Fast space-variant elliptical filtering using box splines

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based on a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using pre-integration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based on the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.Comment: 12 figures; IEEE Transactions on Image Processing, vol. 19, 201

Inference via low-dimensional couplings

We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable "reference" measure (e.g., a standard Gaussian) with a target measure of interest. Direct simulation from the desired measure can then be achieved by pushing forward reference samples through the map. Yet characterizing such a map---e.g., representing and evaluating it---grows challenging in high dimensions. The central contribution of this paper is to establish a link between the Markov properties of the target measure and the existence of low-dimensional couplings, induced by transport maps that are sparse and/or decomposable. Our analysis not only facilitates the construction of transformations in high-dimensional settings, but also suggests new inference methodologies for continuous non-Gaussian graphical models. For instance, in the context of nonlinear state-space models, we describe new variational algorithms for filtering, smoothing, and sequential parameter inference. These algorithms can be understood as the natural generalization---to the non-Gaussian case---of the square-root Rauch-Tung-Striebel Gaussian smoother.Comment: 78 pages, 25 figure

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

Statistical modelling of algorithms for signal processing in systems based on environment perception

One cornerstone for realising automated driving systems is an appropriate handling of uncertainties in the environment perception and situation interpretation. Uncertainties arise due to noisy sensor measurements or the unknown future evolution of a traffic situation. This work contributes to the understanding of these uncertainties by modelling and propagating them with parametric probability distributions

Large Eddy Simulations of gaseous flames in gas turbine combustion chambers

Recent developments in numerical schemes, turbulent combustion models and the regular increase of computing power allow Large Eddy Simulation (LES) to be applied to real industrial burners. In this paper, two types of LES in complex geometry combustors and of specific interest for aeronautical gas turbine burners are reviewed: (1) laboratory-scale combustors, without compressor or turbine, in which advanced measurements are possible and (2) combustion chambers of existing engines operated in realistic operating conditions. Laboratory-scale burners are designed to assess modeling and funda- mental flow aspects in controlled configurations. They are necessary to gauge LES strategies and identify potential limitations. In specific circumstances, they even offer near model-free or DNS-like LES computations. LES in real engines illustrate the potential of the approach in the context of industrial burners but are more difficult to validate due to the limited set of available measurements. Usual approaches for turbulence and combustion sub-grid models including chemistry modeling are first recalled. Limiting cases and range of validity of the models are specifically recalled before a discussion on the numerical breakthrough which have allowed LES to be applied to these complex cases. Specific issues linked to real gas turbine chambers are discussed: multi-perforation, complex acoustic impedances at inlet and outlet, annular chambers.. Examples are provided for mean flow predictions (velocity, temperature and species) as well as unsteady mechanisms (quenching, ignition, combustion instabil- ities). Finally, potential perspectives are proposed to further improve the use of LES for real gas turbine combustor designs

A Neural Model of How the Brain Computes Heading from Optic Flow in Realistic Scenes

Animals avoid obstacles and approach goals in novel cluttered environments using visual information, notably optic flow, to compute heading, or direction of travel, with respect to objects in the environment. We present a neural model of how heading is computed that describes interactions among neurons in several visual areas of the primate magnocellular pathway, from retina through V1, MT+, and MSTd. The model produces outputs which are qualitatively and quantitatively similar to human heading estimation data in response to complex natural scenes. The model estimates heading to within 1.5° in random dot or photo-realistically rendered scenes and within 3° in video streams from driving in real-world environments. Simulated rotations of less than 1 degree per second do not affect model performance, but faster simulated rotation rates deteriorate performance, as in humans. The model is part of a larger navigational system that identifies and tracks objects while navigating in cluttered environments.National Science Foundation (SBE-0354378, BCS-0235398); Office of Naval Research (N00014-01-1-0624); National-Geospatial Intelligence Agency (NMA201-01-1-2016

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

A Bayesian Space-Time Dynamic Linear Model for Radioactivity Deposition after a Nuclear Accident

A three-stage Hierarchical Bayesian Space-Time (HBST) model, an extension of the class of dynamic linear models to space, is proposed for the ground contamination levels (GCL) and related uncertainties caused by polluting discharges in the environment. The model should allow updating the distribution of GCL in time and space as new data in the form of measurements and expert judgements become available to give real-time estimates of deposition levels. An application of the HBST model is proposed for the statistical modelling of radioactivity deposition after a nuclear accident. It explicitly handles uncertainties associated with (i) predictions of depositions from a long-range atmospheric dispersal model, (ii) in-situ gamma ray measurements and (iii) spatial interpolations. Unlike existing environmental statistical models, the HBST model also accounts for an established food chain contamination model called ECOSYS for which it provides data assimilation capabilities. The HBST model permits a fast implementation and full probabilistic inference for the parameters, interpolation and forecasts. Three distinct formulations of the HBST model were applied to assimilate real data of radioactivity deposition from the Chernobyl accident in southern Germany. Two of those formulations differ on the functional form of their spatial covariance matrices while the third, a normal inverse-Wishart model, allows the spatial covariances to "learn" from the data within the usual Bayesian paradigm. The later is shown to outperform the former models both in short and medium term forecasting as well as in a predictive interpolation test that took some measurements as out-of-sample

Retinal vessel segmentation using textons

Segmenting vessels from retinal images, like segmentation in many other medical image domains, is a challenging task, as there is no unified way that can be adopted to extract the vessels accurately. However, it is the most critical stage in automatic assessment of various forms of diseases (e.g. Glaucoma, Age-related macular degeneration, diabetic retinopathy and cardiovascular diseases etc.). Our research aims to investigate retinal image segmentation approaches based on textons as they provide a compact description of texture that can be learnt from a training set. This thesis presents a brief review of those diseases and also includes their current situations, future trends and techniques used for their automatic diagnosis in routine clinical applications. The importance of retinal vessel segmentation is particularly emphasized in such applications. An extensive review of previous work on retinal vessel segmentation and salient texture analysis methods is presented. Five automatic retinal vessel segmentation methods are proposed in this thesis. The first method focuses on addressing the problem of removing pathological anomalies (Drusen, exudates) for retinal vessel segmentation, which have been identified by other researchers as a problem and a common source of error. The results show that the modified method shows some improvement compared to a previously published method. The second novel supervised segmentation method employs textons. We propose a new filter bank (MR11) that includes bar detectors for vascular feature extraction and other kernels to detect edges and photometric variations in the image. The k-means clustering algorithm is adopted for texton generation based on the vessel and non-vessel elements which are identified by ground truth. The third improved supervised method is developed based on the second one, in which textons are generated by k-means clustering and texton maps representing vessels are derived by back projecting pixel clusters onto hand labelled ground truth. A further step is implemented to ensure that the best combinations of textons are represented in the map and subsequently used to identify vessels in the test set. The experimental results on two benchmark datasets show that our proposed method performs well compared to other published work and the results of human experts. A further test of our system on an independent set of optical fundus images verified its consistent performance. The statistical analysis on experimental results also reveals that it is possible to train unified textons for retinal vessel segmentation. In the fourth method a novel scheme using Gabor filter bank for vessel feature extraction is proposed. The ii method is inspired by the human visual system. Machine learning is used to optimize the Gabor filter parameters. The experimental results demonstrate that our method significantly enhances the true positive rate while maintaining a level of specificity that is comparable with other approaches. Finally, we proposed a new unsupervised texton based retinal vessel segmentation method using derivative of SIFT and multi-scale Gabor filers. The lack of sufficient quantities of hand labelled ground truth and the high level of variability in ground truth labels amongst experts provides the motivation for this approach. The evaluation results reveal that our unsupervised segmentation method is comparable with the best other supervised methods and other best state of the art methods

Automatic Fracture Orientation Extraction from SfM Point Clouds

Geology seeks to understand the history of the Earth and its surface processes through charac- terisation of surface formations and rock units. Chief among the geologists’ tools are rock unit orientation measurements, such as Strike, Dip and Dip Direction. These allow an understanding of both surface and sub-structure on both the local and macro scale. Although the way these techniques can be used to characterise geology are well understood, the need to collect these measurements by hand adds time and expense to the work of the geologist, precludes spontaneity in field work, and coverage is limited to where the geologist can physically reach. In robotics and computer vision, multi-view geometry techniques such as Structure from Motion (SfM) allows reconstructions of objects and scenes using multiple camera views. SfM-based techniques provide advantages over Lidar-type techniques, in areas such as cost and flexibility of use in more varied environmental conditions, while sacrificing extreme levels of fidelity. Regardless of this, camera based techniques such as SfM, have developed to the point where accuracy is possible in the decimetre range. Here is presented a system to automate the measurement of Strike, Dip and Dip Direction using multi-view geometry from video. Rather than deriving measurements using a method applied to the images, such as the Hough Transform, this method takes measurements directly from the software generated point cloud. Point cloud noise is mitigated using a Mahalanobis distance implementation. Significant structure is characterised using a k-nearest neighbour region growing algorithm, and final surface orientations are quantified using the plane, and normal direction cosines