A review of non-stationary spatial methods for geodetic least-squares collocation

This paper reviews a field that is herein termed spatial ?non-stationarity?, which is specifically concerned with non-stationarity in the geodetic theory of least-squares collocation (LSC). In practice, many geodesists rely on stationary assumptions in LSC, i.e., using a constant mean and isotropic and spatially invariant covariance for estimation and prediction of geodetic quantities. However, new theories in spatial statistics and geostatistics allow for better statistical methodologies to be used in geodesy. The aim of this paper is to introduce these methodologies and adapt them for dealing with non-stationarity in LSC

Grassmann Learning for Recognition and Classification

Computational performance associated with high-dimensional data is a common challenge for real-world classification and recognition systems. Subspace learning has received considerable attention as a means of finding an efficient low-dimensional representation that leads to better classification and efficient processing. A Grassmann manifold is a space that promotes smooth surfaces, where points represent subspaces and the relationship between points is defined by a mapping of an orthogonal matrix. Grassmann learning involves embedding high dimensional subspaces and kernelizing the embedding onto a projection space where distance computations can be effectively performed. In this dissertation, Grassmann learning and its benefits towards action classification and face recognition in terms of accuracy and performance are investigated and evaluated. Grassmannian Sparse Representation (GSR) and Grassmannian Spectral Regression (GRASP) are proposed as Grassmann inspired subspace learning algorithms. GSR is a novel subspace learning algorithm that combines the benefits of Grassmann manifolds with sparse representations using least squares loss §¤1-norm minimization for improved classification. GRASP is a novel subspace learning algorithm that leverages the benefits of Grassmann manifolds and Spectral Regression in a framework that supports high discrimination between classes and achieves computational benefits by using manifold modeling and avoiding eigen-decomposition. The effectiveness of GSR and GRASP is demonstrated for computationally intensive classification problems: (a) multi-view action classification using the IXMAS Multi-View dataset, the i3DPost Multi-View dataset, and the WVU Multi-View dataset, (b) 3D action classification using the MSRAction3D dataset and MSRGesture3D dataset, and (c) face recognition using the ATT Face Database, Labeled Faces in the Wild (LFW), and the Extended Yale Face Database B (YALE). Additional contributions include the definition of Motion History Surfaces (MHS) and Motion Depth Surfaces (MDS) as descriptors suitable for activity representations in video sequences and 3D depth sequences. An in-depth analysis of Grassmann metrics is applied on high dimensional data with different levels of noise and data distributions which reveals that standardized Grassmann kernels are favorable over geodesic metrics on a Grassmann manifold. Finally, an extensive performance analysis is made that supports Grassmann subspace learning as an effective approach for classification and recognition

Image Understanding and Robotics Research at Columbia University

Over the past year, the research investigations of the Vision/Robotics Laboratory at Columbia University have reflected the interests of its four faculty members, two staff programmers, and 16 Ph.D. students. Several of the projects involve other faculty members in the department or the university, or researchers at AT&T, IBM, or Philips. We list below a summary of our interests and results, together with the principal researchers associated with them. Since it is difficult to separate those aspects of robotic research that are purely visual from those that are vision-like (for example, tactile sensing) or vision-related (for example, integrated vision-robotic systems), we have listed all robotic research that is not purely manipulative. The majority of our current investigations are deepenings of work reported last year; this was the second year of both our basic Image Understanding contract and our Strategic Computing contract. Therefore, the form of this year's report closely resembles last year's. Although there are a few new initiatives, mainly we report the new results we have obtained in the same five basic research areas. Much of this work is summarized on a video tape that is available on request. We also note two service contributions this past year. The Special Issue on Computer Vision of the Proceedings of the IEEE, August, 1988, was co-edited by one of us (John Kender [27]). And, the upcoming IEEE Computer Society Conference on Computer Vision and Pattem Recognition, June, 1989, is co-program chaired by one of us (John Kender [23])

Doctor of Philosophy

dissertationStatistical learning theory has garnered attention during the last decade because it provides the theoretical and mathematical framework for solving pattern recognition problems, such as dimensionality reduction, clustering, and shape analysis. In statis

Object Association Across Multiple Moving Cameras In Planar Scenes

In this dissertation, we address the problem of object detection and object association across multiple cameras over large areas that are well modeled by planes. We present a unifying probabilistic framework that captures the underlying geometry of planar scenes, and present algorithms to estimate geometric relationships between different cameras, which are subsequently used for co-operative association of objects. We first present a local1 object detection scheme that has three fundamental innovations over existing approaches. First, the model of the intensities of image pixels as independent random variables is challenged and it is asserted that useful correlation exists in intensities of spatially proximal pixels. This correlation is exploited to sustain high levels of detection accuracy in the presence of dynamic scene behavior, nominal misalignments and motion due to parallax. By using a non-parametric density estimation method over a joint domain-range representation of image pixels, complex dependencies between the domain (location) and range (color) are directly modeled. We present a model of the background as a single probability density. Second, temporal persistence is introduced as a detection criterion. Unlike previous approaches to object detection that detect objects by building adaptive models of the background, the foreground is modeled to augment the detection of objects (without explicit tracking), since objects detected in the preceding frame contain substantial evidence for detection in the current frame. Finally, the background and foreground models are used competitively in a MAP-MRF decision framework, stressing spatial context as a condition of detecting interesting objects and the posterior function is maximized efficiently by finding the minimum cut of a capacitated graph. Experimental validation of the method is performed and presented on a diverse set of data. We then address the problem of associating objects across multiple cameras in planar scenes. Since cameras may be moving, there is a possibility of both spatial and temporal non-overlap in the fields of view of the camera. We first address the case where spatial and temporal overlap can be assumed. Since the cameras are moving and often widely separated, direct appearance-based or proximity-based constraints cannot be used. Instead, we exploit geometric constraints on the relationship between the motion of each object across cameras, to test multiple correspondence hypotheses, without assuming any prior calibration information. Here, there are three contributions. First, we present a statistically and geometrically meaningful means of evaluating a hypothesized correspondence between multiple objects in multiple cameras. Second, since multiple cameras exist, ensuring coherency in association, i.e. transitive closure is maintained between more than two cameras, is an essential requirement. To ensure such coherency we pose the problem of object associating across cameras as a k-dimensional matching and use an approximation to find the association. We show that, under appropriate conditions, re-entering objects can also be re-associated to their original labels. Third, we show that as a result of associating objects across the cameras, a concurrent visualization of multiple aerial video streams is possible. Results are shown on a number of real and controlled scenarios with multiple objects observed by multiple cameras, validating our qualitative models. Finally, we present a unifying framework for object association across multiple cameras and for estimating inter-camera homographies between (spatially and temporally) overlapping and non-overlapping cameras, whether they are moving or non-moving. By making use of explicit polynomial models for the kinematics of objects, we present algorithms to estimate inter-frame homographies. Under an appropriate measurement noise model, an EM algorithm is applied for the maximum likelihood estimation of the inter-camera homographies and kinematic parameters. Rather than fit curves locally (in each camera) and match them across views, we present an approach that simultaneously refines the estimates of inter-camera homographies and curve coefficients globally. We demonstrate the efficacy of the approach on a number of real sequences taken from aerial cameras, and report quantitative performance during simulations

Parallel algorithms for direct blood flow simulations

Fluid mechanics of blood can be well approximated by a mixture model of a Newtonian fluid and deformable particles representing the red blood cells. Experimental and theoretical evidence suggests that the deformation and rheology of red blood cells is similar to that of phospholipid vesicles. Vesicles and red blood cells are both area preserving closed membranes that resist bending. Beyond red blood cells, vesicles can be used to investigate the behavior of cell membranes, intracellular organelles, and viral particles. Given the importance of vesicle flows, in this thesis we focus in efficient numerical methods for such problems: we present computationally scalable algorithms for the simulation of dilute suspension of deformable vesicles in two and three dimensions. Our method is based on the boundary integral formulation of Stokes flow. We present new schemes for simulating the three-dimensional hydrodynamic interactions of large number of vesicles with viscosity contrast. The algorithms incorporate a stable time-stepping scheme, high-order spatiotemporal discretizations, spectral preconditioners, and a reparametrization scheme capable of resolving extreme mesh distortions in dynamic simulations. The associated linear systems are solved in optimal time using spectral preconditioners. The highlights of our numerical scheme are that (i) the physics of vesicles is faithfully represented by using nonlinear solid mechanics to capture the deformations of each cell, (ii) the long-range, N-body, hydrodynamic interactions between vesicles are accurately resolved using the fast multipole method (FMM), and (iii) our time stepping scheme is unconditionally stable for the flow of single and multiple vesicles with viscosity contrast and its computational cost-per-simulation-unit-time is comparable to or less than that of an explicit scheme. We report scaling of our algorithms to simulations with millions of vesicles on thousands of computational cores.PhDCommittee Chair: Biros, George; Committee Member: Alben, Silas; Committee Member: Fernandez-Nieves, Alberto; Committee Member: Hu, David; Committee Member: Vuduc, Richar