The objective of this work is the super-resolution enhancement of image sequences. We consider in particular images of scenes for which the point-to-point image transformation is a plane projective transformation. We first describe the imaging model, and a maximum likelihood (ML) estimator of the super-resolution image. We demonstrate the extreme noise sensitivity of the unconstrained ML estimator. We show that the Irani and Peleg [9, 10] super-resolution algorithm does not suffer from this sensitivity, and explain that this stability is due to the error back-projection method which effectively constrains the solution. We then propose two estimators suitable for the enhancement of text images: a maximum a posterior (MAP) estimator based on a Huber prior, and an estimator regularized using the Total Variation norm. We demonstrate the improved noise robustness of these approaches over the Irani and Peleg estimator. We also show the effects of a poorly estimated point spread function (PS...

Large-scale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the log-likelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than the commonly used quasi Newton approach for logistic regression. We also compare it with existing linear SVM implementations. 1

We show how features can easily be added to standard generative models for unsupervised learning, without requiring complex new training methods. In particular, each component multinomial of a generative model can be turned into a miniature logistic regression model if feature locality permits. The intuitive EM algorithm still applies, but with a gradient-based M-step familiar from discriminative training of logistic regression models. We apply this technique to part-of-speech induction, grammar induction, word alignment, and word segmentation, incorporating a few linguistically-motivated features into the standard generative model for each task. These feature-enhanced models each outperform their basic counterparts by a substantial margin, and even compete with and surpass more complex state-of-the-art models. 1

Discriminative feature-based methods are widely used in natural language processing, but sentence parsing is still dominated by generative methods. While prior feature-based dynamic programming parsers have restricted training and evaluation to artificially short sentences, we present the first general, featurerich discriminative parser, based on a conditional random field model, which has been successfully scaled to the full WSJ parsing data. Our efficiency is primarily due to the use of stochastic optimization techniques, as well as parallelization and chart prefiltering. On WSJ15, we attain a state-of-the-art F-score of 90.9%, a 14 % relative reduction in error over previous models, while being two orders of magnitude faster. On sentences of length 40, our system achieves an F-score of 89.0%, a 36 % relative reduction in error over a generative baseline. 1

L-BFGS-B is a limited memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems. L-BFGS-B can also be used for unconstrained problems, and in this case performs similarly to its predecessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77. Categories and Subject Descriptors: G.1.6 [Numerical Analysis]: Optimization -- gradient methods; G.4 [Mathematics of Computing]: Mathematical Software. General Terms: Algorithms Additional Key Words and Phrases: variable metric method, large scale optimization, nonlinear optimization, limited memory method. 1 Department of Electrical Engineering and Computer Science, Northwestern University, Evanston Il 60208. These authors were supported by National Science Foundation Grants CCR-9101359 and ASC-9213149, and by Department of Energy Grant DE-...

Figure 1: Geodesic interpolation and extrapolation. The blue input poses of the elephant are geodesically interpolated in an as-isometricas-possible fashion (shown in green), and the resulting path is geodesically continued (shown in purple) to naturally extend the sequence. No semantic information, segmentation, or knowledge of articulated components is used. We present a novel framework to treat shapes in the setting of Riemannian geometry. Shapes – triangular meshes or more generally straight line graphs in Euclidean space – are treated as points in a shape space. We introduce useful Riemannian metrics in this space to aid the user in design and modeling tasks, especially to explore the space of (approximately) isometric deformations of a given shape. Much of the work relies on an efficient algorithm to compute geodesics in shape spaces; to this end, we present a multiresolution framework to solve the interpolation problem – which amounts to solving a boundary value problem – as well as the extrapolation problem – an initial value problem – in shape space. Based on these two operations, several classical concepts like parallel transport and the exponential map can be used in shape space to solve various geometric modeling and geometry processing tasks. Applications include shape morphing, shape deformation, deformation transfer, and intuitive shape exploration.

Abstract. The focus of this dissertation is on matrix decompositions that use a limited amount of computer memory � thereby allowing problems with a very large number of variables to be solved. Speci�cally � we will focus on two applications areas � optimization and information retrieval. We introduce a general algebraic form for the matrix update in limited�memory quasi� Newton methods. Many well�known methods such as limited�memory Broyden Family meth� ods satisfy the general form. We are able to prove several results about methods which sat� isfy the general form. In particular � we show that the only limited�memory Broyden Family method �using exact line searches � that is guaranteed to terminate within n iterations on an n�dimensional strictly convex quadratic is the limited�memory BFGS method. Further� more � we are able to introduce several new variations on the limited�memory BFGS method that retain the quadratic termination property. We also have a new result that shows that full�memory Broyden Family methods �using exact line searches � that skip p updates to the quasi�Newton matrix will terminate in no more than n�p steps on an n�dimensional strictly convex quadratic. We propose several new variations on the limited�memory BFGS method

In this paper we evaluate the classification accuracy of four statistical and three neural network classifiers for two image based pattern classification problems. These are fingerprint classification and optical character recognition (OCR) for isolated handprinted digits. The evaluation results reported here should be useful for designers of practical systems for these two important commercial applications. For the OCR problem, the Karhunen-Lo`eve (K-L) transform of the images is used to generate the input feature set. Similarly for the fingerprint problem, the K-L transform of the ridge directions is used to generate the input feature set. The statistical classifiers used were Euclidean minimum distance, quadratic minimum distance, normal, and k-nearest neighbor. The neural network classifiers used were multilayer perceptron, radial basis function, and probabilistic. The OCR data consisted of 7,480 digit images for training and 23,140 digit images for testing. The fingerprint data co...

We show that a continuation approach to global optimization with global smoothing techniques can be used to obtain "-optimal solutions to distance geometry problems. We show that determining an "-optimal solution is still an NP-hard problem when " is small. A discrete form of the Gaussian transform is proposed based on the Hermite form of Gaussian quadrature. We show that the modified transform can be used whenever the transformed functions cannot be computed analytically. Our numerical results show that the discrete Gauss transform can be used to obtain "-optimal solutions for general distance geometry problems, and in particular, to determine the three-dimensional structure of protein fragments.

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