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A clustering-based approach for discovering interesting places in trajectories / Uma abordagem baseada em clusterização para a descoberta de lugares de interesse em trajetóriasPalma, Andrey Luis Tietbohl January 2008 (has links)
Por causa da grande quantidade de dados de trajetórias producidos por dispositivos móveis, existe um aumento crescente das necessidades de mecanismos para extrair conhecimento a partir desses dados. A maioria dos trabalhos existentes focam nas propriedades geometricas das trajetorias, mas recentemente surgiu o conceito de trajetórias semânticas, nas quais a informação da geografia por baixo da trajetória é integrada aos pontos da trajetória. Nesse novo conceito, trajetórias são observadas como um conjunto de stops e moves, onde stops são as partes mais importantes da trajetória. Os stops e moves são computados pela intersecção das trajetórias com o conjunto de objetos geográficos dados pelo usuário. Nessa dissertação será apresentada uma solução alternativa a descoberta de stops, com a capacidade de achar lugares de interesse que não são esperados pelo usuário. A solução proposta é um método de clusterização espaço-temporal, baseado na velocidade, para ser aplicado em uma trajetória. Foram comparadas duas abordagens diferentes com experimentos baseados em dados reais e mostrado que a computação de stops usando o conceito de velocidade pode ser interessante para várias applicações. / Because of the large amount of trajectory data produced by mobile devices, there is an increasing need for mechanisms to extract knowledge from this data. Most existing works have focused on the geometric properties of trajectories, but recently emerged the concepts of semantic trajectories, in which the background geographic information is integrated to trajectory sample points. In this new concept, trajectories are observed as a set of stops and moves, where stops are the most important parts of the trajectory. Stops and moves have been computed by testing the intersection of trajectories with a set of geographic objects given by the user. In this dissertation we present an alternative solution with the capability of finding interesting places that are not expected by the user. The proposed solution is a spatio-temporal clustering method, based on speed, to work with single trajectories. We compare the two different approaches with experiments on real data and show that the computation of stops using the concept of speed can be interesting for several applications.
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Modélisation et gestion de concepts, en particulier temporels, pour l'assistance à la caractérisation de séquences d'images / Modeling and management of time concepts to support the characterization of image sequencesSimac, Alain 14 June 2011 (has links)
Les techniques habituelles d'indexation de vidéos passent généralement par une phase d'apprentissage qui nécessite préalablement la constitution d'une base d'apprentissage. Même si la taille de cette base est souvent réduite, la phase d'annotation réalisée par un expert de l'application est souvent longue et fastidieuse. Dans le cadre de cette thèse, nous avons développé un dispositif qui permet de pré-sélectionner un ensemble de prototypes susceptibles de contenir le concept qui doit apparaître dans la base d'apprentissage. Cette base réduite de prototypes sera ensuite annotée par l'expert. Nous nous sommes intéressés à des concepts temporels, ce qui nous a amené à étudier particulièrement des caractéristiques liées au mouvement, comme les points d'intérêt spatio-temporels (STIP Spatial Temporal Interest Points). D'autres caractéristiques ont aussi été utilisées concernant la couleur et la présence de formes particulières. Ces caractéristiques sont ensuite exploitées pour structurer la base de vidéos en briques spatio-temporelles homogènes. Cette structuration correspond à une sorte de segmentation de la base en fonction de chacune des caractéristiques. La liaison entre le concept à définir et les briques extraites de la base est en lien avec le fossé sémantique bien connu dans la problématique d'indexation automatique. La création de ce lien nécessite l'utilisation de la connaissance de l'expert de l'application sur le concept. Nous avons développé un système dans lequel cette connaissance est extraite par un système de questions/réponses. Les couples de questions/réponses permettent de sélectionner des briques répondant à la contrainte, de définir des relations entre certaines briques, et enfin de naviguer dans l'arborescence des questions. Des tests ont été réalisés sur des bases de vidéos de provenances diverses telles que des vidéos provenant d'émissions de télévision, de films d'animation, ou encore des vidéos de laboratoire disponibles sur le net, ou réalisées par nos soins. Ces tests montrent les performances satisfaisantes mais aussi les limites de l'approche et ouvrent des perspectives intéressantes, particulièrement sur les aspects collaboratifs et les aspects adaptatifs qui permettraient de capitaliser les connaissances des experts applicatifs et rendraient le système plus efficient. / The usual techniques of video indexing generally go through a learning phase that requires the prior establishment of a training database. Even if the size of the database is often reduced, the annotation phase by an expert of the application is often long and tedious. In this thesis, we developed a system that allows pre-selecting a set of prototypes that can contain the concept that must appear in the training set. This reduced base of prototypes will then be annotated by the expert. We are interested in time concepts, which led us to study particular features related to movement, such as Spatial Temporal Interest Points (STIP). Other features have also been used concerning the color and the presence of particular shapes. These characteristics are then used to structure the video database in homogeneous space-time blocks. This structure corresponds to segmentation related to each characteristic. The link between the concept to define and blocks extracted from the base corresponds to the well known problem of automatic indexing, the semantic gap. The definition of this link requires the introduction of the application expert's knowledge. We developed a system in which this knowledge is extracted by a questions/answers system. The couples of questions/answers allow the system to select blocks corresponding to the constraint, to define relationships between some blocks, and finally to navigate on the questions/answers tree. Tests were performed on video databases from various sources such as videos from tele- vision shows, animated films, laboratory videos available on the net, or made by us. These tests show the satisfying performances but also the limitations of the approach and open interesting perspectives, particularly on the collaborative and adaptive aspects that would capitalize in the application expert knowledge and would make the system more efficient.
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Padrões espaciais de abundância e dinâmica populacional em longo prazo do camarão sete-barbas Xiphopenaeus kroyeri (Heller, 1862) na Enseada de Ubatuba, SP / Long-term pattern of spatial abundance and population dynamics of the seabob shrimp Xiphopenaeus kroyeri (Heller, 1862) in Ubatuba Bay, São Paulo State, BrazilGisele Salgado Heckler 29 August 2014 (has links)
A análise de uma população em longo prazo permite a identificação da ausência ou presença de variações nos padrões de ciclo de vida, de distribuição espaço-temporal e dinâmica populacional. O ciclo de vida do camarão sete-barbas Xiphopenaeus kroyeri foi investigado na Enseada de Ubatuba, litoral norte do Estado de São Paulo (23º25\' - 23º27\'S / 45º00\' - 45º03\' W) ao longo de um intervalo de treze anos. Amostras de material biológico, de água de fundo e de sedimento foram coletadas em quatro pontos de amostragem em três períodos de 12 meses cada: janeiro a dezembro de 1998, julho de 2006 a junho de 2007 e setembro de 2010 a agosto de 2011. Dados obtidos em 1999 foram incluídos para as análises de crescimento individual, de longevidade e de idade de maturação. Altas abundâncias de fêmeas maduras e de jovens foram respectivamente associadas a valores de temperatura da água de fundo acima e abaixo da média da região. Indivíduos adultos predominaram em pontos com variação temporal da composição granulométrica do sedimento enquanto que os jovens se estabeleceram naqueles em que o sedimento permaneceu fino entre os períodos. Em 1998, a abundância de jovens, o peso individual de machos e fêmeas de todas as categorias demográficas, a idade de maturação morfológica e fisiológica e a longevidade foram maiores do que nos outros períodos. Os parâmetros da função de crescimento de machos e fêmeas variaram entre os períodos, sem apresentarem uma tendência temporal clara. Os padrões anuais de reprodução e recrutamento foram bastante semelhantes entre os períodos. As alterações nos fatores ambientais provocadas por variações na dinâmica de massas de água, pela ocorrência de El Niño e alterações na intensidade de pesca foram consideradas como possíveis agentes relacionadas às variações nos padrões do ciclo de vida da espécie na região / Long-term studies on a population provide detection of the presence or absence of interannual variation in patterns of its life cycle, spatio-temporal distribution, and dynamics. This study investigate the population of the seabob shrimp Xiphopenaeus kroyeri within a period of 13 years in Ubatuba Bay, northern coast of São Paulo state, Brazil (23º25\' - 23º27\'S / 45º00\' - 45º03\' W). Shrimp, bottom water and sediment samples were collected from four sampling sites during three 12-month periods: January-December 1998, July 2006-June 2007, and September 2010-August 2011. Monthly data collected in 1999 were included in growth, longevity and maturation age analyses. High abundance of mature females and juveniles were associated to the occurrence of temperature values below and above the region average, respectively. Adults predominated in sites that showed temporal variation of sediment texture while juveniles occurred in sites where sediment remained fine between the study periods. In the 1998 period values of juveniles were more abundant, individual weight of all demographic categories was higher, both morphological and physiological maturity was attained later and lifespan was longer than on the following periods. Growth function parameters of males and females varied between periods with no clear temporal trend. Monthly patterns of reproduction and recruitment were similar between the study periods. Changes in the environmental conditions caused by variations in the dynamics of the local water masses, occurrence of El Niño and fishery intensity were considered as possible factors related to the interannual variations in the life cycle pattern of X. kroyeri in the study region
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A clustering-based approach for discovering interesting places in trajectories / Uma abordagem baseada em clusterização para a descoberta de lugares de interesse em trajetóriasPalma, Andrey Luis Tietbohl January 2008 (has links)
Por causa da grande quantidade de dados de trajetórias producidos por dispositivos móveis, existe um aumento crescente das necessidades de mecanismos para extrair conhecimento a partir desses dados. A maioria dos trabalhos existentes focam nas propriedades geometricas das trajetorias, mas recentemente surgiu o conceito de trajetórias semânticas, nas quais a informação da geografia por baixo da trajetória é integrada aos pontos da trajetória. Nesse novo conceito, trajetórias são observadas como um conjunto de stops e moves, onde stops são as partes mais importantes da trajetória. Os stops e moves são computados pela intersecção das trajetórias com o conjunto de objetos geográficos dados pelo usuário. Nessa dissertação será apresentada uma solução alternativa a descoberta de stops, com a capacidade de achar lugares de interesse que não são esperados pelo usuário. A solução proposta é um método de clusterização espaço-temporal, baseado na velocidade, para ser aplicado em uma trajetória. Foram comparadas duas abordagens diferentes com experimentos baseados em dados reais e mostrado que a computação de stops usando o conceito de velocidade pode ser interessante para várias applicações. / Because of the large amount of trajectory data produced by mobile devices, there is an increasing need for mechanisms to extract knowledge from this data. Most existing works have focused on the geometric properties of trajectories, but recently emerged the concepts of semantic trajectories, in which the background geographic information is integrated to trajectory sample points. In this new concept, trajectories are observed as a set of stops and moves, where stops are the most important parts of the trajectory. Stops and moves have been computed by testing the intersection of trajectories with a set of geographic objects given by the user. In this dissertation we present an alternative solution with the capability of finding interesting places that are not expected by the user. The proposed solution is a spatio-temporal clustering method, based on speed, to work with single trajectories. We compare the two different approaches with experiments on real data and show that the computation of stops using the concept of speed can be interesting for several applications.
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Supporting real-time mobility services with scalable flock pattern miningLACERDA, Thiago de Barros 29 July 2016 (has links)
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Previous issue date: 2016-07-29 / Pattern mining in spatio-temporal datasets is a really relevant subject in the academia and the
industry nowadays, due to its wide applicability in helping to solve real-world problems. Many
of them can be found in the context of Smart Cities, like Traffic Management, Surveillance
and Security and City Planning, to name a few. Among the various spatio-temporal patterns
that one can extract from a spatio-temporal dataset, the flock pattern is one that has gained a
lot of attention, because of its intrinsic relation with the aforementioned problems. A lot of
work has been done in the academia, in order to provide algorithms able to identify the flock
pattern. However, none of them could perform that task efficiently nor be able to scale well
when a large dataset was the analysis target. Additionally, we found that there was no system
architecture proposal that could be simple and modular enough to be used in that spatio-temporal
pattern detection problem. Given that context, this dissertation proposes a modular system
archicture designed to help solving flock pattern mining problems and possibly be reused to
other spatio-temporal mining experiments. We then use such architecture as the infrastructure
to implement an efficient flock detection algorithm, aiming at achieving considerable gains
in execution time without compromising accuracy, thus targeting real-time deployment and
on-line processing in Smart Cities. Last, but not least, we remodel our algorithm in order to take
advantage of multi-core architectures present in modern computers. Our results indicate that
our proposal outperforms the current state-of-the-art techniques, by achieving 99% CPU time
improvement. Moreover, with our multi-thread model, we were able to reduce the processing
time of our proposed algorithm by 96% in some cases. We prove the efficiency of our solution
by performing evaluation with both real and synthetic large datasets. / Detecção de padrões em dados espaço-temporais tem se mostrado um tema de muita relevância
nos dias atuais, tanto na academia quanto na indústria, devido a sua vasta aplicabilidade em
auxiliar a solucionar problemas enfrentados na sociedade. Muitos desses problemas podem
ser classificados no conexto de Cidades Inteligentes (Smart Cities), como Gerenciamento de
Tráfego, Segurança e Planejamento de Cidades. Dentre os vários padrões espaço-temporais
que podem ser extraídos de uma base de dados, o padrão de flock é um que vem atraindo
muita atenção, devido a sua relação intrínseca com os problemas mencionados anteriormente.
Muitas pesquisas vêm sendo feitas na academia, visando desenvolver algoritmos capazes de
identificar esse padrão de movimentação. Porém, nenhum deles foi capaz de executar tal tarefa
eficientemente, nem conseguiu escalar de maneira aceitável quando uma base de dados de
grande tamanho foi analisada. Além disso, não foi encontrado nos trabalhos relacionados uma
arquitetura de software que conseguisse ser simples e modular o suficiente para ser usada no
problema de detecção de padrões de flock em dados espaço-temporais. Com isso em mente, essa
dissertação propõe uma arquitetura de software modular, direcionada para solucionar problemas
de detecção desse padrão e possivelmente ser utilizada para outros experimentos envolvendo
mineração de padrões em dados espaço-temporais. Tal arquitetura foi então usada como base na
implementação de um algoritmo de detecção de flock, focando em alcançar grandes ganhos em
tempo de processamento, sem comprometer a precisão, visando então cenários de aplicações de
tempo real em Cidades Inteligentes. No fim, nós propomos uma remodelagem no nosso algoritmo
para poder utilizar ao máximo o poder de processamento oferecido pelas arquiteturas multi-core
dos processadores modernos. Nossos resultados mostraram que nossa solução conseguiu superar
propostas do estado da arte, alcançando 99% de redução no tempo de processamento total. Além
disso, nossa remodelagem multi-thread conseguiu melhorar os resultados da nossa solução em
até 96% em alguns casos. A eficiência e performance da nossa proposta foi comprovada com
avaliações feitas com bases de dados geradas sinteticamente e coletadas em experimentos reais.
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Alinhamento Espaço-Temporal em Sistemas Multissensoriais Heterogêneos / Alignment Space-Time Heterogeneous Systems multisensoryFroner, Diego da Silva 29 February 2012 (has links)
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Previous issue date: 2012-02-29 / Fundação de Amparo à Pesquisa do Estado do Amazonas / This work presents the use of different sensors improving the information to perform spatio-temporal alignment of sequential images. The existing proposals called feature-based uses the dynamics of scenes as a major indicator that simultaneously events are ocurring at the same time, and lately indicating their relative position in space. Adding motion sensors to a multiple video cameras system with overlapping fields of coverage, it s possible to acquire information about positions of the monitored objects that serves to aid the alignment between images. / Este trabalho apresenta a utilização de diferentes sensores no aprimoramento da informação necessária para realizar o alinhamento espaço-temporal de imagens sequenciais. As propostas existentes chamadas feature-based utilizam-se da dinâmica da cena como maior indicador de que eventos estão ocorrendo simultaneamente no tempo, e assim posteriormente indicando suas posições relativas no espaço. Adicionando sensores de movimentação a um sistema com múltiplas câmeras de vídeo que possuam sobreposição de campos de cobertura, é possível adquirir informações de posicionamento dos objetos monitorados, servindo assim de auxílio para o alinhamento entre as imagens.
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Um estudo sobre a distribuição da raiva no Estado do Paraná de 1981 a 2012 / A study on the rabies distribution on Paraná State from 1981 to 2012Thaisa Lucas Sandri 17 March 2014 (has links)
A raiva é uma zoonose viral que afeta o Sistema Nervoso Central (SNC) causando encefalite e meningoencefalite, de evolução aguda e fatal, que acomete mamíferos carnívoros e morcegos, e periodicamente se manifesta sob a forma de epizootias ou surtos epidêmicos em populações humanas. Neste estudo foram analisadas 16.190 amostras de bovinos, equídeos e morcegos, e menos frequentemente de outros mamíferos durante o período de 1981 a 2012, provenientes do Estado do Paraná. Desse total, 2.766 amostras foram positivas para raiva; 81,74% foram de bovinos, 10,34% de equídeos, 4,05% de morcegos, 2,31% em animais de produção não bovinos, 1,52% em caninos e 0,04%em outros animais. Ao longo da série histórica, há, para os bovinos, uma tendência de aumento das notificações e não foram observadas variação sazonal e cíclica. Na análise espaço-temporal foi detectado um aglomerado mais provável de notificações de raiva em bovinos, envolvendo 20 municípios da região litorânea e metropolitana de Curitiba entre 1981 e 1987. Além dele, foram detectados seis aglomerados secundários sugerindo uma migração da raiva ao longo do tempo no Estado do Paraná. Ao longo da série histórica dos equídeos há uma tendência de diminuição das notificações e não foram observadas variação sazonal e cíclica. Os clusters encontrados na análise espaço-temporal da raiva nos equídeos corroboram com aqueles encontrados na análise dos bovinos localizados nas mesmas regiões durante no mesmo período, sugerindo a migração do vírus da raiva no mesmo sentido da observada na análise dos bovinos. Durante o período de 1981 a 1997, os casos de raiva em morcegos acompanham o trajeto da migração dos aglomerados dos bovinos e dos equídeos, o que demonstra que a raiva ocorre endemicamente no território do Estado do Paraná em herbívoros e morcegos. / Rabies is a viral zoonosis that affects the central nervous system (CNS) causing encephalitis and meningoencephalitis, acute and fatal outcome, which affects mammalian carnivores and bats, and periodically manifests itself in the form of epidemics or outbreaks in human populations. In this study 16,190 samples of cattle, horses and bats, and less frequently other mammals were analyzed during the period 1981 to 2012, from the State of Paraná. Of this total, 2,766 samples were positive for rabies; 81.74 % were bovine, equine 10.34 %, 4.05 % of bats, 2.31 % in livestock no bovine, 1.52 % in canine, and 0.04% in other animals. Throughout the time series, there is, for cattle, a trend of increased reporting and no seasonal or cyclical variations were observed. In spatio-temporal analysis, more likely to notifications of rabies in cattle, a cluster involving 20 municipalities in coastal and metropolitan Curitiba between 1981 and 1987 was detected. Besides this, six sub clusters were detected suggesting a migration of anger over time in the state of Paraná. Throughout the historical series of equine there is a downward trend in notifications and no seasonal and cyclical variations were observed. Clusters found in the spatio-temporal analysis of rabies in horses corroborate those found in the analysis of cattle located in the same regions during the same period, suggesting the migration of rabies virus in the same direction as that observed in the cattle analysis. During the period from 1981 to 1997, cases of rabies in bats follow the migration path of clusters of bovine and equine. This shows that rabies is endemic in the state of Paraná in herbivores and bats.
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Dynamique spatio-temporelle dans un piège magnéto-optique / Spatio-temporal dynamics in a magneto-optical trapRomain, Rudy 09 December 2013 (has links)
Cette thèse a pour objectif d'étudier la dynamique spatio-temporelle des atomes refroidis par laser dans un piège magnéto-optique (PMO). Il a été montré qu'un nuage d'atomes froids dans le régime de diffusion multiple peut présenter un comportement instable sans modulation externe du système. Cependant, ces instabilités n'ont pas encore été modélisées de façon satisfaisante. Une nouvelle configuration du PMO a été mise en oeuvre pour tenter d'étudier des instabilités dans une seule direction. Ce PMO, qualifié d'anisotrope, n'utilise pas des lasers de mêmes fréquences dans chaque direction de l'espace. Il met en évidence les forts couplages existants entre les directions du piège, si bien qu'il n'est pas possible de l'utiliser pour réduire le nombre de dimensions dans lesquelles les instabilités s'établissent. Toutefois, cette étude constitue un premier pas vers une meilleure description tridimensionnelle du piège. Elle nous a notamment permis de mesurer la probabilité pour qu'un photon diffusé soit réabsorbé à l'intérieur du nuage. Cette quantité est caractéristique du PMO mais elle n'avait jusqu'à là jamais été mesurée. Nous avons également établi un modèle spatio-temporel unidimensionnel du PMO. Il est constitué d'un système d'équations non-linéaires couplées reliant la densité atomique et les intensités des faisceaux lasers. Ce système contient notamment une équation de Vlasov-Fokker-Planck, rencontrée dans de nombreux domaines de la physique. Des simulations numériques ont été effectuées dans un cas simple. D'un point de vue expérimental, l'utilisation d'une caméra rapide nous a permis de mettre en évidence la structure spatiale d'instabilités de type stochastique. / The aim of this thesis is to study the spatio-temporal dynamics of laser cooled atoms in a magneto-optical trap (MOT). Recent works have shown that in the multiple scattering regime, an atomic cloud can have an unstable behavior without external modulation of the system. Nevertheless, these instabilities have not yet been modeled in a satisfactory way. A new configuration of the MOT has been built up as a possible way to study instabilities in only one direction. This trap, called anisotropic MOT, is not made of laser beams with the same laser frequencies along each direction of space. It exhibits the strong couplings between the directions of the trap, with the result that it cannot be used to reduce the number of directions in which instabilities grow up. However, this study can be considered as a new step to a better 3D description of the MOT physics. In particular, it gives us a way to measure the probability that a scattered photon is reabsorbed inside the atomic cloud. This quantity is a characteristic of the MOT but it has never been measured so far. We also develop a 1D spatio-temporal model of the MOT. It consists in a set of coupled nonlinear equations linking the atomic density and the laser intensities. This set contains a Vlasov-Fokker-Planck equation which is used to model a lot of systems in various fields and not only in physics. Numerical simulations have been done in a simple case. In the experiment, the use of a fast video camera allows us to observe the spatial structure of one type of instabilities, the so-called stochastic instabilities.
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Spatio-Temporal Pre-Processing Methods for Region-of-Interest Video CodingKarlsson, Linda S. January 2007 (has links)
In video transmission at low bit rates the challenge is to compress the video with a minimal reduction of the percieved quality. The compression can be adapted to knowledge of which regions in the video sequence are of most interest to the viewer. Region of interest (ROI) video coding uses this information to control the allocation of bits to the background and the ROI. The aim is to increase the quality in the ROI at the expense of the quality in the background. In order for this to occur the typical content of an ROI for a particular application is firstly determined and the actual detection is performed based on this information. The allocation of bits can then be controlled based on the result of the detection. In this licenciate thesis existing methods to control bit allocation in ROI video coding are investigated. In particular pre-processing methods that are applied independently of the codec or standard. This makes it possible to apply the method directly to the video sequence without modifications to the codec. Three filters are proposed in this thesis based on previous approaches. The spatial filter that only modifies the background within a single frame and the temporal filter that uses information from the previous frame. These two filters are also combined into a spatio-temporal filter. The abilities of these filters to reduce the number of bits necessary to encode the background and to successfully re-allocate these to the ROI are investigated. In addition the computational compexities of the algorithms are analysed. The theoretical analysis is verified by quantitative tests. These include measuring the quality using both the PSNR of the ROI and the border of the background, as well as subjective tests with human test subjects and an analysis of motion vector statistics. The qualitative analysis shows that the spatio-temporal filter has a better coding efficiency than the other filters and it successfully re-allocates the bits from the foreground to the background. The spatio-temporal filter gives an improvement in average PSNR in the ROI of more than 1.32 dB or a reduction in bitrate of 31 % compared to the encoding of the original sequence. This result is similar to or slightly better than the spatial filter. However, the spatio-temporal filter has a better performance, since its computational complexity is lower than that of the spatial filter.
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Using Rigid Landmarks to Infer Inter-Temporal Spatial Relations in Spatio-Temporal ReasoningBränd, Stefan January 2015 (has links)
Spatio-temporal reasoning is the area of automated reasoning about space and time and is important in the field of robotics. It is desirable for an autonomous robot to have the ability to reason about both time and space. ST0 is a logic that allows for such reasoning by, among other things, defining a formalism used to describe the relationship between spatial regions and a calculus that allows for deducing further information regarding such spatial relations. An extension of ST0 is ST1 that can be used to describe the relationship between spatial entities across time-points (inter-temporal relations) while ST0 is constrained to doing so within a single time-point. This allows for a better ability of expressing how spatial entities change over time. A major obstacle in using ST1 in practise however, is the fact that any observations made regarding spatial relations between regions is constrained to the time-point in which the observation was made, so we are unable to observe inter-temporal relations. Further complicating things is the fact that deducing such inter-temporal relations is not possible without a frame of reference. This thesis examines one method of overcoming these problems by considering the concept of rigid regions which are assumed to always be unchanging and using them as the frame of reference, or as landmarks. The effectiveness of this method is studied by conducting experiments where a comparison is made between various landmark ratios with respect to the total number of regions under consideration. Results show that when a high degree of intra-temporal relations are fully or partially known, increasing the number of landmark regions will reduce the percentage of inter-temporal relations to be completely unknown. Despite this, very few inter-temporal relations can be fully determined even with a high ratio of landmark regions.
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