Results 1  10
of
45
Unsupervised, informationtheoretic, adaptive image filtering for image restoration
 IEEE TRANS. PAMI
, 2006
"... Image restoration is an important and widely studied problem in computer vision and image processing. Various image filtering strategies have been effective, but invariably make strong assumptions about the properties of the signal and/or degradation. Hence, these methods lack the generality to be e ..."
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Cited by 53 (3 self)
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Image restoration is an important and widely studied problem in computer vision and image processing. Various image filtering strategies have been effective, but invariably make strong assumptions about the properties of the signal and/or degradation. Hence, these methods lack the generality to be easily applied to new applications or diverse image collections. This paper describes a novel unsupervised, informationtheoretic, adaptive filter (UINTA) that improves the predictability of pixel intensities from their neighborhoods by decreasing their joint entropy. In this way, UINTA automatically discovers the statistical properties of the signal and can thereby restore a wide spectrum of images. The paper describes the formulation to minimize the joint entropy measure and presents several important practical considerations in estimating neighborhood statistics. It presents a series of results on both real and synthetic data along with comparisons with current stateoftheart techniques, including novel applications to medical image processing.
Inpainting and the Fundamental Problem of Image Processing
 SIAM News
, 2003
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Shannon sampling and function reconstruction from point values
 BULL. AM. MATH. SOC
, 2004
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Multiscale 3d shape representation and segmentation using spherical wavelets
 Trans. on Medical Imaging
, 2006
"... Abstract—This paper presents a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform. This work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation ..."
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Cited by 28 (3 self)
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Abstract—This paper presents a novel multiscale shape representation and segmentation algorithm based on the spherical wavelet transform. This work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation and shape analysis of deep brain structures, such as the caudate nucleus or the hippocampus. Our proposed shape representation can be optimized to compactly encode shape variations in a population at the needed scale and spatial locations, enabling the construction of more descriptive, nonglobal, nonuniform shape probability priors to be included in the segmentation and shape analysis framework. In particular, this representation addresses the shortcomings of techniques that learn a global shape prior at a single scale of analysis and cannot represent fine, local variations in a population of shapes in the presence of a limited dataset.
Simultaneous Total Variation Image Inpainting and Blind Deconvolution
, 2004
"... We propose a total variation based model for simultaneous image inpainting and blind deconvolution. ..."
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Cited by 17 (0 self)
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We propose a total variation based model for simultaneous image inpainting and blind deconvolution.
Advances in Studies and Applications of Centroidal Voronoi Tessellations
"... Centroidal Voronoi tessellations (CVTs) have become a useful tool in many applications ranging from geometric modeling, image and data analysis, and numerical partial differential equations, to problems in physics, astrophysics, chemistry, and biology. In this paper, we briefly review the CVT concep ..."
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Cited by 15 (4 self)
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Centroidal Voronoi tessellations (CVTs) have become a useful tool in many applications ranging from geometric modeling, image and data analysis, and numerical partial differential equations, to problems in physics, astrophysics, chemistry, and biology. In this paper, we briefly review the CVT concept and a few of its generalizations and wellknown properties. We then present an overview of recent advances in both mathematical and computational studies and in practical applications of CVTs. Whenever possible, we point out some outstanding issues that still need investigating.
Theory and Computation of Variational Image Deblurring
, 2005
"... To recover a sharp image from its blurry observation is the problem known as image deblurring. It frequently arises in imaging sciences and technologies, including optical, medical, and astronomical applications, and is crucial for allowing to detect important features and patterns such as those of ..."
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Cited by 10 (1 self)
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To recover a sharp image from its blurry observation is the problem known as image deblurring. It frequently arises in imaging sciences and technologies, including optical, medical, and astronomical applications, and is crucial for allowing to detect important features and patterns such as those of a distant planet or some microscopic tissue. Mathematically, image deblurring is intimately connected to backward diffusion processes (e.g., inverting the heat equation), which are notoriously unstable. As inverse problem solvers, deblurring models therefore crucially depend upon proper regularizers or conditioners that help secure stability, often at the necessary cost of losing certain highfrequency details in the original images. Such regularization techniques can ensure the existence, uniqueness, or stability of deblurred images. The present work follows closely the general framework described in our recent monograph [18], but also contains more updated views and approaches to image deblurring, including, e.g., more discussion on stochastic signals, the Bayesian/Tikhonov approach to Wiener filtering, and the iteratedshrinkage algorithm of Daubechies et al. [30,31] for waveletbased deblurring. The work thus contributes to the development of generic, systematic, and unified frameworks in contemporary image processing.
Mathematical Methods in Medical Image Processing
 BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
, 2006
"... In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial di#erential equations in conjunction with standard si ..."
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Cited by 8 (0 self)
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In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial di#erential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many imageguided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area including image enhancement, registration, and segmentation.
A computational approach to fisher information geometry with applications to image analysis
 Proceedings of the EMMCVPR
, 2005
"... Abstract. We develop a computational approach to nonparametric Fisher information geometry and algorithms to calculate geodesic paths in this geometry. Geodesics are used to quantify divergence of probability density functions and to develop tools of data analysis in information manifolds. The met ..."
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Cited by 8 (0 self)
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Abstract. We develop a computational approach to nonparametric Fisher information geometry and algorithms to calculate geodesic paths in this geometry. Geodesics are used to quantify divergence of probability density functions and to develop tools of data analysis in information manifolds. The methodology developed is applied to several image analysis problems using a representation of textures based on the statistics of multiple spectral components. Histograms of filter responses are viewed as elements of a nonparametric statistical manifold, and local texture patterns are compared using information geometry. Appearancebased object recognition experiments, as well as regionbased image segmentation experiments are carried out to test both the representation and metric. The proposed representation of textures is also applied to the development of a spectral cartoon model of images. 1
Weberized MumfordShah model with BoseEinstein photon noise
 Appl. Math. Optim
, 2006
"... Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber’s Law. The current paper de ..."
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Cited by 7 (3 self)
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Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber’s Law. The current paper develops a new segmentation model based on the integration of both Weber’s Law and the celebrated Mumford–Shah segmentation model (Comm. Pure Applied Math., 42, pp. 577685, 1989). Explained in details are issues concerning why the classical Mumford–Shah model lacks light adaptivity, and why its “weberized ” version can more faithfully reflect human vision’s superior segmentation capability in a variety of illuminance conditions from dawn to dusk. It is also argued that the popular Gaussian noise model is physically inappropriate for the weberization procedure. As a result, the intrinsic thermal noise of photon ensembles is introduced based on Bose and Einstein’s distributions in quantum statistics, which turns out to be compatible with weberization both analytically and computationally. The current paper focuses on both the theory and computation of the weberized Mumford–Shah model with Bose–Einstein noise. In particular, AmbrosioTortorelli’s Γconvergence approximation theory is adapted (Boll. Un. Mat. Ital., 6B, pp. 105123,1992), and stable numerical algorithms are developed for the associated pair of nonlinear EulerLagrange PDEs.