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1.
Remco Duits Michael Felsberg Gösta Granlund Bart ter Haar Romeny 《International Journal of Computer Vision》2007,72(1):79-102
Inspired by the early visual system of many mammalians we consider the construction of-and reconstruction from- an orientation
score
as a local orientation representation of an image,
. The mapping
is a wavelet transform
corresponding to a reducible representation of the Euclidean motion group onto
and oriented wavelet
. This wavelet transform is a special case of a recently developed generalization of the standard wavelet theory and has the
practical advantage over the usual wavelet approaches in image analysis (constructed by irreducible representations of the
similitude group) that it allows a stable reconstruction from one (single scale) orientation score. Since our wavelet transform
is a unitary mapping with stable inverse, we directly relate operations on orientation scores to operations on images in a
robust manner.
Furthermore, by geometrical examination of the Euclidean motion group
, which is the domain of our orientation scores, we deduce that an operator Φ on orientation scores must be left invariant
to ensure that the corresponding operator
on images is Euclidean invariant. As an example we consider all linear second order left invariant evolutions on orientation
scores corresponding to stochastic processes on G. As an application we detect elongated structures in (medical) images and automatically close the gaps between them.
Finally, we consider robust orientation estimates by means of channel representations, where we combine robust orientation
estimation and learning of wavelets resulting in an auto-associative processing of orientation features. Here linear averaging
of the channel representation is equivalent to robust orientation estimation and an adaptation of the wavelet to the statistics
of the considered image class leads to an auto-associative behavior of the system.
The Netherlands Organization for Scientific Research is gratefully acknowledged for financial support. This work has been
supported by EC Grant IST-2003-004176 COSPAL. 相似文献
2.
Sang-Eon Han 《Journal of Mathematical Imaging and Vision》2008,31(1):1-16
In order to discuss digital topological properties of a digital image (X,k), many recent papers have used the digital fundamental group and several digital topological invariants such as the k-linking number, the k-topological number, and so forth. Owing to some difficulties of an establishment of the multiplicative property of the digital
fundamental group, a k-homotopic thinning method can be essentially used in calculating the digital fundamental group of a digital product with
k-adjacency. More precisely, let
be a simple closed k
i
-curve with l
i
elements in
. For some k-adjacency of the digital product
which is a torus-like set, proceeding with the k-homotopic thinning of
, we obtain its k-homotopic thinning set denoted by DT
k
. Writing an algorithm for calculating the digital fundamental group of
, we investigate the k-fundamental group of
by the use of various properties of a digital covering (Z×Z,p
1×p
2,DT
k
), a strong k-deformation retract, and algebraic topological tools. Finally, we find the pseudo-multiplicative property (contrary to the
multiplicative property) of the digital fundamental group. This property can be used in classifying digital images from the
view points of both digital k-homotopy theory and mathematical morphology.
相似文献
Sang-Eon HanEmail: Email: |
3.
4.
W. Hackbusch 《Computing》2007,80(2):137-168
Usually, the fast evaluation of a convolution integral
requires that the functions f, g are discretised on an equidistant grid in order to apply the fast Fourier transform. Here we discuss the efficient performance
of the convolution in locally refined grids. More precisely, the convolution result is projected into some given locally refined
grid (Galerkin approximation). Under certain conditions, the overall costs are still
where N is the sum of the dimensions of the subspaces containing f, g and the resulting function. 相似文献
5.
6.
We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Our algorithms compute the determinant, characteristic polynomial, Frobenius normal form and Smith normal form of a dense n × n matrix A with integer entries in
and
bit operations; here
denotes the largest entry in absolute value and the exponent adjustment by +o(1) captures additional factors
for positive real constants C1, C2, C3. The bit complexity
results from using the classical cubic matrix multiplication algorithm. Our algorithms are randomized, and we can certify that the output is the determinant of A in a Las Vegas fashion. The second category of problems deals with the setting where the matrix A has elements from an abstract commutative ring, that is, when no divisions in the domain of entries are possible. We present algorithms that deterministically compute the determinant, characteristic polynomial and adjoint of A with n3.2+o(1) and O(n2.697263) ring additions, subtractions and multiplications.To B. David Saunders on the occasion of his 60th birthday 相似文献
7.
Free binary decision diagrams (FBDDs) are graph-based data structures representing Boolean functions with the constraint (additional
to binary decision diagram) that each variable is tested at most once during the computation. The function EARn is the following Boolean function defined for n × n Boolean matrices: EARn(M) = 1 iff the matrix M contains two equal adjacent rows. We prove that each FBDD computing EARn has size at least
and we present a construction of such diagrams of size approximately
. 相似文献
8.
Given a k-uniform hypergraph, the Maximum k -Set Packing problem is to find the maximum disjoint set of edges. We prove that this problem cannot be efficiently approximated to within
a factor of
unless P = NP. This improves the previous hardness of approximation factor of
by Trevisan. This result extends to the problem of k-Dimensional-Matching. 相似文献
9.
Avram Sidi 《Journal of scientific computing》2007,31(3):391-417
Variable transformations for numerical integration have been used for improving the accuracy of the trapezoidal rule. Specifically,
one first transforms the integral via a variable transformation that maps [0,1] to itself, and then approximates the resulting transformed integral by the trapezoidal rule. In this work, we propose a new class of symmetric and nonsymmetric variable transformations which
we denote , where r and s are positive scalars assigned by the user. A simple representative of this class is . We show that, in case , or but has algebraic (endpoint) singularities at x = 0 and/or x = 1, the trapezoidal rule on the transformed integral produces exceptionally high accuracies for special values of r and s. In particular, when and we employ , the error in the approximation is (i) O(h
r
) for arbitrary r and (ii) O(h
2r
) if r is a positive odd integer at least 3, h being the integration step. We illustrate the use of these transformations and the accompanying theory with numerical examples.
相似文献
10.
11.
Emanuele Viola 《Computational Complexity》2005,13(3-4):147-188
We study the complexity of constructing pseudorandom generators (PRGs) from hard functions, focussing on constant-depth circuits. We show that, starting from a function
computable in alternating time O(l) with O(1) alternations that is hard on average (i.e. there is a constant
such that every circuit of size
fails to compute f on at least a 1/poly(l) fraction of inputs) we can construct a
computable by DLOGTIME-uniform constant-depth circuits of size polynomial in n. Such a PRG implies
under DLOGTIME-uniformity. On the negative side, we prove that starting from a worst-case hard function
(i.e. there is a constant
such that every circuit of size
fails to compute f on some input) for every positive constant
there is no black-box construction of a
computable by constant-depth circuits of size polynomial in n. We also study worst-case hardness amplification, which is the related problem of producing an average-case hard function starting from a worst-case hard one. In particular, we deduce that there is no blackbox worst-case hardness amplification within the polynomial time hierarchy. These negative results are obtained by showing that polynomialsize constant-depth circuits cannot compute good extractors and listdecodable codes. 相似文献
12.
R. F. Streater 《Open Systems & Information Dynamics》2004,11(4):359-375
Let H0 be a selfadjoint operator such that Tr
is of trace class for some
, and let
denote the set of ε-bounded forms, i.e.,
for some
0 $$" align="middle" border="0">
. Let χ := Span
. Let
denote the underlying set of the quantum information manifold of states of the form
. We show that if Tr
,
Presented at the 36th Symposium on Mathematical Physics, ‘Open Systems & Quantum Information’, Toruń, Poland, June 9-12, 2004. 相似文献
1. | the map Φ,
| |
2. | The Orlicz space defined by Φ is the tangent space of at ρ0; its affine structure is defined by the (+1)-connection of Amari | |
3. | The subset of a ‘hood of ρ0, consisting of p-nearby states (those obeying for some 1$$" align="middle" border="0"> ) admits a flat affine connection known as the (-1) connection, and the span of this set is part of the cotangent space of | |
4. | These dual structures extend to the completions in the Luxemburg norms. |
13.
14.
Every Linear Threshold Function has a Low-Weight Approximator 总被引:1,自引:1,他引:0
Rocco A. Servedio 《Computational Complexity》2007,16(2):180-209
15.
Christian Ronse 《Journal of Mathematical Imaging and Vision》2006,26(1-2):185-216
Flat morphological operators, also called stack filters, are the natural extension of increasing set operators to grey-level images. The latter are usually modeled as functions
, where T is a closed subset of
(for instance,
or [a,b]).
We give here a general theory of flat morphological operators for functions defined on a space E of points and taking their values in an arbitrary complete lattice V of values. Several examples of such lattices have been considered in the litterature, and we illustrate our therory with
them. Our approach relies on the usual techniques of thresholding and stacking. Some of the usual properties of flat operators
for numerical functions extend unconditionally to this general framework. Others do not, unless the lattice V is completely distributive.
This paper is dedicated to Henk Heijmans, who made major contributions to the theory of Mathematical Morphology, until a health
accident in March 2004 ended his scientific career.
Christian Ronse was born in 1954. He studied pure mathematics at the Université Libre de Bruxelles (Licence, 1976) and the University of
Oxford (M.Sc., 1977; Ph.D., 1979), specializing in group theory. Between 1979 and 1991 he was Member of Scientific Staff at
the Philips Research Laboratory Brussels, where he conducted research on combinatorics of switching circuits, feedback shift
registers, discrete geometry, image processing, and mathematical morphology. During the academic year 1991–1992 he worked
at the Université Bordeaux-1, where he obtained his Habilitation diploma. Since October 1992, he has been Professor of Computer
Science at the Université Louis Pasteur, Strasbourg (promotion to First Class Professorship in 2001), where he contributed
to the development of a research group on image analysis, and the teaching of image processing to students at various levels.
His scientific interests include imaging theory, mathematical morphology, image segmentation and medical imaging. 相似文献
16.
17.
Eric Allender Anna Bernasconi Carsten Damm Joachim von zur Gathen Michael Saks Igor Shparlinski 《Computational Complexity》2003,12(1-2):23-47
We study various combinatorial complexity measures of
Boolean functions related to some natural arithmetic problems about
binary polynomials, that is, polynomials over
.
In particular, we consider
the Boolean function deciding whether a given polynomial over
is squarefree. We obtain an exponential lower bound on the size of a
decision tree for this function, and derive an asymptotic formula, having
a linear main term, for its average sensitivity. This allows us to estimate
other complexity characteristics such as the formula size, the average decision
tree depth and the degrees of exact and approximative polynomial
representations of this function. Finally, using a different method, we
show that testing squarefreeness and irreducibility of polynomials over
cannot be done in
for any odd prime p. Similar results are
obtained for deciding coprimality of two polynomials over
as well. 相似文献
18.
Representation of the Fourier Transform by Fourier Series 总被引:1,自引:0,他引:1
Artyom M. Grigoryan 《Journal of Mathematical Imaging and Vision》2006,25(1):87-105
The analysis of the mathematical structure of the integral Fourier transform shows that the transform can be split and represented
by certain sets of frequencies as coefficients of Fourier series of periodic functions in the interval
. In this paper we describe such periodic functions for the one- and two-dimensional Fourier transforms. The approximation
of the inverse Fourier transform by periodic functions is described. The application of the new representation is considered
for the discrete Fourier transform, when the transform is split into a set of short and separable 1-D transforms, and the
discrete signal is represented as a set of short signals. Properties of such representation, which is called the paired representation,
are considered and the basis paired functions are described. An effective application of new forms of representation of a
two-dimensional image by splitting-signals is described for image enhancement. It is shown that by processing only one splitting-signal,
one can achieve an enhancement that may exceed results of traditional methods of image enhancement. 相似文献
19.
Agent Communication Languages (ACLs) have been developed to provide a way for agents to communicate with each other supporting
cooperation in Multi-Agent Systems (MAS). In the past few years many ACLs have been proposed for MAS and new standards are
emerging such as the ACL developed by the Foundation for Intelligent Physical Agents (FIPA). Despite these efforts, an important
issue in the research on ACLs is still open and concerns how these languages should deal with failures of agents in asynchronous MAS. The Fault Tolerant Agent Communication Language (
-
) presented in this paper addresses this issue dealing with crash failures of agents.
-
provides high-level communication primitives which support a fault-tolerant anonymous interaction protocol designed for open
MAS. We present a formal semantics for
-
and a formal specification of the underlying agent architecture. This formal framework allows us to prove that the ACL satisfies
a set of well defined knowledge-level programming requirements. To illustrate the language features we show how
-
can be effectively used to write high-level executable specifications of fault tolerant protocols, such as the Contract Net
one. 相似文献
20.
Abstract We obtain a multivariate extension of a classical result of Schoenberg on cardinal spline interpolation. Specifically, we
prove the existence of a unique function in
, polyharmonic of order p on each strip
,
, and periodic in its last n variables, whose restriction to the parallel hyperplanes
,
, coincides with a prescribed sequence of n-variate periodic data functions satisfying a growth condition in
. The constructive proof is based on separation of variables and on Micchelli’s theory of univariate cardinal
-splines.
Keywords: cardinal
-splines, polyharmonic functions, multivariable interpolation
Mathematics Subject Classification (2000): 41A05, 41A15, 41A63 相似文献