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26
Efficient multiscale regularization with applications to the computation of optical flow
 IEEE Trans. Image Process
, 1994
"... AbsfruetA new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial d ..."
Abstract

Cited by 97 (33 self)
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AbsfruetA new approach to regularization methods for image processing is introduced and developed using as a vehicle the problem of computing dense optical flow fields in an image sequence. Standard formulations of this problem require the computationally intensive solution of an elliptic partial differential equation that arises from the often used “smoothness constraint” ’yl”. regularization. The interpretation of the smoothness constraint is utilized as a “fractal prior ” to motivate regularization based on a recently introduced class of multiscale stochastic models. The solution of the new problem formulation is computed with an efficient multiscale algorithm. Experiments on several image sequences demonstrate the substantial computational savings that can be achieved due to the fact that the algorithm is noniterative and in fact has a per pixel computational complexity that is independent of image size. The new approach also has a number of other important advantages. Specifically, multiresolution flow field estimates are available, allowing great flexibility in dealing with the tradeoff between resolution and accuracy. Multiscale error covariance information is also available, which is of considerable use in assessing the accuracy of the estimates. In particular, these error statistics can be used as the basis for a rational procedure for determining the spatiallyvarying optimal reconstruction resolution. Furthermore, if there are compelling reasons to insist upon a standard smoothness constraint, our algorithm provides an excellent initialization for the iterative algorithms associated with the smoothness constraint problem formulation. Finally, the usefulness of our approach should extend to a wide variety of illposed inverse problems in which variational techniques seeking a “smooth ” solution are generally Used. I.
Kolmogorov Complexity and Chaotic Phenomena
 International Journal of Engineering Science
, 2002
"... Born about three decades ago, Kolmogorov Complexity Theory (KC) led to important discoveries that, in particular, give a new understanding of the fundamental problem: interrelations between classical continuum mathematics and reality (physics, biology, engineering sciences, . . . ). ..."
Abstract

Cited by 8 (7 self)
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Born about three decades ago, Kolmogorov Complexity Theory (KC) led to important discoveries that, in particular, give a new understanding of the fundamental problem: interrelations between classical continuum mathematics and reality (physics, biology, engineering sciences, . . . ).
Quantitative estimates of unique continuation for parabolic equations, determination of unknown timevarying boundaries and optimal stability estimates
, 2007
"... ..."
Lipschitz stability of a nonstandard problem for the nonstationary transport equation via Carleman estimate, Inverse Problems
"... The Lipschitz stability estimate for the nonstationary singlespeed transport equation with the lateral boundary data is obtained. The method of Carleman estimates is used. Uniqueness of the solution follows. 1. ..."
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Cited by 4 (3 self)
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The Lipschitz stability estimate for the nonstationary singlespeed transport equation with the lateral boundary data is obtained. The method of Carleman estimates is used. Uniqueness of the solution follows. 1.
Stability In Line Unique Continuation Of Harmonic Functions: General Dimensions
 J. INVERSE AND ILLPOSED PROBLEMS
, 1998
"... In this paper, we discuss unique continuation for harmonic functions on lines in R n (n 3) which is an intermediate property between the classical unique continuation for a harmonic function and the analytic continuation for a holomorphic function. We obtain a conditional stability estimate. ..."
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Cited by 4 (4 self)
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In this paper, we discuss unique continuation for harmonic functions on lines in R n (n 3) which is an intermediate property between the classical unique continuation for a harmonic function and the analytic continuation for a holomorphic function. We obtain a conditional stability estimate.
Injectivity of the spherical means operator
, 2002
"... Let S be a surface in R n which divides the space into two connected components D1 and D2. Let f ∈ C0(R n) be some realvalued compactly supported function with supp f ⊂ ..."
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Cited by 3 (0 self)
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Let S be a surface in R n which divides the space into two connected components D1 and D2. Let f ∈ C0(R n) be some realvalued compactly supported function with supp f ⊂
Continuous Dependence of Nonnegative Solutions of the Heat Equation on Noncharacteristic Cauchy Data
, 1994
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Conditional stability for illposed elliptic Cauchy problems : the case
 of C 1,1 domains (part I). Rapport INRIA n6585
, 2008
"... apport de recherche ..."
Lipschitz stability for a coefficient inverse problem for the nonstationary transport equation via Carleman estimate, Http://www.ma.utexas.edu/mp_arc/, preprint number
"... The Lipschitz stability estimate for a coefficient inverse problem for the nonstationary singlespeed transport equation with the lateral boundary data is obtained. The method of Carleman estimates is used. Uniqueness of the solution follows. 1. ..."
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Cited by 1 (1 self)
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The Lipschitz stability estimate for a coefficient inverse problem for the nonstationary singlespeed transport equation with the lateral boundary data is obtained. The method of Carleman estimates is used. Uniqueness of the solution follows. 1.