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Fast approximate energy minimization via graph cuts

by Yuri Boykov, Olga Veksler, Ramin Zabih - IEEE Transactions on Pattern Analysis and Machine Intelligence , 2001
"... In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when v ..."
Abstract - Cited by 2120 (61 self) - Add to MetaCart
In this paper we address the problem of minimizing a large class of energy functions that occur in early vision. The major restriction is that the energy function’s smoothness term must only involve pairs of pixels. We propose two algorithms that use graph cuts to compute a local minimum even when

What energy functions can be minimized via graph cuts?

by Vladimir Kolmogorov, Ramin Zabih - IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE , 2004
"... In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are co ..."
Abstract - Cited by 1047 (23 self) - Add to MetaCart
that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who

EIGENVALUES AND EXPANDERS

by N. Alon - COMBINATORICA , 1986
"... Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander ifandonly if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian mani ..."
Abstract - Cited by 400 (20 self) - Add to MetaCart
Linear expanders have numerous applications to theoretical computer science. Here we show that a regular bipartite graph is an expander ifandonly if the second largest eigenvalue of its adjacency matrix is well separated from the first. This result, which has an analytic analogue for Riemannian

Expander Graphs and their Applications

by Nati Linial, Avi Wigderson , 2003
"... ..."
Abstract - Cited by 359 (5 self) - Add to MetaCart
Abstract not found

Finding community structure in networks using the eigenvectors of matrices

by M. E. J. Newman , 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
Abstract - Cited by 502 (0 self) - Add to MetaCart
divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a

Distortion invariant object recognition in the dynamic link architecture

by Martin Lades, Jan C. Vorbrüggen, Joachim Buhmann, Christoph v. d. Malsburg, Rolf P. Würtz, Wolfgang Konen - IEEE TRANSACTIONS ON COMPUTERS , 1993
"... We present an object recognition system based on the Dynamic Link Architecture, which is an extension to classical Artificial Neural Networks. The Dynamic Link Architecture ex-ploits correlations in the fine-scale temporal structure of cellular signals in order to group neurons dynamically into hig ..."
Abstract - Cited by 637 (80 self) - Add to MetaCart
are represented by sparse graphs, whose vertices are labeled by a multi-resolution description in terms of a local power spectrum, and whose edges are labeled by geometrical distance vectors. Object recognition can be formulated as elastic graph matching, which is performed here by stochastic optimization of a

Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features

by Wolfgang Kabsch, Christian Sander , 1983
"... For a successful analysis of the relation between amino acid sequence and protein structure, an unambiguous and physically meaningful definition of secondary structure is essential. We have developed a set of simple and physically motivated criteria for secondary structure, programmed as a pattern-r ..."
Abstract - Cited by 2096 (5 self) - Add to MetaCart
. ” Geometric structure is defined in terms of the concepts torsion and curvature of differential geometry. Local chain “chirality ” is the torsional handedness of four consecutive Ca positions and is positive for right-handed helices and negative for ideal twisted @-sheets. Curved pieces are defined as “bends

Tabu Search -- Part I

by Fred Glover , 1989
"... This paper presents the fundamental principles underlying tabu search as a strategy for combinatorial optimization problems. Tabu search has achieved impressive practical successes in applications ranging from scheduling and computer channel balancing to cluster analysis and space planning, and more ..."
Abstract - Cited by 680 (11 self) - Add to MetaCart
, and more recently has demonstrated its value in treating classical problems such as the traveling salesman and graph coloring problems. Nevertheless, the approach is still in its infancy, and a good deal remains to be discovered about its most effective forms of implementation and about the range

Ecology of the family as a context for human development: Research perspectives.

by Urie Bronfenbrenner , Josephine Arastah , Mavis Hetherington , Richard Lerner , Jeylan T Mortimer , Joseph H Pleck , Lea Pulkinnen , Michael Rutter , Klaus Schneewind , Diana Slaughter - Developmental Psychology, , 1986
"... This review collates and examines critically a theoretically convergent but widely dispersed body of research on the influence of external environments on the functioning of families as contexts of human development. Investigations falling within this expanding domain include studies of the interac ..."
Abstract - Cited by 518 (0 self) - Add to MetaCart
This review collates and examines critically a theoretically convergent but widely dispersed body of research on the influence of external environments on the functioning of families as contexts of human development. Investigations falling within this expanding domain include studies

Loopy belief propagation for approximate inference: An empirical study. In:

by Kevin P Murphy , Yair Weiss , Michael I Jordan - Proceedings of Uncertainty in AI, , 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" -the use of Pearl's polytree algorithm in a Bayesian network with loops -can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon-limit performanc ..."
Abstract - Cited by 676 (15 self) - Add to MetaCart
with loops (undirected cycles). The algorithm is an exact inference algorithm for singly connected networks -the beliefs converge to the cor rect marginals in a number of iterations equal to the diameter of the graph.1 However, as Pearl noted, the same algorithm will not give the correct beliefs for mul
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