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  • 1.
    Danielson, Mats
    et al.
    Department of Computer and System Science, Stockholm University, Kista, Sweden.
    Ekenberg, Love
    Department of Computer and System Science, Stockholm University, Kista, Sweden.
    Hansson, Karin
    Department of Computer and System Science, Stockholm University, Kista, Sweden.
    Idefeldt, Jim
    Department of Computer and System Science, Stockholm University, Kista, Sweden.
    Larsson, Aron
    Department of Computer and System Science, Stockholm University, Kista, Sweden.
    Påhlman, Mona
    Department of Computer and System Science, Stockholm University, Kista, Sweden.
    Riabacke, Ari
    Department of Computer and System Science, Stockholm University, Kista, Sweden.
    Sundgren, David
    Department of Computer and System Science, Stockholm University, Kista, Sweden.
    Cross-disciplinary research in analytic decision support systems2006In: ITI 2006: Proceedings of the 28th International Conference on Information Technology Interfaces, Zagreb: University Computing Centre SRCE, University of Zagreb , 2006, p. 123-128Conference paper (Refereed)
    Abstract [en]

    A main problem in nearly all contexts is that unguided decision making is tremendously difficult and can lead to inefficient decision processes and undesired consequences. Therefore, decision support systems (DSSs) are of prime concern to any organization and there have been numerous approaches to such from, e.g., computational, mathematical, financial, philosophical, psychological, and sociological angles. However, a key observation is that efficient decision making is not easily performed by using methods from one discipline only. The case is rather that if real world decision making is taken seriously, several aspects must be included. This article describes some efforts of the DECIDE research group for approaching decision making and developing DSSs in a cross-disciplinary environment.

  • 2. Danielson, Mats
    et al.
    Ekenberg, Love
    Sundgren, David
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Structure information in decision trees and similar formalisms2007In: Proceedings of the Twentieth International Florida Artificial Intelligence Research Society Conference, Menlo Park, CA: AAAI Press , 2007, p. 62-67Conference paper (Refereed)
    Abstract [en]

    In attempting to address real-life decision problems, where uncertainty about input data prevails, some kind of representation of imprecise information is important and several have been proposed over the years. In particular, first-order representations of imprecision, such as sets of probability measures, upper and lower probabilities, and interval probabilities and utilities of various kinds, have been suggested for enabling a better representation of the input sentences. A common problem is, however, that pure interval analyses in many cases cannot discriminate sufficiently between the various strategies under consideration, which, needless to say, is a substantial problem in real-life decision making in agents as well as decision support tools. This is one reason prohibiting a more wide-spread use. In this article we demonstrate that in many situations, the discrimination can be made much clearer by using information inherent in the decision structure. It is discussed using

    second-order probabilities which, even when they are implicit, add information when handling aggregations of imprecise representations, as is the case in decision trees and probabilistic networks. The important conclusion is that since structure carries information, the structure of the decision problem influences evaluations of all interval representations and is quantifiable.

  • 3.
    Sundgren, David
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Discrete Second-order Probability Distributions that Factor into Marginals2011In: Proceedings of the Seventh International Symposium on Imprecise Probabilities: Theories and Applications / [ed] Frank Coolen, Gert de Cooman, Thomas Fetz, Michael Oberguggenberger, SIPTA , 2011, p. 335-342Conference paper (Refereed)
    Abstract [en]

    In realistic decision problems there is more often than not uncertainty in the background information. As for representation of uncertain or imprecise probability values, second-order probability, i.e. probability distributions over probabilities, offers an option. With a subjective view of probability second-order probability would seem to be impractical since it is hard for a person to construct a second-order distributions that reflects his or her beliefs. From the perspective of probability as relative frequency the task of constructing or updating a second-order probability distribution from data is somewhat easier. Here a very simple model for updating lower bounds of probabilities is employed. But the difficulties in choosing second-order distributions may be further alleviated if structural properties are considered. Either some of the probability values are dependent in some way, e.g. that they are known to be almost equal, or they are not dependent in any other way than what follows from that the values sum to one. In this work we present the unique family of discrete second-order probability distributions that correspond to the case where dependence is limited. These distributions are shown to have the property that the joint distributions are equal to normalised products of marginal distributions. The distribution family introduced here is a generalisation of a special case of the multivariate Pólya distribution and is shown to be conjugate prior to a compound hypergeometric distribution.

  • 4.
    Sundgren, David
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Distribution of expected utility in second-order decision analysis2007Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In decision analysis maximising the expected utility is an often used approach in choosing the optimal alternative. But when probabilities and utilities are vague or imprecise expected utility is fraught with complications. Studying second-order effects on decision analysis casts light on the importance of the structure of decision problems, pointing out some pitfalls in decision making and suggesting an easy to implement and easy to understand method of comparing decision alternatives. The topic of this thesis is such second-order effects of decision analysis, particularly with regards to expected utility and interval-bound probabilities. Explicit expressions for the second-order distributions inherent in interval-bound probabilities in general and likewise for distributions of expected utility for small decision problems are produced. By investigating these distributions the phenomenon of warping, that is concentration of belief, is studied.

  • 5.
    Sundgren, David
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Expected Utility from Multinomial Second-order Probability Distributions2010In: Polibits, ISSN 1870-9044, no 42, p. 71-75Article in journal (Refereed)
    Abstract [en]

    We consider the problem of maximizing expected utility when utilities and probabilities are given by discrete probability dis- tributions so that expected utility is a discrete stochastic variable. As for discrete second-order distributions, that is probability distributions where the variables are themselves probabilities, the multinomial family is a reasonable choice at least if first-order probabilities are interpreted as relative frequencies. We suggest a decision rule that reflects the uncertainty present in distribution-based probabilities and utilities and we show an example of this rule in action with multinomial second-order distributions.

     

  • 6.
    Sundgren, David
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    The Apparent Arbitrariness of Second-Order Probability Distributions2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Adequate representation of imprecise probabilities is a crucial and non-trivial problem in decision analysis. Second-order probability distributions is the model for imprecise probabilitoes whose merits are discussed in this thesis.

    That imprecise probabilities may be represented by second-order probability distributions is well known but there has been little attention to specific distributions. Since different probability distributions have different properties, the study of the desired properties of models of imprecise probabilities with respect to second-order models require analysis of particular second-order distributions.

    An often held objection to second-order probabilities is the apparent arbitrarines in the choice of distribution. We find some evidence that the structure of second-order distributions is an important factor that prohibits arbitrary choice of distributions. In particular, the properties of two second-order distributions are investigated; the uniform joint distribution and a variant of the Dirichlet distribution that has the property of being the normalised product of its own marginal distributions.

    The joint uniform distribution is in this thesis shown to have marginal distributions that belie the supposed non-informativeness of a uniform distribution. On the other hand, the modified Dirichlet distribution  discovered here has its information content evenly divided among the joint and marginal distributions in that the total correlation of the variables is minimal.

    It is also argued in the thesis that discrete distributions, as opposed to the continuous distributions mentioned above, would have the advantage of providing a natural setting for updating of lower bounds, and computation of expected utility is made more efficient.

  • 7.
    Sundgren, David
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Danielson, Mats
    Ekenberg, Love
    Some second order effects on interval based probabilities2006In: Proceedings of the Nineteenth International Florida Artificial Intelligence Research Society Conference, Menlo Park, CA: AAAI Press , 2006, p. 848-853Conference paper (Refereed)
    Abstract [en]

    In real-life decision analysis, the probabilities and values of consequences are in general vague and imprecise. One way to model imprecise probabilities is to represent a probability with the interval between the lowest possible and the highest possible probability, respectively. However, there are disadvantages with this approach, one being that when an event has several possible outcomes, the distributions of belief in the different probabilities

    are heavily concentrated to their centers of mass, meaning that much of the information of the original intervals are lost. Representing an imprecise probability with the distribution’s center of mass therefore in practice gives much the same result as using an interval, but a single number instead of an interval is computationally easier and avoids problems such as overlapping intervals. Using this, we demonstrate why second-order

    calculations can add information when handling imprecise representations, as is the case of decision trees or probabilistic networks. We suggest a measure of belief density for such intervals. We also demonstrate important properties when operating on general distributions. The results herein apply also to approaches which do not explicitly deal with second-order distributions, instead

    using only first-order concepts such as upper and lower bounds.

  • 8.
    Sundgren, David
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Danielson, Mats
    Deptartment of Computer and Systems Sciences, Stockholm University and TH, Kista, Sweden.
    Ekenberg, Love
    Deptartment of Computer and Systems Sciences, Stockholm University and TH, Kista, Sweden.
    Warp effects on calculating interval probabilities2009In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 50, no 9, p. 1360-1368Article in journal (Refereed)
    Abstract [en]

    In real-life decision analysis, the probabilities and utilities of consequences are in general vague and imprecise. One way to model imprecise probabilities is to represent a probability with the interval between the lowest possible and the highest possible probability, respectively. However, there are disadvantages with this approach; one being that when an event has several possible outcomes, the distributions of belief in the different probabilities are heavily concentrated toward their centres of mass, meaning that much of the information of the original intervals are lost. Representing an imprecise probability with the distribution’s centre of mass therefore in practice gives much the same result as using an interval, but a single number instead of an interval is computationally easier and avoids problems such as overlapping intervals. We demonstrate why second-order calculations add information when handling imprecise representations, as is the case of decision trees or probabilistic networks. We suggest a measure of belief density for such intervals. We also discuss properties applicable to general distributions. The results herein apply also to approaches which do not explicitly deal with second-order distributions, instead using only first-order concepts such as upper and lower bounds.

  • 9.
    Sundgren, David
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Ekenberg, Love
    Danielson, Mats
    Shifted Dirichlet Distributions as Second-Order Probability Distributions that Factors into Marginals2009In: Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications, 2009, p. 405-410Conference paper (Refereed)
    Abstract [en]

    In classic decision theory it is assumed that a decision-maker can assign precise numerical values corresponding to the true value of each consequence, as well as precise numerical probabilities for their occurrences. In attempting to address real-life problems, where uncertainty in the input data prevails, some kind of representation of imprecise information is important. Second-order distributions, probability distributions over probabilities, is one way to achieve such a representation. However, it is hard to intuitively understand statements in a multi-dimensional space and user statements must be provided more locally. But the information-theoretic interplay between joint and marginal distributions may give rise to unwanted effects on the global level. We consider this problem in a setting of second-order probability distributions and find a family of distributions that normalised over the probability simplex equals its own product of marginals. For such distributions, there is no flow of information between the joint distributions and the marginal distributions other than the trivial fact that the variables belong to the probability simplex. marginal distributions may give rise to unwanted effects on the global level.

  • 10.
    Sundgren, David
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Ekenberg, Love
    Danielson, Mats
    Some properties of aggregated distributions over expected values2008In: MICAI 2008: Advances in Artificial Intelligence: 7th Mexican International Conference on Artificial Intelligence, Atizapán de Zaragoza, Mexico, October 27-31, 2008, Proceedings, Berlin, Heidelberg: Springer , 2008, p. 699-709Conference paper (Refereed)
    Abstract [en]

    Software agents and humans alike face severe difficulties in making decisions in uncertain contexts. One approach is to formalise the decision situation by means of decision theory, i.e. probabilities and utilities leading to the principle of maximising the expected utility. Expected utility is here considered as a stochastic variable; under the assumption that all utility values are equally likely, and that each vector of probability values is equally likely, the probability distribution of expected utility is calculated for two, three, and four possible outcomes. The effect of these probability distributions concentrating around the middle value is explored and its significance for making decisions.

  • 11.
    Åhlén, Julia
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för datavetenskap.
    Bengtsson, E
    Sundgren, David
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Evaluation of Underwater Spectral Data for Colour Correction Applications2006In: CSECS'06 Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing, 2006Conference paper (Other academic)
    Abstract [en]

    The inherent properties of water column usually affect underwater imagery by suppressing high-energy wavelengths. One of the inherent properties, diffuse attenuation, can be estimated from multi or hyper spectral data and thus give information on how fast light of different wavelengths decreases with increasing depth. Based on exact depth measurements and data from a spectrometer incoming light on an object can be calculated and diffuse attenuation coefficient can be estimated. In this work the authors introduce a mathematical model that suggests the most stable wavelengths, which corresponds to estimated coefficients, based on spectral information from each depth. These values are then used in reconstruction of colours in underwater imagery. Since there are no digital hyper spectral cameras yet we are for the time being confined to point data, but the method is general and we show how it can be applied on multi spectral images.

  • 12.
    Åhlén, Julia
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för datavetenskap.
    Bengtsson, Ewert
    Sundgren, David
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Optimisation of Underwater Hyper Spectral Data for Colour Correction of Pseudo Hyper Spectral Images2006In: WSEAS Transactions on Signal Processing, ISSN 1790-5022, Vol. 2, no 11, p. 1473-1479Article in journal (Other academic)
  • 13.
    Åhlén, Julia
    et al.
    Uppsala universitet.
    Sundgren, David
    Stockholms universitet.
    Bottom Reflectance Influence on a Color Correction Algorithm for Underwater Images2003In: Proceedings of the 13th Scandinavinan Conference on Image Analysis / [ed] Bigun, J., Gustavsson, T., Berlin: Springer , 2003, p. 922-926Conference paper (Refereed)
    Abstract [en]

    Diminishing the negative effects of water column introduced on digital underwater images is the aim of a color correction algorithm presented by the authors in a previous paper. The present paper describes an experimental result and set of calculations for determining the impact of bottom reflectance on the algorithm's performance. This concept is based on the estimation of the relative reflectance of various bottom types such as sand, bleached corals and algae. We describe the adverse effects of extremely low and high bottom reflectances on the algorithm.

  • 14.
    Åhlén, Julia
    et al.
    Uppsala universitet.
    Sundgren, David
    Stockholms universitet.
    Bottom Reflectance Influence on a Color Correction Algorithm for Underwater Images2003In: SCIA, Scandinavian Conference on Image Analysis, Göteborg, 29 juni-2 juli / [ed] Bigun, J., Gustavsson, T.,, Berlin: Springer , 2003, p. 922-926Conference paper (Other academic)
  • 15.
    Åhlén, Julia
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för datavetenskap.
    Sundgren, David
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Recognition of video sequences using low frequencies and color2008In: Advanced topics on signal processing, robotics and automation: proceedings of the 7th WSEAS International Conference on Signal Processing, Robotics and Automation (ISPRA '08), Cambridge, UK, February 20-22 2008, WSEAS , 2008, p. 204-207Conference paper (Refereed)
    Abstract [en]

    This paper presents a method for descriptive feature matching between two video streams of the same scene. The second video is a corrupted copy of the first video. Examples of reliable recognition of an original scene that is subjected for compression and noise are presented. The algorithm is invariant to image scale and rotation, providing robust matching across a substantial range of video signals. This paper shows an approach to using descriptive features for randomly chosen frames from video stream. By involving color information as a feature we increase the robustness of the identification process. The median of low frequencies is measured, followed by an average of spectral information from the same frame to identify clusters belonging to a scene in a film. Finally, a comparison analysis is done to verify the originality of the film.

  • 16.
    Åhlén, Julia
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för datavetenskap.
    Sundgren, David
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Recognition of video signal by matching with the original video sequence2008In: Proceedings on CD-ROM, IADIS International Conference, 2008Conference paper (Refereed)
    Abstract [en]

    An adequate analysis of the originality of the video is of a great importance in video processing field. This paper presents a method for feature matching between two video streams. One of the video streams is subjected for severe compression, noise and rotation. These two copies represent the same movie but only one of the versions is original. Examples of reliable recognition of an original scene that is subjected for compression and noise are presented. The algorithm is invariant to image scale and rotation, providing robust matching across a substantial range of video signals. This paper shows an approach to using descriptive features for randomly chosen unstructured frames from video stream. By involving color information as a feature together with intensity profile for frame blocks we increase the robustness of the identification process. The median of low frequencies is measured, followed by an average of spectral information from the same frame to identify clusters belonging to a scene in a film. Finally, a comparison of mean squares of the difference is done to verify the originality of the film.

  • 17.
    Åhlén, Julia
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för datavetenskap.
    Sundgren, David
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Bengtsson, Ewert
    CBA.
    Application of underwater hyperspectral data for color correction purposes2007In: Pattern recognition and image analysis, ISSN 1555-6212, Vol. 17, no 1, p. 170-173Article in journal (Refereed)
    Abstract [en]

    Color correction of underwater images has been considered a difficult task for a number of reasons. Those include severe absorption of the water column, the unpredictable behavior of light under the water surface, limited access to reliable data for correction purposes, and the fact that we are only able to process three spectral channels, which is insufficient for most color correction applications. Here, the authors present a method to estimate a hyperspectral image from an RGB image and pointwise hyperspectral data. This is then used to color correct the hyperspectral underwater image and transform it back into RGB color space.

  • 18.
    Åhlén, Julia
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för datavetenskap.
    Sundgren, David
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Bengtsson, Ewert
    Pre-Processing of Underwater Images Taken in Shallow Waters for Color Reconstruction Purposes2005In: Proceedings of the 7th IASTED International Conference on Signal and Image Processing, 2005Conference paper (Refereed)
    Abstract [en]

    Coral reefs are monitored with different techniques in order to examine their health. Digital cameras, which provide an economically defendable tool for marine scientists to collect underwater data, tend to produce bluish images due to severe absorption of light at longer wavelengths. In this paper we study the possibilities of correcting for this color distortion through image processing. The decrease of red light by depth can be predicted by Beer's law. Another parameter that has to be taken into account is the image enhancement functions built into the camera. We use a spectrometer and a reflectance standard to obtain the data needed to approximate the joint effect of these functions. This model is used to pre-process the underwater images taken by digital cameras so that the red, green and blue channels show correct values before the images are subjected to correction for the effects of water column through application of Beer's law. This process is fully automatic and the amount of processed images is limited only by the speed of computer system. Experimental results show that the proposed method works well for correcting images taken at different depths with two different cameras.

  • 19.
    Åhlén, Julia
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för datavetenskap.
    Sundgren, David
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Lindell, Tommy
    Dissolved Organic Matters Impact on Color Reconstruction of Underwater Images2005In: Proceedings of the 14th Scandinavian Conference on Image Analysis, 2005, p. 1148-1156Conference paper (Refereed)
    Abstract [en]

    The natural properties of water column usually affect underwater imagery by supressing high-energy light. In application such as color correction of underwater images estimation of water column parameters is crucial. Diffuse attenuation coefficients are estimated and used for further processing of underwater taken data. The coeeficients will give information on how fast light of different wavelengths decreases with increasing depth. Based on the exact depth measurements and data from a spectrometrer the calculation of downwelling irradiance will be done. Chlorophyll concentration and a yellow substance factor contribute to a great variety of values of attenuation coefficients at different depth. By taking advantage of variations in depth, a method is presented to estimate the influence of dissolved organic matters and chlorophyll on color correction. Attenuation coefficients that depends on concentration of dissolved organic matters in water gives an indication on how well any spectral band is suited for color correction algorithm.

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