| 1. |
- Schellwat, Holger
(författare)
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Induced Cayley graphs and double covers
- 1995
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Ingår i: Linear and multilinear algebra. - 0308-1087 .- 1563-5139. ; 39:1-2, s. 161-164
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Tidskriftsartikel (refereegranskat)
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| 2. |
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| 3. |
- Lindeberg, Tony, 1964-
(författare)
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Discrete Scale-Space Theory and the Scale-Space Primal Sketch
- 1991
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis, within the subfield of computer science known as computer vision, deals with the use of scale-space analysis in early low-level processing of visual information. The main contributions comprise the following five subjects:The formulation of a scale-space theory for discrete signals. Previously, the scale-space concept has been expressed for continuous signals only. We propose that the canonical way to construct a scale-space for discrete signals is by convolution with a kernel called the discrete analogue of the Gaussian kernel, or equivalently by solving a semi-discretized version of the diffusion equation. Both the one-dimensional and two-dimensional cases are covered. An extensive analysis of discrete smoothing kernels is carried out for one-dimensional signals and the discrete scale-space properties of the most common discretizations to the continuous theory are analysed.A representation, called the scale-space primal sketch, which gives a formal description of the hierarchical relations between structures at different levels of scale. It is aimed at making information in the scale-space representation explicit. We give a theory for its construction and an algorithm for computing it.A theory for extracting significant image structures and determining the scales of these structures from this representation in a solely bottom-up data-driven way.Examples demonstrating how such qualitative information extracted from the scale-space primal sketch can be used for guiding and simplifying other early visual processes. Applications are given to edge detection, histogram analysis and classification based on local features. Among other possible applications one can mention perceptual grouping, texture analysis, stereo matching, model matching and motion.A detailed theoretical analysis of the evolution properties of critical points and blobs in scale-space, comprising drift velocity estimates under scale-space smoothing, a classification of the possible types of generic events at bifurcation situations and estimates of how the number of local extrema in a signal can be expected to decrease as function of the scale parameter. For two-dimensional signals the generic bifurcation events are annihilations and creations of extremum-saddle point pairs. Interpreted in terms of blobs, these transitions correspond to annihilations, merges, splits and creations.Experiments on different types of real imagery demonstrate that the proposed theory gives perceptually intuitive results.
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| 4. |
- Svanström, Mattias
(författare)
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Ternary Codes with Weight Constraints
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study the problem of maximizing the size of a ternary block code with given length and minimum Hamming distance. The problem is further restricted in two different ways. Either we require all codewords to have constant Hamming weight, or we require all codewords to have constant composition. We let the alphabet consist of the symbols zero, one and two. In a constant-composition code the number of zeros, the number of ones and the number of twos in each codeword are fixed, while in a constant-weight code only the total number of ones and twos in each codeword is fixed.For both code classes several upper bounds are presented. We give a number of constructions of codes that meet the upper bounds. A construction of perfect ternary constant-weight codes with minimum distance three is presented. We have also compiled tables of the best possible upper and lower bounds on the code size.
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| 5. |
- Lindeberg, Tony, 1964-
(författare)
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Discrete Derivative Approximations with Scale-Space Properties : A Basis for Low-Level Feature Extraction
- 1993
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Ingår i: Journal of Mathematical Imaging and Vision. - : Kluwer Academic Publishers. - 0924-9907 .- 1573-7683. ; 3:4, s. 349-376
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Tidskriftsartikel (refereegranskat)abstract
- This article shows how discrete derivative approximations can be defined so thatscale-space properties hold exactly also in the discrete domain. Starting from a set of natural requirements on the first processing stages of a visual system,the visual front end, it gives an axiomatic derivation of how a multiscale representation of derivative approximations can be constructed from a discrete signal, so that it possesses analgebraic structure similar to that possessed by the derivatives of the traditional scale-space representation in the continuous domain. A family of kernels is derived that constitutediscrete analogues to the continuous Gaussian derivatives.The representation has theoretical advantages over other discretizations of the scale-space theory in the sense that operators that commute before discretizationcommute after discretization. Some computational implications of this are that derivative approximations can be computeddirectly from smoothed data and that this will giveexactly the same result as convolution with the corresponding derivative approximation kernel. Moreover, a number ofnormalization conditions are automatically satisfied.The proposed methodology leads to a scheme of computations of multiscale low-level feature extraction that is conceptually very simple and consists of four basic steps: (i)large support convolution smoothing, (ii)small support difference computations, (iii)point operations for computing differential geometric entities, and (iv)nearest-neighbour operations for feature detection.Applications demonstrate how the proposed scheme can be used for edge detection and junction detection based on derivatives up to order three.
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| 6. |
- Sladoje, Nataša
(författare)
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Ellipses estimation from their digitization
- 1997
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Ingår i: International Conference on Discrete Geometry for Computer Imagery. - Berlin, Heidelberg : Springer Berlin/Heidelberg. - 9783540638841 ; , s. 187-198
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Konferensbidrag (refereegranskat)
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| 7. |
- Rakus-Andersson, Elisabeth
(författare)
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A Fuzzy Decision Making Model Applied to the Choice of the Therapy in the Case of Symptoms not Disappearing after the Treatment
- 1999
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Konferensbidrag (refereegranskat)abstract
- Fuzzy set theory has used many auxiliary methods into the trials of solutions of some medical problems. One of the attempts was the evaluation of the optimal level of the drug action in the case when the clinical symptoms disappeared completely after the treatment. However, there can occur such a morbid process in which the symptoms prevail after the treatment. The medication improves too high or too low level of the quantitative symptom but it still indicates the presence of the illness. It is not so easy to choose the medicine, which acts best because it can happen that most of them influence the same symptoms, while they do not improve the others. A fuzzy decision making model tries to make easier to find such a drug which affects most of the symptoms in the highest degree. In the next attempt of solving the problem we propose the using of discrete membership functions in the model instead of the continuous ones. It should improve the thoroughness of the method and heighten the reliability of the accepted decision.
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| 8. |
- Asadzadeh, Mohammad, 1952, et al.
(författare)
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The discrete ordinates method for the neutron transport equation in an infinite cylindrical domain
- 1992
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Ingår i: Mathematical Models and Methods in Applied Science. ; 2:3, s. 317-338
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Tidskriftsartikel (refereegranskat)abstract
- We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain. The theorem states that the solution has almost two derivatives in L1, and is proved using Besov space techniques. This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation. We derive an error estimate in the L1-norm for the scalar flux, and as a consequence, we obtain an error bound for the critical eigenvalue.
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| 9. |
- Andersson, Håkan
(författare)
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Error-Correcting Codes Based on Chaotic Dynamical Systems
- 1998
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation treats a novel class of error-correcting codes based on chaotic dynamical systems. The codes are defined over a continuous alphabet whereas the information that is to be transmitted belongs to a discrete set of symbols. Simple expressions can be given for the encoders, and the codewords can be described by a parity-check relation. However, the most interesting approach is to view the codewords as orbits of iterated dynamical systems described by integer matrices.Under some rather natural assumptions, the codes are shown to be group codes. The minimum distance is proved to be well-defined and strictly greater than zero. An algorithm for calculating it is also given. Initially, no robust sliding-window encoder inverses exist, but this deficiency is remedied by the introduction of fractal signal sets. The problem of catastrophic encoders is also solved by the introduction of these totally disconnected signal sets.Decoding strategies are discussed, and it is shown why the Viterbi algorithm does not work in higher dimensions for this type of codes. So-called list decoding emerges as a good alternative and its merits are considered. Simulations and comparisons with binary antipodal signaling are performed. The setting of the work is in two dimensions. However, the strength of this code construction is that it easily generalizes to higher dimensions.
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| 10. |
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