Results 1  10
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177
Snakes, Shapes, and Gradient Vector Flow
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 1998
"... Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new extern ..."
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Cited by 485 (16 self)
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Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a graylevel or binary edge map derived from the image. It differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation. Using several twodimensional (2D) examples and one threedimensional (3D) example, we show that GVF has a large capture range and is able to move snakes into boundary concavities.
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 128 (1 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Integrable Structure of Conformal Field Theory II. Qoperator and DDV equation
, 1996
"... This paper is a direct continuation of [1] where we begun the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators Q \Sigma () which act in highest weight Virasoro module and commute for different values of the parameter . These operators appear ..."
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Cited by 92 (14 self)
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This paper is a direct continuation of [1] where we begun the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators Q \Sigma () which act in highest weight Virasoro module and commute for different values of the parameter . These operators appear to be the CFT analogs of the Q  matrix of Baxter [2], in particular they satisfy famous Baxter's T \Gamma Q equation. We also show that under natural assumptions about analytic properties of the operators Q() as the functions of the Baxter's relation allows one to derive the nonlinear integral equations of Destride Vega (DDV) [3] for the eigenvalues of the Qoperators. We then use the DDV equation to obtain the asymptotic expansions of the Q  operators at large ; it is remarkable that unlike the expansions of the T operators of [1], the asymptotic series for Q() contains the "dual" nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the ...
Computational anatomy and functional architecture of striate cortex: a spatial mapping approach to perceptual coding
 Vision Research
, 1980
"... AbstractThe spatial inhomogeneity of the retinostriate syslem is summarized by the vector cortical magnification factor. The logarithm of retinal eccentricity provides a good fit to the integrated cortical magnification factor. Under the assumption that the cortical map is analytic (conformal), th ..."
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Cited by 82 (5 self)
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AbstractThe spatial inhomogeneity of the retinostriate syslem is summarized by the vector cortical magnification factor. The logarithm of retinal eccentricity provides a good fit to the integrated cortical magnification factor. Under the assumption that the cortical map is analytic (conformal), this implies that a complex logarithmic function of retinal coordinates describes the twodimensional structure of the cortical representation of a visual stimulus. This hypothesis is in good agreement with the measured global structure of rhesus, squirrel, and owl monkey retinostriate mappings, as well as that of the upper visual field of the cat. The geometric structure of the local hypercolumnar unit of striate cortex may also be characterized in terms of the complex Logarithmic mapping: thus. the retinocortical system may be thought of as a concatenated cornplex logarithmic mapping. A simple developmental mechanism is capable of constructing a map of this form, and the general mathematical properties of conformal mappings allow some Insight into the nature of the minimal coding requirements which must be specified to encode a neural map. Complex logarithmic mapping yields a cortical "Gestalt " which is pseudoinvariant to size, rotation. and projection scaling: these symmetries. for a given fixation point. result in a linear shift of an invariant
Convergent Multiplicative Processes Repelled from Zero
 Power Laws and Truncated Power Laws, Journal de Physique I France
, 1997
"... Levy and Solomon have found that random multiplicative processes wt = λ1λ2...λt (with λj> 0) lead, in the presence of a boundary constraint, to a distribution P(wt) in the form of a power law w −(1+µ) t. We provide a simple exact physically intuitive derivation of this result based on a random walk ..."
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Cited by 47 (11 self)
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Levy and Solomon have found that random multiplicative processes wt = λ1λ2...λt (with λj> 0) lead, in the presence of a boundary constraint, to a distribution P(wt) in the form of a power law w −(1+µ) t. We provide a simple exact physically intuitive derivation of this result based on a random walk analogy and show the following: 1) the result applies to the asymptotic (t → ∞) distribution of wt and should be distinguished from the central limit theorem which is a statement on the asymptotic distribution of the reduced variable 1 √ (log wt − 〈log wt〉); 2) the two necessary and sufficient conditions for P(wt) t to be a power law are that 〈log λj 〉 < 0 (corresponding to a drift wt → 0) and that wt not be allowed to become too small. We discuss several models, previously thought unrelated, showing the common underlying mechanism for the generation of power laws by multiplicative processes: the variable log wt
Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model
 Geophysics
, 1999
"... and verification in a physical scale model ..."
The scale representation
 IEEE Transactions on Signal Processing
, 1993
"... scaleable automated quality assurance technique for semantic ..."
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Cited by 39 (3 self)
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scaleable automated quality assurance technique for semantic
A normal distribution for tensorvalued random variables: Applications to diffusion tensor MRI
 IEEE Trans. Med. Imag
, 2003
"... Abstract—Diffusion tensor magnetic resonance imaging (DTMRI) provides a statistical estimate of a symmetric, secondorder diffusion tensor of water, , in each voxel within an imaging volume. We propose a new normal distribution, ( ) exp ( 1 2: :), which describes the variability of in an ideal DTM ..."
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Cited by 30 (3 self)
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Abstract—Diffusion tensor magnetic resonance imaging (DTMRI) provides a statistical estimate of a symmetric, secondorder diffusion tensor of water, , in each voxel within an imaging volume. We propose a new normal distribution, ( ) exp ( 1 2: :), which describes the variability of in an ideal DTMRI experiment. The scalar invariant,: : , is the contraction of a positive definite symmetric, fourthorder precision tensor, , and. A correspondence is established between: : and the elastic strain energy density function in continuum mechanics—specifically between and the secondorder infinitesimal strain tensor, and between and the fourthorder tensor of elastic coefficients. We show that can be further classified according to different classical elastic symmetries (i.e., isotropy, transverse isotropy, orthotropy, planar symmetry, and anisotropy). When is an isotropic fourthorder
A Fingerprint Orientation Model Based on 2D Fourier Expansion (FOMFE) and Its Application to SingularPoint Detection and Fingerprint Indexing
, 2007
"... In this paper, we have proposed a fingerprint orientation model based on 2D Fourier expansions (FOMFE) in the phase plane. The FOMFE does not require prior knowledge of singular points (SPs). It is able to describe the overall ridge topology seamlessly, including the SP regions, even for noisy finge ..."
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Cited by 26 (11 self)
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In this paper, we have proposed a fingerprint orientation model based on 2D Fourier expansions (FOMFE) in the phase plane. The FOMFE does not require prior knowledge of singular points (SPs). It is able to describe the overall ridge topology seamlessly, including the SP regions, even for noisy fingerprints. Our statistical experiments on a public database show that the proposed FOMFE can significantly improve the accuracy of fingerprint feature extraction and thus that of fingerprint matching. Moreover, the FOMFE has a lowcomputational cost and can work very efficiently on large fingerprint databases. The FOMFE provides a comprehensive description for orientation features, which has enabled its beneficial use in featurerelated applications such as fingerprint indexing. Unlike most indexing schemes using raw orientation data, we exploit FOMFE model coefficients to generate the feature vector. Our indexing experiments show remarkable results using different fingerprint databases.
Constrained Motion Control Using Vector Potential Fields
, 2000
"... This paper discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and wellbehaved path to a desired target. The proposed concept of navigation control along with the tools necessary for its construction achieve this goal ..."
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Cited by 24 (9 self)
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This paper discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and wellbehaved path to a desired target. The proposed concept of navigation control along with the tools necessary for its construction achieve this goal. The most significant tool is the artificial vector potential field which shows a better ability to steer motion than does a scalar potential field. The synthesis procedure emphasizes flexibility so that the effort needed to modify the control is commensurate with the change in the geometry of the workspace. Theoretical development along with simulation results are provided.