thesis (M. Eng.)(Electronic)--University of Pretoria, 2005. / Summaries in English and Afrikaans. Includes bibliographical references.

Thesis (M.S.)--University of Wisconsin--Madison. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 259-264).

Filtragem é uma das mais importantes operações em processamento de imagens e vídeos. Em particular, filtros de altas dimensões são ferramentas fundamentais para diversas aplicações, tendo recebido recentemente significativa atenção de pesquisadores da área. Infelizmente, implementações ingênuas desta importante classe de filtros são demasiadamente lentas para muitos usos práticos, especialmente tendo em vista o aumento contínuo na resolução de imagens capturadas digitalmente. Esta dissertação descreve três novas abordagens para filtragem eficiente em altas dimensões: a domain transform, os adaptive manifolds, e uma formulação matemática para a aplicação de filtros recursivos em sinais amostrados não-uniformemente. A domain transform, representa o estado-da-arte em termos de algoritmos para filtragem utilizando métrica geodésica. A inovação desta abordagem é a utilização de um procedimento simples de redução de dimensionalidade para implementar eficientemente filtros de alta dimensão. Isto nos permite a primeira demonstração de filtragem com preservação de arestas em tempo real para vídeos coloridos de alta resolução (full HD). Os adaptive manifolds, representam o estado-da-arte em termos de algoritmos para filtragem utilizando métrica Euclidiana. A inovação desta abordagem é a ideia de subdividir o espaço de alta dimensão em fatias não-lineares de mais baixa dimensão, as quais são filtradas independentemente e finalmente interpoladas para obter uma filtragem de alta dimensão com métrica Euclidiana. Com isto obtemos diversos avanços em relação a técnicas anteriores, como filtragem mais rápida e requerendo menos memória, além da derivação do primeiro filtro Euclidiano com custo linear tanto no número de pixels da imagem (ou vídeo) quanto na dimensionalidade do espaço onde o filtro está operando. Finalmente, introduzimos uma formulação matemática que descreve a aplicação de um filtro recursivo em sinais amostrados de maneira não-uniforme. Esta formulação estende a ideia de filtragem geodésica para filtros recursivos arbitrários (tanto passa-baixa quanto passa-alta e passa-banda). Esta extensão fornece maior controle sobre as respostas desejadas para os filtros, as quais podem então ser melhor adaptadas para aplicações específicas. Como exemplo, demonstramos—pela primeira vez na literatura—filtros geodésicos com formato Gaussiano, Laplaciana do Gaussiano, Butterworth, e Cauer, dentre outros. Com a possibilidade de se trabalhar com filtros arbitrários, nosso método permite uma nova variedade de efeitos para aplicações em imagens e vídeos. / Filtering is arguably the single most important operation in image and video processing. In particular, high-dimensional filters are a fundamental building block for several applications, having recently received considerable attention from the research community. Unfortunately, naive implementations of such an important class of filters are too slow for many practical uses, specially in light of the ever increasing resolution of digitally captured images. This dissertation describes three novel approaches to efficiently perform high-dimensional filtering: the domain transform, the adaptive manifolds, and a mathematical formulation for recursive filtering of non-uniformly sampled signals. The domain transform defines an isometry between curves on the 2D image manifold in 5D and the real line. It preserves the geodesic distance between points on these curves, adaptively warping the input signal so that high-dimensional geodesic filtering can be efficiently performed in linear time. Its computational cost is not affected by the choice of the filter parameters; and the resulting filters are the first to work on color images at arbitrary scales in real time, without resorting to subsampling or quantization. The adaptive manifolds compute the filter’s response at a reduced set of sampling points, and use these for interpolation at all input pixels, so that high-dimensional Euclidean filtering can be efficiently performed in linear time. We show that for a proper choice of sampling points, the total cost of the filtering operation is linear both in the number of pixels and in the dimension of the space in which the filter operates. As such, ours is the first high-dimensional filter with such a complexity. We present formal derivations for the equations that define our filter, providing a sound theoretical justification. Finally, we introduce a mathematical formulation for linear-time recursive filtering of non-uniformly sampled signals. This formulation enables, for the first time, geodesic edge-aware evaluation of arbitrary recursive infinite impulse response filters (not only low-pass), which allows practically unlimited control over the shape of the filtering kernel. By providing the ability to experiment with the design and composition of new digital filters, our method has the potential do enable a greater variety of image and video effects. The high-dimensional filters we propose provide the fastest performance (both on CPU and GPU) for a variety of real-world applications. Thus, our filters are a valuable tool for the image and video processing, computer graphics, computer vision, and computational photography communities.

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