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Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and c ..."
Abstract

Cited by 633 (20 self)
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We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and combines aspects of snakes/balloons and region growing. Indeed the classic snakes/balloons and region growing algorithms can be directly derived from our approach. We provide theoretical analysis of region competition including accuracy of boundary location, criteria for initial conditions, and the relationship to edge detection using filters. It is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on grey level images, color images and texture images. The novel color model allows us to eliminate intensity gradients and shadows, thereby obtaining segmentation based on the albedos of objects. It also helps detect highlight regions. 1 Division of Appli...
Spectral Approximation of Multiplication Operators
 New York J. Math
, 1995
"... . A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of the Hilbert space. For an operator that is not compact such approximations cannot converge in the norm topology on the space of operators. Multiplication operators on spaces of L 2 fun ..."
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Cited by 9 (0 self)
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. A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of the Hilbert space. For an operator that is not compact such approximations cannot converge in the norm topology on the space of operators. Multiplication operators on spaces of L 2 functions are never compact; for them we consider how well the eigenvalues of the matrices approximate the spectrum of the multiplication operator, which is the essential range of the multiplier. The choice of the orthonormal basis strongly affects the convergence. Toeplitz matrices arise when using the Fourier basis of exponentials exp(ik`). We also consider the basis of Legendre polynomials and the basis of Walsh functions. Contents 1. Introduction 75 2. Multiplication operators 78 2.1. Toeplitz Matrices 78 2.2. Matrices Associated to Legendre Polynomials 78 2.3. WalshToeplitz Matrices 79 3. Spectral Convergence 81 4. Spectral convergence for Toeplitz matrices 83 5. Spectral Convergence wit...
Region Competition and its Analysis: A Unified Theory for Image Segmentation
, 1995
"... We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and c ..."
Abstract

Cited by 2 (0 self)
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We present a novel statistical and variational approach to image segmentation based on a new algorithm named region competition. This algorithm is derived by minimizing a generalized Bayes/MDL criterion using the variational principle. The algorithm is guaranteed to converge to a local minimum and combines aspects of snakes/balloons and region growing. Indeed the classic snakes/balloons and region growing algorithms can be directly derived from our approach. We provide theoretical analysis of region competition including accuracy of boundary location, criteria for initial conditions, and the relationship to edge detection using filters. It is straightforward to generalize the algorithm to multiband segmentation and we demonstrate it on grey level images, color images and texture images. The novel color model allows us to eliminate intensity gradients and shadows, thereby obtaining segmentation based on the albedos of objects, and it also helps detect highlight regions. A short version ...
Image Warping for Shape Recovery and Recognition
 Computer Vision and Image Understanding
, 1998
"... We demonstrate that, for a large class of reflectance functions, there is a direct relationship between image warps and the corresponding geometric deformations of the underlying threedimensional objects. This helps explain the hidden geometrical assumptions in object recognition schemes which invo ..."
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Cited by 2 (2 self)
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We demonstrate that, for a large class of reflectance functions, there is a direct relationship between image warps and the corresponding geometric deformations of the underlying threedimensional objects. This helps explain the hidden geometrical assumptions in object recognition schemes which involve twodimensional image warping computed by matching image intensity. In addition, it allows us to propose a novel variant of shape from shading which we call shape from image warping. The idea is that the threedimensional shape of an object is estimated by determining how much the image of the object is warped with respect to the image of a known prototype shape. Therefore detecting the image warp relative to a prototype of known shape allows us to reconstruct the shape of the imaged object. We derive properties of these shape warps and illustrate the results by recovering the shapes of faces. 2 Symbols Roman characters in equations. ~a denotes a vector. p b denotes "square root. ...
Ambiguity Analysis And Joint Inversion Of Potential
"... Given a potential field on a plane, the set of source distributions that could generate the field is easily represented in the Fourier domain. The resulting solutions show a range of variability far larger than expected by many practitioners. This variability can be reduced or eliminated by seeking ..."
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Given a potential field on a plane, the set of source distributions that could generate the field is easily represented in the Fourier domain. The resulting solutions show a range of variability far larger than expected by many practitioners. This variability can be reduced or eliminated by seeking solutions that also minimize a regularizing functional expressing extra information regarding the solution. Unique, smooth solutions are obtained from Tikhonov stabilization using completely regularizing elliptic functionals. Our investigations indicate that novel partial regularization is effective in guiding the search towards nonsmooth solutions resembling a given regional geological style. However, partial regularization using geostatistical and texture based criteria do not necessarily yield unique solutions. Additional partial regularization using limited underground sampling of the source distribution significantly reduces the remaining variability.
A Parallel, FiniteVolume Algorithm for
"... A parallel, finitevolume algorithm has been developed for largeeddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear leastsquare reconstruction, trilinear finiteelement interpolation, Roe fluxdifference splitting, and secondorder MacCormack time marchi ..."
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A parallel, finitevolume algorithm has been developed for largeeddy simulation (LES) of compressible turbulent flows. This algorithm includes piecewise linear leastsquare reconstruction, trilinear finiteelement interpolation, Roe fluxdifference splitting, and secondorder MacCormack time marching. Parallel implementation is done using the messagepassing programming model. In this paper, the numerical algorithm is described. To validate the numerical method for turbulence simulation, LES of fully developed turbulent flow in a square duct is performed for a Reynolds number of 320 based on the average friction velocity and the hydraulic diameter of the duct. Direct numerical simulation (DNS) results are available for this test case, and the accuracy of this algorithm for turbulence simulations can be ascertained by comparing the LES solutions with the DNS results. The effects of grid resolution, upwind numerical dissipation, and subgridscale dissipation on the accuracy of the LES are examined. Comparison with DNS results shows that the standard Roe fluxdifference splitting dissipation adversely affects the accuracy of the turbulence simulation. For accurate turbulence simulations, only 35 percent of the standard Roe fluxdifference splitting dissipation is needed.
A Review Of Infinite Element Methods
, 1999
"... this paper is outlined as follows. In section 2 we present the rigid scattering problem and a derivation of the various IE formulations. Section 3 is devoted to an overview of earlier research work on the IE methodology and more recent contributions are discussed in section 4. The generalization of ..."
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this paper is outlined as follows. In section 2 we present the rigid scattering problem and a derivation of the various IE formulations. Section 3 is devoted to an overview of earlier research work on the IE methodology and more recent contributions are discussed in section 4. The generalization of IE to scatterers of general shape are presented in section 5 and we finish the presentation with conclusions in section 6