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  • 451.
    Zagal, Juan Cristobal
    et al.
    KTH, Tidigare Institutioner, Numerisk analys och datalogi, NADA.
    Björkman, Eva
    Lindeberg, Tony
    KTH, Tidigare Institutioner, Numerisk analys och datalogi, NADA.
    Roland, P.
    Signficance determination for the scale-space primal sketch by comparison of statistics of scale-space blob volumes computed from PET signals vs. residual noise2000Ingår i: : HBM'00 published in Neuroimage, volume 11, number 5, 2000, 2000, Vol. 11, s. 493-493Konferensbidrag (Refereegranskat)
    Abstract [en]

    A dominant approach to brain mapping is to define functional regions in the brain by analyzing brain activation images obtained by PET or fMRI. In [1], it has been shown that the scale-space primal sketch provides a useful tool for such analysis. Some attractive properties of this method are that it only makes few assumptions about the data and the process for extracting activations is fully automatic.

    In the present version of the scale-space primal sketch, however, there is no method for determining p-values. The purpose here is to present a new methodology for addressing this question, by introducing a descriptor referred to as the -curve, which serves as a first step towards determining the probability of false positives, i.e. alpha.

  • 452.
    Zhang, Cheng
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Ek, Carl Henrik
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Damianou, Andreas
    The University of Sheffield.
    Kjellström, Hedvig
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Factorized Topic Models2013Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper we present a modification to a latent topic model, which makes themodel exploit supervision to produce a factorized representation of the observeddata. The structured parameterization separately encodes variance that is sharedbetween classes from variance that is private to each class by the introduction of anew prior over the topic space. The approach allows for a more efficient inferenceand provides an intuitive interpretation of the data in terms of an informative signaltogether with structured noise. The factorized representation is shown to enhanceinference performance for image, text, and video classification.

  • 453.
    Zhang, Cheng
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Ek, Carl Henrik
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Gratal, Xavi
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Pokorny, Florian T.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Kjellström, Hedvig
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Supervised Hierarchical Dirichlet Processes with Variational Inference2013Ingår i: 2013 IEEE International Conference on Computer Vision Workshops (ICCVW), IEEE , 2013, s. 254-261Konferensbidrag (Refereegranskat)
    Abstract [en]

    We present an extension to the Hierarchical Dirichlet Process (HDP), which allows for the inclusion of supervision. Our model marries the non-parametric benefits of HDP with those of Supervised Latent Dirichlet Allocation (SLDA) to enable learning the topic space directly from data while simultaneously including the labels within the model. The proposed model is learned using variational inference which allows for the efficient use of a large training dataset. We also present the online version of variational inference, which makes the method scalable to very large datasets. We show results comparing our model to a traditional supervised parametric topic model, SLDA, and show that it outperforms SLDA on a number of benchmark datasets.

  • 454.
    Zhang, Cheng
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Kjellström, Hedvig
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    How to Supervise Topic Models2014Ingår i: Computer Vision - ECCV 2014 Workshops: Zurich, Switzerland, September 6-7 and 12, 2014, Proceedings, Part II / [ed] Agapito, Bronstein, Rother, Zurich: Springer Publishing Company, 2014, s. 500-515Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    Supervised topic models are important machine learning tools whichhave been widely used in computer vision as well as in other domains. However,there is a gap in the understanding of the supervision impact on the model. Inthis paper, we present a thorough analysis on the behaviour of supervised topicmodels using Supervised Latent Dirichlet Allocation (SLDA) and propose twofactorized supervised topic models, which factorize the topics into signal andnoise. Experimental results on both synthetic data and real-world data for computer vision tasks show that supervision need to be boosted to be effective andfactorized topic models are able to enhance the performance.

  • 455.
    Zhang, Cheng
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Robotik, perception och lärande, RPL.
    Kjellström, Hedvig
    KTH, Skolan för datavetenskap och kommunikation (CSC), Robotik, perception och lärande, RPL.
    Ek, C. H.
    Inter-battery topic representation learning2016Ingår i: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer, 2016, s. 210-226Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we present the Inter-Battery Topic Model (IBTM). Our approach extends traditional topic models by learning a factorized latent variable representation. The structured representation leads to a model that marries benefits traditionally associated with a discriminative approach, such as feature selection, with those of a generative model, such as principled regularization and ability to handle missing data. The factorization is provided by representing data in terms of aligned pairs of observations as different views. This provides means for selecting a representation that separately models topics that exist in both views from the topics that are unique to a single view. This structured consolidation allows for efficient and robust inference and provides a compact and efficient representation. Learning is performed in a Bayesian fashion by maximizing a rigorous bound on the log-likelihood. Firstly, we illustrate the benefits of the model on a synthetic dataset. The model is then evaluated in both uni- and multi-modality settings on two different classification tasks with off-the-shelf convolutional neural network (CNN) features which generate state-of-the-art results with extremely compact representations.

  • 456.
    Zhang, Cheng
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Song, Dan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Kjellström, Hedvig
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP. KTH, Skolan för datavetenskap och kommunikation (CSC), Centra, Centrum för Autonoma System, CAS.
    Contextual Modeling with Labeled Multi-LDA2013Ingår i: 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE , 2013, s. 2264-2271Konferensbidrag (Refereegranskat)
    Abstract [en]

    Learning about activities and object affordances from human demonstration are important cognitive capabilities for robots functioning in human environments, for example, being able to classify objects and knowing how to grasp them for different tasks. To achieve such capabilities, we propose a Labeled Multi-modal Latent Dirichlet Allocation (LM-LDA), which is a generative classifier trained with two different data cues, for instance, one cue can be traditional visual observation and another cue can be contextual information. The novel aspects of the LM-LDA classifier, compared to other methods for encoding contextual information are that, I) even with only one of the cues present at execution time, the classification will be better than single cue classification since cue correlations are encoded in the model, II) one of the cues (e.g., common grasps for the observed object class) can be inferred from the other cue (e.g., the appearance of the observed object). This makes the method suitable for robot online and transfer learning; a capability highly desirable in cognitive robotic applications. Our experiments show a clear improvement for classification and a reasonable inference of the missing data.

  • 457.
    Zhang, Silun
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Ringh, Axel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Hu, Xiaoming
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    Karlsson, Johan
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
    A moment-based approach to modeling collective behaviors2018Ingår i: 2018 IEEE Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, s. 1681-1687, artikel-id 8619389Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this work we introduce an approach for modeling and analyzing collective behavior of a group of agents using moments. We represent the occupation measure of the group of agents by their moments and show how the dynamics of the moments can be modeled. Then approximate trajectories of the moments can be computed and an inverse problem is solved to recover macro-scale properties of the group of agents. To illustrate the theory, a numerical example with interactions between the agents is given.

  • 458.
    Zhong, Yang
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Hedman, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Li, Haibo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    How Good Can a Face Identifier Be Without Learning2016Ingår i: Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Constructing discriminative features is an essential issue in developing face recognition algorithms. There are two schools in how features are constructed: hand-crafted features and learned features from data. A clear trend in the face recognition community is to use learned features to replace hand-crafted ones for face recognition, due to the superb performance achieved by learned features through Deep Learning networks. Given the negative aspects of database-dependent solutions, we consider an alternative and demonstrate that, for good generalization performance, developing face recognition algorithms by using handcrafted features is surprisingly promising when the training dataset is small or medium sized. We show how to build such a face identifier with our Block Matching method which leverages the power of the Gabor phase in face images. Although no learning process is involved, empirical results show that the performance of this “designed” identifier is comparable (superior) to state-of-the-art identifiers and even close to Deep Learning approaches.

  • 459.
    Zhong, Yang
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Hedman, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Li, Haibo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    How good can a face identifier be without learning?2017Ingår i: 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, VISIGRAPP 2016, Springer, 2017, Vol. 693, s. 515-533Konferensbidrag (Refereegranskat)
    Abstract [en]

    Constructing discriminative features is an essential issue in developing face recognition algorithms. There are two schools in how features are constructed: hand-crafted features and learned features from data. A clear trend in the face recognition community is to use learned features to replace hand-crafted ones for face recognition, due to the superb performance achieved by learned features through Deep Learning networks. Given the negative aspects of database-dependent solutions, we consider an alternative and demonstrate that, for good generalization performance, developing face recognition algorithms by using hand-crafted features is surprisingly promising when the training dataset is small or medium sized. We show how to build such a face identifier with our Block Matching method which leverages the power of the Gabor phase in face images. Although no learning process is involved, empirical results show that the performance of this “designed” identifier is comparable (superior) to state-of-the-art identifiers and even close to Deep Learning approaches.

  • 460. Zhong, Yang
    et al.
    Li, Haibo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Is block matching an alternative tool to LBP for face recognition?2014Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper, we introduce the Block Matching (BM) as an alternative patch-based local matching approach for solving the face recognition problem. The Block Matching enables an image patch of the probe face image to search for its best matching from displaced positions in the gallery face image. This matching strategy is very effective for handling spatial shift between two images and it is radically different from that of the widely used LBP type patch-based local matching approaches. Our evaluations on the FERET and CMU-PIE databases show that the performance of this simple method is well comparable (superior) to that of the popular LBP approach. We argue that the Block Matching could provide face recognition a new approach with more flexible algorithm architecture. One can expect that it could lead to much higher performance when combining with other feature extraction techniques, like Gabor wavelet and deep learning.

  • 461.
    Zhong, Yang
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Li, Haibo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Leveraging Gabor Phase for Face Identification in Controlled Scenarios2016Ingår i: Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, Science and Technology Publications,Lda , 2016, s. 49-58Konferensbidrag (Refereegranskat)
    Abstract [en]

    Gabor features have been widely employed in solving face recognition problems in controlled scenarios. To construct discriminative face features from the complex Gabor space, the amplitude information is commonly preferred, while the other one — the phase — is not well utilized due to its spatial shift sensitivity. In this paper, we address the problem of face recognition in controlled scenarios. Our focus is on the selection of a suitable signal representation and the development of a better strategy for face feature construction. We demonstrate that through our Block Matching scheme Gabor phase information is powerful enough to improve the performance of face identification. Compared to state of the art Gabor filtering based approaches, the proposed algorithm features much lower algorithmic complexity. This is mainly due to our Block Matching enables the employment of high definition Gabor phase. Thus, a single-scale Gabor frequency band is sufficient for discrimination. Furthermore, learning process is not involved in the facial feature construction, which avoids the risk of building a database-dependent algorithm. Benchmark evaluations show that the proposed learning-free algorith outperforms state-of-the-art Gabor approaches and is even comparable to Deep Learning solutions.

  • 462.
    Zhong, Yang
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Sullivan, Josephine
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Li, Haibo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Face Attribute Prediction Using Off-The-Shelf CNN Features2016Ingår i: 2016 International Conference on Biometrics, ICB 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, artikel-id 7550092Konferensbidrag (Refereegranskat)
    Abstract [en]

    Predicting attributes from face images in the wild is a challenging computer vision problem. To automatically describe face attributes from face containing images, traditionally one needs to cascade three technical blocks — face localization, facial descriptor construction, and attribute classification — in a pipeline. As a typical classification problem, face attribute preiction has been addressed using deep learning. Current state-of-the-art performance was achieved by using two cascaded Convolutional Neural Networks (CNNs), which were specifically trained to learn face localization and attribute description. In this paper, we experiment with an alternative way of employing the power of deep representations from CNNs. Combining with conventional face localization techniques, we use off-the-shelf architectures trained for face recognition to build facial descriptors. Recognizing that the describable face attributes are diverse, our face descriptors are constructed from different levels of the CNNs for different attributes to best facilitate face attribute prediction. Experiments on two large datasets, LFWA and CelebA, show that our approach is entirely comparable to the state-of-the-art. Our findings not only demonstrate an efficient face attribute prediction approach, but also raise an important question: how to leverage the power of off-the-shelf CNN representations for novel tasks

  • 463.
    Zhong, Yang
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Sullivan, Josephine
    KTH, Skolan för datavetenskap och kommunikation (CSC), Robotik, perception och lärande, RPL.
    Li, Haibo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Leveraging Mid-level Deep Representations for Prediction Face Attributes in the Wild2016Ingår i: 2016 IEEE International Conference on Image Processing (ICIP), Institute of Electrical and Electronics Engineers (IEEE), 2016Konferensbidrag (Refereegranskat)
  • 464.
    Zhong, Yang
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC).
    Sullivan, Josephine
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Li, Haibo
    KTH, Skolan för datavetenskap och kommunikation (CSC), Medieteknik och interaktionsdesign, MID.
    Transferring from Face Recognition to Face Attribute Prediction through Adaptive Selection of Off-the-shelf CNN RepresentationsManuskript (preprint) (Övrigt vetenskapligt)
  • 465.
    Zhu, Biwen
    KTH, Skolan för elektroteknik och datavetenskap (EECS), Kommunikationssystem, CoS, Radio Systems Laboratory (RS Lab).
    Visual Tracking with Deep Learning: Automatic tracking of farm animals2018Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Automatisk spårning av övervakning i gårdens område kan bidra till att stödja jordbruket management. I detta projekt till ett automatiserat system för upptäckt upptäcka suggor från övervaknings filmer kommer att utformas med djupa lärande och datorseende metoder. Av hänsyn till Diskhantering och tid och hastighet Krav över nätverket för att uppnå realtidsscenarier i framtiden är spårning i komprimerade videoströmmar är avgörande.

    Det föreslagna systemet i detta projekt skulle använda en DCF (diskriminerande korrelationsfilter) som en klassificerare att upptäcka mål. Spårningen modell kommer att uppdateras genom att utbilda klassificeraren med online inlärningsmetoder. Compression teknik kodar videodata och minskar bithastigheter där videosignaler sänds kan hjälpa videoöverföring anpassar bättre i begränsad nätverk. det kan dock reducera bildkvaliteten på videoklipp och leder exakt hastighet av vårt spårningssystem för att minska. Därför undersöker vi utvärderingen av prestanda av befintlig visuella spårningsalgoritmer på videosekvenser Det ultimata målet med videokomprimering är att bidra till att bygga ett spårningssystem med samma prestanda men kräver färre nätverksresurser.

    Den föreslagna spårning algoritm spår framgångsrikt varje sugga i konsekutiva ramar i de flesta fall prestanda vår tracker var jämföras med två state-of-art spårning algoritmer:. Siamese Fully-Convolutional (FC) och Efficient Convolution Operators (ECO) utvärdering av prestanda Resultatet visar vår föreslagna tracker blir liknande prestanda med Siamese FC och ECO.

    I jämförelse med den ursprungliga spårningen uppnådde den föreslagna spårningen liknande spårningseffektivitet, samtidigt som det krävde mycket mindre lagring och alstra en lägre bitrate när videon komprimerades med lämpliga parametrar. Systemet är mycket långsammare än det behövs för spårning i realtid på grund av hög beräkningskomplexitet; därför behövs mer optimala metoder för att uppdatera spårningsmodellen för att uppnå realtidsspårning.

  • 466.
    Ögren, Petter
    et al.
    Mech. & Aerosp. Eng. Dept., Princeton Univ., NJ, USA.
    Leonard, Naomi Ehrich
    Mech. & Aerosp. Eng. Dept., Princeton Univ., NJ, USA.
    A Convergent Dynamic Window Approach to Obstacle Avoidance2005Ingår i: IEEE Transactions on robotics, ISSN 1552-3098, E-ISSN 1941-0468, Vol. 21, nr 2, s. 188-195Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The dynamic window approach (DWA) is a well-known navigation scheme developed by Fox et al. and extended by Brock and Khatib. It is safe by construction, and has been shown to perform very efficiently in experimental setups. However, one can construct examples where the proposed scheme fails to attain the goal configuration. What has been lacking is a theoretical treatment of the algorithm's convergence properties. Here we present such a treatment by merging the ideas of the DWA with the convergent, but less performance-oriented, scheme suggested by Rimon and Koditschek. Viewing the DWA as a model predictive control (MPC) method and using the control Lyapunov function (CLF) framework of Rimon and Koditschek, we draw inspiration from an MPC/CLF framework put forth by Primbs to propose a version of the DWA that is tractable and convergent.

  • 467.
    Ögren, Petter
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Robinson, John W.C.
    Swedish Defence Research Agency (FOI), Department of Aeronautics .
    A Model Based Approach to Modular Multi-Objective Robot Control2011Ingår i: Journal of Intelligent and Robotic Systems, ISSN 0921-0296, E-ISSN 1573-0409, Vol. 63, nr 2, s. 257-282Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Two broad classes of robot controllers are the modular, and the model based approaches. The modular approaches include the Reactive or Behavior Based designs. They do not rely on mathematical system models, but are easy to design, modify and extend. In the model based approaches, a model is used to design a single controller with verifiable system properties. The resulting designs are however often hard to extend, without jeopardizing the previously proven properties. This paper describes an attempt to narrow the gap between the flexibility of the modular approaches, and the predictability of the model based approaches, by proposing a modular design that does the combination, or arbitration, of the different modules in a model based way. By taking the (model based) time derivatives of scalar, Lyapunov-like, objective functions into account, the arbitration module can keep track of the time evolution of the objectives. This enables it to handle objective tradeoffs in a predictable way by finding controls that preserve an important objective that is currently met, while striving to satisfy another, less important one that is not yet achieved. To illustrate the approach a UAV control problem from the literature is solved, resulting in comparable, or better, performance.

  • 468.
    Ögren, Petter
    et al.
    Department of Autonomous Systems Swedish Defence Research Agency.
    Winstrand, Maja
    Minimizing Mission Risk in Fuel Constrained UAV Path Planning2008Ingår i: Journal of Guidance Control and Dynamics, ISSN 0731-5090, E-ISSN 1533-3884, Vol. 31, nr 5, s. 1497-1500Artikel i tidskrift (Refereegranskat)
  • 469.
    Öktem, Ozan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Chen, Chong
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). Chinese Academy of Sciences, China.
    Onur Domaniç, N.
    Ravikumar, P.
    Bajaj, C.
    Shape-based image reconstruction using linearized deformations2017Ingår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 33, nr 3, artikel-id 035004Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce a reconstruction framework that can account for shape related prior information in imaging-related inverse problems. It is a variational scheme that uses a shape functional, whose definition is based on deformable template machinery from computational anatomy. We prove existence and, as a proof of concept, we apply the proposed shape-based reconstruction to 2D tomography with very sparse and/or highly noisy measurements.

  • 470.
    Šarić, Marin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Ek, Carl Henrik
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Kragić, Danica
    KTH, Skolan för datavetenskap och kommunikation (CSC), Datorseende och robotik, CVAP.
    Dimensionality Reduction via Euclidean Distance Embeddings2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This report provides a mathematically thorough review and investigation of Metric Multidimensional scaling (MDS) through the analysis of Euclidean distances in input and output spaces. By combining a geometric approach with modern linear algebra and multivariate analysis, Metric MDS is viewed as a Euclidean distance embedding transformation that converts between coordinate and coordinate-free representations of data. In this work we link Mercer kernel functions, data in infinite-dimensional Hilbert space and coordinate-free distance metrics to a finite-dimensional Euclidean representation. We further set a foundation for a principled treatment of non-linear extensions of MDS as optimization programs on kernel matrices and Euclidean distances.

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