AbstractIn 2011, the Swedish government created a new curriculum for the compulsory school. This curriculum included stricter guidelines about what was to be taught in a variety of subjects taught in public and many private schools. This policy, entitled Lgr 11, has potential to influence a generation or more of Swedes regarding their understanding of the postcolonial world and future dealings with that part of the world and its peoples. In this paper, elements of postmodern and postcolonial historiography is employed when analyzing Lgr 11’s history syllabus. How the postcolonial world and its histories are represented in Lgr 11‘s narrative(s) is investigated. The importance of this document to Swedes is that, with a significant proportion of the Swedish population recent immigrants from the postcolonial world, the perspectives of that region are important in the development of identity for recent immigrants, Swedes themselves and in understandings of a large portion of the world for less recent immigrant Swedes. Swedish identity now includes postcolonial histories.

<p>In this thesis, we study three different image interpolation applications in high definition (HD) video processing: video de-interlacing, frame rate up-conversion, and view interpolation. We propose novel methods for these applications which are based on the concept of Nonlocal-Means (NL-Means).</p> <p>In the first part of this thesis, we introduce a new de-interlacing method which uses NL-Means algorithm. In this method, every interpolated pixel is set to a weighted average of its neighboring pixels in the current, previous, and the next frames. Weights of the pixels used in this filtering are calculated according to the radiometric distance between the surrounding areas of the pixel being interpolated and the neighboring pixels. One of the main challenges of the NL-Means is finding a suitable size for the neighborhoods (similarity window) that we want to find radiometric distance for them. We address this problem by using a steering kernel in our distance function to adapt the effective size of similarity window to the local information of the image. In order to calculate the weights of the filter, we need to have an estimate of the progressive frames. Therefore, we introduce a low computational initial de-interlacing method. This method interpolates the missing pixel along a direction based on two criteria of having minimum variation and being used by the above or below pixels. This method preserves the edge structures and yields superior visual quality compared to the simple edge-based line-averaging and many other simple iv de-interlacing methods.</p> <p>The second part of this thesis is devoted to the frame rate up-conversion application. Our frame rate up-conversion method is based on two main steps: NL-Means and foreground /background segmentation. In this method, for every pixel being interpolated first we check whether it belongs to the background or foreground. If the pixel belongs to the background and the values of the next and previous frames’ pixels are the same, we simply set the pixel intensity to the intensity of its location in the previous or next frame. If the pixel belongs to the foreground, we use NL-Means based interpolation for it. We adjust the equations of the NL-means for frame rate up-conversion so that we do not need to have the neighborhoods of the intermediate for calculating the weights of the filter. The comparison of our method with other existing methods shows the better performance of our method.</p> <p>In the third part of this thesis, we introduce a novel view interpolation method without using disparity estimation. In this method, we let every pixel in the intermediate view be the output of the NL-means using the pixels in the reference views. The experimental results demonstrate the better quality of our results compared with other algorithms which use disparity estimation.</p> / Master of Applied Science (MASc)

Image interpolation is the process of generating a new image utilizing a set of available images. The available images may be taken with a camera at different times, or with multiple cameras and from different viewpoints. Usually, the interpolation problem in the first scenario is called Frame Rate-Up Conversion (FRUC), and the second one view synthesis. This thesis focuses on image interpolation and addresses both FRUC and view synthesis problems. We propose a novel FRUC method using optical flow motion estimation and a patch-based reconstruction scheme. FRUC interpolates new frames between original frames of a video to increase the number of frames, and increases motion continuity. In our approach first, forward and backward motion vectors are obtained using an optical flow algorithm, and reconstructed versions of the current and previous frames are generated by our patch-based reconstruction scheme. Using the original and reconstructed versions of the current and previous frames, two mismatch masks are obtained. Then two versions of the middle frame are generated using a patch-based scheme, with estimated motion vectors and the current and previous frames. Finally, a middle mask, which identifies the mismatch areas of the two middle frames is reconstructed. Using these three masks, the best candidates for interpolation are selected and fused to obtain the final middle frame. Due to the patch-based nature of our interpolation scheme most of the holes and cracks will be filled. Although there is always a probability of having holes, the size and number of such holes are much smaller than those that would be generated using pixel-based mapping. The rare holes are filled using existing hole-filling algorithms. With fewer and smaller holes, simpler hole-filling algorithms can be applied to the image and the overall complexity of the required post processing decreases. View synthesis is the process of generating a new (virtual) view using available ones. Depending on the amount of available geometric information, view synthesis techniques can be divided into three categories: Image Based Rendering (IBR), Depth Image Based Rendering (DIBR), and Model Based Rendering (MBR). We introduce an adaptive version, patch-based scheme for IBR. This patch-based scheme reduces the size and number of holes during reconstruction. The size of patch is determined in response to edge information for better reconstruction, especially near the boundaries. In the first stage of the algorithm, disparity is obtained using optical flow estimation. Then, a reconstructed version of the left and right views are generated using our adaptive patch-based algorithm. The mismatches between each view and its reconstructed version are obtained in the mismatch detection steps. This stage results in two masks as outputs, which help with the refinement of disparities and the selection of the best patches for final synthesis. Finally, the remaining holes are filled using our simple hole filling scheme and the refined disparities. The adaptive version still benefits from the overlapping effect of the patches for hole reduction. However, compared with our fixed-size version, it results in better reconstruction near the edges, object boundaries, and inside the highly textured areas. We also propose an adaptive patch-based scheme for DIBR. The proposed method avoids unnecessary warping which is a computationally expensive step in DIBR. We divide nearby views into blocks, and only warp the center of each block. To have a better reconstruction near the edges and depth discontinuities, the block size is selected adaptively. In the blending step, an approach is introduced to calculate and refine the blending weights. Many of the existing DIBR schemes warp all pixels of nearby views during interpolation which is unnecessary. We show that using our adaptive patch-based scheme, it is possible to reduce the number of required warping without degrading the overall quality compared with existing schemes. / Thesis / Doctor of Philosophy (PhD)

In this dissertation, we solve multivariable Nevanlinna-Pick type interpolation problems. Particularly, we consider the left tangential interpolation problems on the commutative or noncommutative unit ball. For the commutative setting, we discuss left-tangential operator-argument interpolation problems for Schur-class multipliers on the Drury-Arveson space and for the noncommutative setting, we discuss interpolation problems for Schur-class multipliers on Fock space. We apply the Krein-space geometry approach (also known as the Grassmannian Approach). To implement this approach J-versions of Beurling-Lax representers for shift-invariant subspaces are required. Here we obtain these J-Beurling-Lax theorems by the state-space method for both settings. We see that the Krein-space geometry method is particularly simple in solving the interpolation problems when the Beurling-Lax representer is bounded. The Potapov approach applies equally well whether the representer is bounded or not. / Ph. D.

Bilinear systems are a class of nonlinear dynamical systems that arise in a variety of applications. In order to obtain a sufficiently accurate representation of the underlying physical phenomenon, these models frequently have state-spaces of very large dimension, resulting in the need for model reduction. In this work, we introduce two new methods for the model reduction of bilinear systems in an interpolation framework. Our first approach is to construct reduced models that satisfy multipoint interpolation constraints defined on the Volterra kernels of the full model. We show that this approach can be used to develop an asymptotically optimal solution to the H_2 model reduction problem for bilinear systems. In our second approach, we construct a solution to a bilinear system realization problem posed in terms of constructing a bilinear realization whose kth-order transfer functions satisfy interpolation conditions in k complex variables. The solution to this realization problem can be used to construct a bilinear system realization directly from sampling data on the kth-order transfer functions, without requiring the formation of the realization matrices for the full bilinear system. / Ph. D.

This thesis deals with non-linear non-quadratic optimal control problems in an autonomous system and a related iterative numerical method, the Kleinman-Newton method, for solving the problem. The thesis proves the local convergence of Kleinman-Newton method using the contraction mapping theorem and then describes how this Kleinman-Newton method may be used to numerically solve for the optimal control and the corresponding solution. In order to show the proof and the related numerical work, it is necessary to review some of earlier work in the beginning of Chapter 1 [Zhang], and to introduce the Kleinman-Newton method at the end of the chapter. In Chapter 2 we will demonstrate the proof. In Chapter 3 we will show the related numerical work and results. / Ph. D.

I ett alltmer urbaniserat samhälle har forskning uppmärksammat behovet av tillgång till gröna och tysta områden för att främja god hälsa hos människor. Befolkningstillväxten och förtätningen ökar i kommunerna i Stockholms län, vilket orsaker mer trafik och mer buller. Denna studie syftar till att undersöka hur buller från motorvägar sprids i stadsnära naturreservat. Studiens frågeställningar berör vilken inverkan vegetation och topografi har för bullerspridningen, vilka avstånd som krävs från bullerkällan för att bullret inte ska upplevas som störande och slutligen om en mobiltelefon som GNSS-mottagare är tillräcklig för positionering av mätpunkter. Det utvalda studieområdet var Järvafältet, en samling sammanhängande naturreservat omgivet av tätbebyggda kommuner och högtrafikerade motorvägar. Datainsamling bestod av 72 mätpunkter där flertalet data samlades in, bland annat decibelnivå, koordinater, avstånd till närmaste motorväg, höjddata, vindhastighet, väder, vegetation och en subjektiv uppskattning av störning från trafikbuller. Sju av variablerna behandlades i en principal-komponentanalys där den viktigaste komponenten bestod av decibelnivå, avstånd till motorväg, grad av bullerskydd och lufttemperatur. Subjektiv uppskattning av störning ingick inte i principalkomponentanalysen. En ljudmodell skapades med hjälp av interpolationsverktyget Kriging. I principalkomponentanalysen fastslogs att fyra av variablerna byggde upp en extraherad komponent: decibelnivå, avstånd till motorväg, grad av bullerskydd och lufttemperatur. Variablerna decibelnivå och avstånd till motorväg var negativt korrelerade till -0,78. Drygt 500 meter från bullerkällan visade sig sänkningen av decibelnivån plana ut. Även variabeln bullerskydd var korrelerad med decibelnivån, men det gick inte att fastställa om detta samband var mer kopplat till decibelnivån eller till avstånd från motorvägarna. Variabeln vegetation visade liten eller ingen korrelation med decibelnivåer. Lufttemperatur visade viss korrelation med decibelnivå, men detta samband var sannolikt falskt och berodde högst troligen på årstidsväxlingar. Avstånd till motorväg klassificerades i sju kategorier beroende på avstånd till motorväg. I varje kategori testade olika korrelationer mellan decibelnivå och tre olika variabler. Inom cirka 240 meter från motorvägen visade sig graden av bullerskydd vara stark negativt korrelerad med decibelnivå, men längre bort blev denna korrelation svag. Kontrolljudmätningar utfördes efter interpolationsmodellering för att validera resultatet. Kontrollmätningar avvek med i genomsnitt 1,5 dBA. Mobiltelefonens positionerings-precision jämfördes med en dedikerad GNSS-mottagare. Mobiltelefonen avvek med i genomsnitt 8,33 meter (13,16 meter inklusive en utliggare), ett resultat som ansågs fullgott för denna typ av ljudstudie. / In a more urbanised society research has shown the need for green spaces in order to favour human health. This study aims to explore how traffic noise travel through nature reserves close to metropolitan areas. Furthermore, the study tries to answer whether topography and vegetation have impact on noise level, distance required for the noise to stop being an inconvenience and if a mobile phone is sufficient as a GNSS-receiver for positioning of sound measuring points. The study area consists of Järvafältet, north of Stockholm, a collection of nature reserves surrounded by freeways. A total of 72 measuring points were selected, where several data were collected. A principal component analysis was used to extract components from the most important variables: decibel levels, distance to freeways, noise protection and air temperature. Decibel levels and distance to freeways were negatively correlated by -0.78. Vegetations show little correlation with decibel levels and correlation between noise protection and decibel levels are inconclusive but seem to have some correlation when analysed close to the source of noise. Kriging interpolation was used to model sound maps and control measurements resulted in an average deviation of 1,5 dBA in comparison to the created model. It was also found that a mobile phone GNSS receiver is not as precise as a dedicated GNSS receiver but is sufficient for this kind of sound study.

Yes / Purpose: To demonstrate methods that enable visual field sensitivities to be compared with normative data without restriction to a fixed test pattern. Methods: Healthy participants (n = 60, age 19–50) undertook microperimetry (MAIA-2) using 237 spatially dense locations up to 13° eccentricity. Surfaces were fit to the mean, variance, and 5th percentile sensitivities. Goodness-of-fit was assessed by refitting the surfaces 1000 times to the dataset and comparing estimated and measured sensitivities at 50 randomly excluded locations. A leave-one-out method was used to compare individual data with the 5th percentile surface. We also considered cases with unknown fovea location by adding error sampled from the distribution of relative fovea–optic disc positions to the test locations and comparing shifted data to the fixed surface. Results: Root mean square (RMS) difference between estimated and measured sensitivities were less than 0.5 dB and less than 1.0 dB for the mean and 5th percentile surfaces, respectively. Root mean square differences were greater for the variance surface, median 1.4 dB, range 0.8 to 2.7 dB. Across all participants 3.9% (interquartile range, 1.8–8.9%) of sensitivities fell beneath the 5th percentile surface, close to the expected 5%. Positional error added to the test grid altered the number of locations falling beneath the 5th percentile surface by less than 1.3% in 95% of participants. Conclusions: Spatial interpolation of normative data enables comparison of sensitivity measurements from varied visual field locations. Conventional indices and probability maps familiar from standard automated perimetry can be produced. These methods may enhance the clinical use of microperimetry, especially in cases of nonfoveal fixation.

The United States of Army Corp of Engineers (USACE) closely monitors the changing depths of navigation channels throughout the U.S. and Western Europe. The main issue with their surveying methodology is that the USACE surveys in linear cross sections, perpendicular to the channel direction. Depending on the channel length and width, these cross sections are spaced 100 - 400 feet apart, which produces large unmapped areas within each cross section of a survey. Using a variety of spatial interpolation methods, depths of these unmapped areas were produced. The choice of spatial interpolator varied upon which method adequately produced surfaces from large hydrographic survey data sets with the lowest amount of prediction error. The data used for this research consisted of multibeam and singlebeam surveys. These surveys were taken in a systematic manner of linear cross-sections that produced tens of thousands of data points. Nine interpolation techniques (inverse distance weighting, completely regularized spline, spline with tension, thin plate spline, multiquadratic spline, inverse multiquadratic spline, ordinary kriging, simple kriging, and universal kriging) were compared for their ability to accurately produce bathymetric surfaces of navigation channels. Each interpolation method was tested for effectiveness in determining depths at "unknown" areas. The level of accuracy was tested through validation and cross validation of training and test data sets for a particular hydrographic survey. By using interpolation, grid surfaces were created at 15, 30, 60, and 90-meter resolution for each survey of the study site, the Atlantic Ocean Channel. These surfaces are used to produce shoaling amounts, which are taken in the form of volumes (yd.³). Because the Atlantic Ocean Channel is a large channel with a small gradual change in depth, a comparison of grid resolution was conducted to determine what difference, if any, exists between the calculated volumes from varying grid resolutions. Also, a comparison of TIN model volume calculations was compared to grid volume estimates. Volumes are used to determine the amount of shoaling and at what rate shoaling is occurring in a navigation channel. Shoaling in each channel was calculated for the entire channel length. Volumes from varying grid resolutions were produced from the Atlantic Ocean Channel over a seven-year period from 1994-2001. Using randomly arranged test and training datasets, spline with tension and thin plate spline produced the mean total error when interpolating using singlebeam and multibeam hydrographic data respectively. Thin plate spline and simple kriging produced the lowest mean total error in full cross validation testing of entire singlebeam and multibeam hydrographic datasets respectively. Volume analysis of varying grid resolution indicates that finer grid resolution provides volume estimates comparable to TIN modeling, the USACE's technique for determining sediment volume estimates. The coarser the resolution, the less similar the volume estimates are in comparison to TIN modeling. All grid resolutions indicate that the Atlantic Ocean Channel is shoaling. Using a plan depth of 53 feet, TIN modeling displayed an annual average increase of 928,985 cubic yards of sediment from 1994 - 2001. / Master of Science

In this thesis, we develop the a new immersed finite element(IFE) space formed by piecewise linear polynomials defined on sub-elements cut by the actual interface curve for solving elliptic interface problems on interface independent meshes. A group of geometric identities and estimates on interface elements are derived. Based on these geometric identities and estimates, we establish a multi-point Taylor expansion of the true solutions and show the estimates for the second order terms in the expansion. Then, we construct the local IFE spaces by imposing the weak jump conditions and nodal value conditions on the piecewise polynomials. The unisolvence of the IFE shape functions is proven by the invertibility of the well-known Sherman-Morrison system. Furthermore we derive a group of fundamental identities about the IFE shape functions, which show that the two polynomial components in an IFE shape function are highly related. Finally we employ these fundamental identities and the multi-point Taylor expansion to derive the estimates for IFE interpolation errors in L2 and semi-H1 norms. / Master of Science