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117
A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
, 1999
"... Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for 1dimensional problems and blockToeplitz Toeplitzblock matrices for 2dim ..."
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Cited by 106 (25 self)
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Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for 1dimensional problems and blockToeplitz Toeplitzblock matrices for 2dimensional cases. They are computationally intensive to invert especially in the block case. If the periodic boundary condition is used, the matrices become (block) circulant and can be diagonalized by discrete Fourier transform matrices. In this paper, we consider the use of the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary). The resulting matrices are (block) Toeplitzplus Hankel matrices. We show that for symmetric blurring functions, these blurring matrices can always be diagonalized by discrete cosine transform matrices. Thus the cost of inversion is significantly lower than that of using the zero or periodic boundary conditions. We also s...
Spectral quadrangulation with orientation and alignment control
 IN ACM SIGGRAPH ASIA
, 2008
"... This paper presents a new quadrangulation algorithm, extending the spectral surface quadrangulation approach where the coarse quadrangular structure is derived from the MorseSmale complex of an eigenfunction of the Laplacian operator on the input mesh. In contrast to the original scheme, we provi ..."
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Cited by 37 (10 self)
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This paper presents a new quadrangulation algorithm, extending the spectral surface quadrangulation approach where the coarse quadrangular structure is derived from the MorseSmale complex of an eigenfunction of the Laplacian operator on the input mesh. In contrast to the original scheme, we provide flexible explicit controls of the shape, size, orientation and feature alignment of the quadrangular faces. We achieve this by proper selection of the optimal eigenvalue (shape), by adaption of the area term in the Laplacian operator (size), and by adding special constraints to the Laplace eigenproblem (orientation and alignment). By solving a generalized eigenproblem we can generate a scalar field on the mesh whose MorseSmale complex is of high quality and satisfies all the user requirements. The final quadrilateral mesh is generated from the MorseSmale complex by computing a globally smooth parametrization. Here we additionally introduce edge constraints to preserve user specified feature lines accurately.
The Discrete Cosine Transform (DCT): Theory and Application”. Department of electrical & computing engineering
, 2003
"... This document is intended to be tutorial in nature. No prior knowledge of image processing concepts is ECE 802 – 602: Information Theory and Coding Seminar 1 – The Discrete Cosine Transform: Theory and Application Transform coding constitutes an integral component of contemporary image/video process ..."
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Cited by 36 (0 self)
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This document is intended to be tutorial in nature. No prior knowledge of image processing concepts is ECE 802 – 602: Information Theory and Coding Seminar 1 – The Discrete Cosine Transform: Theory and Application Transform coding constitutes an integral component of contemporary image/video processing applications. Transform coding relies on the premise that pixels in an image exhibit a certain
A scaled gradient projection method for constrained image deblurring
 INVERSE PROBLEMS 25
, 2009
"... A class of scaled gradient projection methods for optimization problems with simple constraints is considered. These iterative algorithms can be useful in variational approaches to image deblurring that lead to minimize convex nonlinear functions subject to nonnegativity constraints and, in some ca ..."
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Cited by 35 (9 self)
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A class of scaled gradient projection methods for optimization problems with simple constraints is considered. These iterative algorithms can be useful in variational approaches to image deblurring that lead to minimize convex nonlinear functions subject to nonnegativity constraints and, in some cases, to an additional flux conservation constraint. A special gradient projection method is introduced that exploits effective scaling strategies and steplength updating rules, appropriately designed for improving the convergence rate. We give convergence results for this scheme and we evaluate its effectiveness by means of an extensive computational study on the minimization problems arising from the maximum likelihood approach to image deblurring. Comparisons with the standard expectation maximization algorithm and with other iterative regularization schemes are also reported to show the computational gain provided by the proposed method.
Robust localization using an omnidirectional appearancebased subspace model of environment
 Robotics and Autonomous Systems
, 2003
"... Appearancebased visual learning and recognition techniques that are based on models derived from a training set of 2D images are being widely used in computer vision applications. In robotics, they have received most attention in visual servoing and navigation. In this paper we discuss a framework ..."
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Cited by 32 (1 self)
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Appearancebased visual learning and recognition techniques that are based on models derived from a training set of 2D images are being widely used in computer vision applications. In robotics, they have received most attention in visual servoing and navigation. In this paper we discuss a framework for visual selflocalization of mobile robots using a parametric model built from panoramic snapshots of the environment. In particular, we propose solutions to the problems related to robustness against occlusions and invariance to the rotation of the sensor. Our principal contribution is an “eigenspace of spinningimages”, i.e., a model of the environment which successfully exploits some of the specific properties of panoramic images in order to efficiently calculate the optimal subspace in terms of principal components analysis (PCA) of a set of training snapshots without actually decomposing the covariance matrix. By integrating a robust recoverandselect algorithm for the computation of image parameters we achieve reliable localization even in the case when the input images are partly occluded or noisy. In this way, the robot is capable of localizing itself in realistic environments.
Continuous Multiclass Labeling Approaches and Algorithms
 SIAM J. Imag. Sci
, 2011
"... We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the originally combinatorial problem. We focus on two specific r ..."
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Cited by 27 (4 self)
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We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the originally combinatorial problem. We focus on two specific relaxations that differ in flexibility and simplicity – one can be used to tightly relax any metric interaction potential, while the other one only covers Euclidean metrics but requires less computational effort. For solving the nonsmooth discretized problem, we propose a globally convergent DouglasRachford scheme, and show that a sequence of dual iterates can be recovered in order to provide a posteriori optimality bounds. In a quantitative comparison to two other firstorder methods, the approach shows competitive performance on synthetical and realworld images. By combining the method with an improved binarization technique for nonstandard potentials, we were able to routinely recover discrete solutions within 1%–5 % of the global optimum for the combinatorial image labeling problem. 1 Problem Formulation The multiclass image labeling problem consists in finding, for each pixel x in the image domain Ω ⊆ Rd, a label `(x) ∈ {1,..., l} which assigns one of l class labels to x so that the labeling function ` adheres to some local data fidelity as well as nonlocal spatial coherency constraints. This problem class occurs in many applications, such as segmentation, multiview reconstruction, stitching, and inpainting [PCF06]. We consider the variational formulation inf `:Ω→{1,...,l} f(`), f(`):= Ω s(x, `(x))dx ︸ ︷ ︷ ︸ data term + J(`). ︸ ︷ ︷ ︸ regularizer
Cosine Transform Preconditioners for High Resolution Image Reconstruction
, 2000
"... This paper studies the application of preconditioned conjugate gradient methods in high resolution image reconstruction problems. We consider reconstructing high resolution images from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The resulting blurring matrices ..."
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Cited by 20 (8 self)
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This paper studies the application of preconditioned conjugate gradient methods in high resolution image reconstruction problems. We consider reconstructing high resolution images from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The resulting blurring matrices are spatially variant. The classical Tikhonov regularization and the Neumann boundary condition are used in the reconstruction process. The preconditioners are derived by taking the cosine transform approximation of the blurring matrices. We prove that when the L 2 or H 1 norm regularization functional is used, the spectra of the preconditioned normal systems are clustered around 1 for sufficiently small subpixel displacement errors. Conjugate gradient methods will hence converge very quickly when applied to solving these preconditioned normal equations. Numerical examples are given to illustrate the fast convergence. 1 Introduction Due to hardware limitations, imaging systems often provide...
Data Analysis and Representation on a General Domain using Eigenfunctions of Laplacian
, 2007
"... We propose a new method to analyze and represent data recorded on a domain of general shape in R d by computing the eigenfunctions of Laplacian defined over there and expanding the data into these eigenfunctions. Instead of directly solving the eigenvalue problem on such a domain via the Helmholtz ..."
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Cited by 20 (1 self)
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We propose a new method to analyze and represent data recorded on a domain of general shape in R d by computing the eigenfunctions of Laplacian defined over there and expanding the data into these eigenfunctions. Instead of directly solving the eigenvalue problem on such a domain via the Helmholtz equation (which can be quite complicated and costly), we find the integral operator commuting with the Laplacian and diagonalize that operator. Although our eigenfunctions satisfy neither the Dirichlet nor the Neumann boundary condition, computing our eigenfunctions via the integral operator is simple and has a potential to utilize modern fast algorithms to accelerate the computation. We also show that our method is better suited for small sample data than the KarhunenLoève Transform/Principal Component Analysis. In fact, our eigenfunctions depend only on the shape of the domain, not the statistics of the data. As a further application, we demonstrate the use of our Laplacian eigenfunctions for solving the heat equation on a complicated domain.
Feature Analysis for Automatic Speechreading
 In Proc. Int’l Workshop Multimedia Signal Processing
, 2001
"... AudioVisual Automatic Speech Recognition systems use visual information to enhance ASR systems in clean and noisy environments. This paper compares of a number of different visual feature extraction methods. When performing visual speech recognition the visual feature vector requires a base level o ..."
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Cited by 17 (2 self)
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AudioVisual Automatic Speech Recognition systems use visual information to enhance ASR systems in clean and noisy environments. This paper compares of a number of different visual feature extraction methods. When performing visual speech recognition the visual feature vector requires a base level of detail for optimum recognition. Geometric feature extraction provides lower recognition than pixel based methods due to the loss of characteristic speech information such as ftuck, protrusion etc. Downsampling of images reduces visual recognition scores due to the loss of detail in the images. Also, the role of dynamic features was investigated for improved recognition. It was observed that the use of static features only, provided higher recognition scores than with a feature vector of the same length containing both static and dynamic features. These results illustrate the need for a base level of detail in the feature vector for improved visual recognition scores.