Robust regression, HCCM estimators, and an Empirical Bayes application

Ankara : The Institute of Economics and Social Sciences of Bilkent Univ., 1999.Thesis (Ph. D.) -- Bilkent University, 1999.Includes bibliographical references leaves 84-93.This Ph.D. thesis includes three topics of econometrics where the chapters of the whole study are devoted to robust regression analysis, research on the estimators for the covariance matrix of a heteroskedastic regression and finally an application of the Empirical Bayes method to some real data from Istanbul Stock Exchange. Some robust regression techniques are applied to some data sets to show how outliers of a data set may lead to wrong inferences. The results reveal that the former studies have gone through some wrong results with the effect of the outliers that were not detected. Second chapter makes a thorough evaluation of the existing heteroskedasticity consistent covariance matrix estimators where the Maximum Likelyhood estimator recently promoted to the literature by Zaman is also taken into consideration. Finally, some empirical study is carried out in the last part of the thesis. The firms of ISE are categorized into sectors and some estimation is done over an equation which is very common and simple in the finance literature.Orhan, MehmetPh.D

Investigating Polynomial Fitting Schemes for Image Compression

Image compression is a means to perform transmission or storage of visual data in the most economical way. Though many algorithms have been reported, research is still needed to cope with the continuous demand for more efficient transmission or storage. This research work explores and implements polynomial fitting techniques as means to perform block-based lossy image compression. In an attempt to investigate nonpolynomial models, a region-based scheme is implemented to fit the whole image using bell-shaped functions. The idea is simply to view an image as a 3D geographical map consisting of hills and valleys. However, the scheme suffers from high computational demands and inferiority to many available image compression schemes. Hence, only polynomial models get further considerations. A first order polynomial (plane) model is designed to work in a multiplication- and division-free (MDF) environment. The intensity values of each image block are fitted to a plane and the parameters are then quantized and coded. Blocking artefacts, a common drawback of block-based image compression techniques, are reduced using an MDF line-fitting scheme at blocks’ boundaries. It is shown that a compression ratio of 62:1 at 28.8dB is attainable for the standard image PEPPER, outperforming JPEG, both objectively and subjectively for this part of the rate-distortion characteristics. Inter-block prediction can substantially improve the compression performance of the plane model to reach a compression ratio of 112:1 at 27.9dB. This improvement, however, slightly increases computational complexity and reduces pipelining capability. Although JPEG2000 is not a block-based scheme, it is encouraging that the proposed prediction scheme performs better in comparison to JPEG 2000, computationally and qualitatively. However, more experiments are needed to have a more concrete comparison. To reduce blocking artefacts, a new postprocessing scheme, based on Weber’s law, is employed. It is reported that images postprocessed using this scheme are subjectively more pleasing with a marginal increase in PSNR (<0.3 dB). The Weber’s law is modified to perform edge detection and quality assessment tasks. These results motivate the exploration of higher order polynomials, using three parameters to maintain comparable compression performance. To investigate the impact of higher order polynomials, through an approximate asymptotic behaviour, a novel linear mapping scheme is designed. Though computationally demanding, the performances of higher order polynomial approximation schemes are comparable to that of the plane model. This clearly demonstrates the powerful approximation capability of the plane model. As such, the proposed linear mapping scheme constitutes a new approach in image modeling, and hence worth future consideration

A Novel Multi-Symbol Curve Fit based CABAC Framework for Hybrid Video Codec's with Improved Coding Efficiency and Throughput

Video compression is an essential component of present-day applications and a decisive factor between the success or failure of a business model. There is an ever increasing demand to transmit larger number of superior-quality video channels into the available transmission bandwidth. Consumers are increasingly discerning about the quality and performance of video-based products and there is therefore a strong incentive for continuous improvement in video coding technology for companies to have market edge over its competitors. Even though processor speeds and network bandwidths continue to increase, a better video compression results in a more competitive product. This drive to improve video compression technology has led to a revolution in the last decade. In this thesis we addresses some of these data compression problems in a practical multimedia system that employ Hybrid video coding schemes. Typically Real life video signals show non-stationary statistical behavior. The statistics of these signals largely depend on the video content and the acquisition process. Hybrid video coding schemes like H264/AVC exploits some of the non-stationary characteristics but certainly not all of it. Moreover, higher order statistical dependencies on a syntax element level are mostly neglected in existing video coding schemes. Designing a video coding scheme for a video coder by taking into consideration these typically observed statistical properties, however, offers room for significant improvements in coding efficiency.In this thesis work a new frequency domain curve-fitting compression framework is proposed as an extension to H264 Context Adaptive Binary Arithmetic Coder (CABAC) that achieves better compression efficiency at reduced complexity. The proposed Curve-Fitting extension to H264 CABAC, henceforth called as CF-CABAC, is modularly designed to conveniently fit into existing block based H264 Hybrid video Entropy coding algorithms. Traditionally there have been many proposals in the literature to fuse surfaces/curve fitting with Block-based, Region based, Training-based (VQ, fractals) compression algorithms primarily to exploiting pixel- domain redundancies. Though the compression efficiency of these are expectantly better than DCT transform based compression, but their main drawback is the high computational demand which make the former techniques non-competitive for real-time applications over the latter. The curve fitting techniques proposed so far have been on the pixel domain. The video characteristic on the pixel domain are highly non-stationary making curve fitting techniques not very efficient in terms of video quality, compression ratio and complexity. In this thesis, we explore using curve fitting techniques to Quantized frequency domain coefficients. we fuse this powerful technique to H264 CABAC Entropy coding. Based on some predictable characteristics of Quantized DCT coefficients, a computationally in-expensive curve fitting technique is explored that fits into the existing H264 CABAC framework. Also Due to the lossy nature of video compression and the strong demand for bandwidth and computation resources in a multimedia system, one of the key design issues for video coding is to optimize trade-off among quality (distortion) vs compression (rate) vs complexity. This thesis also briefly studies the existing rate distortion (RD) optimization approaches proposed to video coding for exploring the best RD performance of a video codec. Further, we propose a graph based algorithm for Rate-distortion. optimization of quantized coefficient indices for the proposed CF-CABAC entropy coding

Some Basis Function Methods for Surface Approximation

This thesis considers issues in surface reconstruction such as identifying approximation methods that work well for certain applications and developing efficient methods to compute and manipulate these approximations. The first part of the thesis illustrates a new fast evaluation scheme to efficiently calculate thin-plate splines in two dimensions. In the fast multipole method scheme, exponential expansions/approximations are used as an intermediate step in converting far field series to local polynomial approximations. The contributions here are extending the scheme to the thin-plate spline and a new error analysis. The error analysis covers the practically important case where truncated series are used throughout, and through off line computation of error constants gives sharp error bounds. In the second part of this thesis, we investigates fitting a surface to an object using blobby models as a coarse level approximation. The aim is to achieve a given quality of approximation with relatively few parameters. This process involves an optimization procedure where a number of blobs (ellipses or ellipsoids) are separately fitted to a cloud of points. Then the optimized blobs are combined to yield an implicit surface approximating the cloud of points. The results for our test cases in 2 and 3 dimensions are very encouraging. For many applications, the coarse level blobby model itself will be sufficient. For example adding texture on top of the blobby surface can give a surprisingly realistic image. The last part of the thesis describes a method to reconstruct surfaces with known discontinuities. We fit a surface to the data points by performing a scattered data interpolation using compactly supported RBFs with respect to a geodesic distance. Techniques from computational geometry such as the visibility graph are used to compute the shortest Euclidean distance between two points, avoiding any obstacles. Results have shown that discontinuities on the surface were clearly reconstructed, and th

Statistical Diffusion Tensor Imaging

Magnetic resonance diffusion tensor imaging (DTI) allows to infere the ultrastructure of living tissue. In brain mapping, neural fiber trajectories can be identified by exploiting the anisotropy of diffusion processes. Manifold statistical methods may be linked into the comprehensive processing chain that is spanned between DTI raw images and the reliable visualization of fibers. In this work, a space varying coefficients model (SVCM) using penalized B-splines was developed to integrate diffusion tensor estimation, regularization and interpolation into a unified framework. The implementation challenges originating in multiple 3d space varying coefficient surfaces and the large dimensions of realistic datasets were met by incorporating matrix sparsity and efficient model approximation. Superiority of B-spline based SVCM to the standard approach was demonstrable from simulation studies in terms of the precision and accuracy of the individual tensor elements. The integration with a probabilistic fiber tractography algorithm and application on real brain data revealed that the unified approach is at least equivalent to the serial application of voxelwise estimation, smoothing and interpolation. From the error analysis using boxplots and visual inspection the conclusion was drawn that both the standard approach and the B-spline based SVCM may suffer from low local adaptivity. Therefore, wavelet basis functions were employed for filtering diffusion tensor fields. While excellent local smoothing was indeed achieved by combining voxelwise tensor estimation with wavelet filtering, no immediate improvement was gained for fiber tracking. However, the thresholding strategy needs to be refined and the proposed model of an incorporation of wavelets into an SVCM needs to be implemented to finally assess their utility for DTI data processing. In summary, an SVCM with specific consideration of the demands of human brain DTI data was developed and implemented, eventually representing a unified postprocessing framework. This represents an experimental and statistical platform to further improve the reliability of tractography

Three-dimensional localization and mapping of static environments by means of mobile perception

Model-based task planning is one of the main capabilities of autonomous mobile robots. Especially for model-based localization and path planning, a large-scale description of the operation environment is required. Cognitive communication between man and his machine could be based on a common, three-dimensional understanding of the environment. In the case of a personal service robot, the operation environment may comprise both indoor and outdoor spaces. In this thesis, a method for the generation of a three-dimensional geometric model for large scale, structured and natural environments is presented. The environment mapping method, which uses range images as measurement data, consists of three main phases: first, geometric features are extracted from each of the range images. Secondly, the relative coordinate transformations (i.e. registrations) between the sensor viewpoint locations, where the range data was measured, are computed. And, finally, an integrated map is formed by transforming the sub-map data into a common frame of reference. Two types of geometric features are extracted from the range images: cylinder segments (or more generally truncated cone segments) and straight-line segments. With cylinder segments tree trunks and other elongated cylindrical objects can be modeled, whereas the straight line segments correspond to the upper corners of vertical walls. The features are utilized as natural landmarks for registration computation. The presented method is tested by mapping three test sites representing structured, semi-structured and natural environments. The structured environment corresponds to a part of the premises of an office building, the semi-structured environment corresponds to the surroundings of a parking lot and the natural environment is a small forest area. The dimensions of the test sites are about 50 meters, 120 meters and 40 meters square, respectively. A simple incremental approach is used to build an integrated model for the parking lot and office corridor environments. For the principal mapping experiment, concerning the small forest area, a statistically more sound, optimal approach is applied. With respect to the feature extraction methods and the computation of the relative coordinate transformations between the viewpoints, robustness to outlier data and failure modes of the methods are discussed in more detail.reviewe

Automatic creation of boundary-representation models from single line drawings

This thesis presents methods for the automatic creation of boundary-representation models of polyhedral objects from single line drawings depicting the objects. This topic is important in that automated interpretation of freehand sketches would remove a bottleneck in current engineering design methods. The thesis does not consider conversion of freehand sketches to line drawings or methods which require manual intervention or multiple drawings. The thesis contains a number of novel contributions to the art of machine interpretation of line drawings. Line labelling has been extended by cataloguing the possible tetrahedral junctions and by development of heuristics aimed at selecting a preferred labelling from many possible. The ”bundling” method of grouping probably-parallel lines, and the use of feature detection to detect and classify hole loops, are both believed to be original. The junction-line-pair formalisation which translates the problem of depth estimation into a system of linear equations is new. Treating topological reconstruction as a tree-search is not only a new approach but tackles a problem which has not been fully investigated in previous work