13019795
Large deformation diffeomorphic metric mapping of fiber orientations
This paper proposes a method to match diffusion tensor magnetic resonance images (DT-MRI) through the large deformation diffeomorphic metric mapping of vector fields, focusing on the fiber orientations, considered as unit vector fields on the image volume. We study a suitable action of diffeomorphisms on such vector fields, and provide an extension of the large deformation diffeomorphic metric-mapping framework to this type of dataset, resulting in optimizing for geodesies on the space of diffeomorphisms connecting two images. Two different distance function of vector fields are considered. Existence of the minimizers under smoothness assumptions on the compared vector fields is proved, and coarse to fine hierarchical strategies are detailed, to reduce both ambiguities and computation load. This is illustrated by numerical experiments on DT-MRI heart and brain images
15180139
Bayesian Segmentation via Asymptotic Partition Functions
Asymptotic approximations to the partition function of Gaussian random fields are derived. Textures are characterized via Gaussian random fields induced by stochastic difference equations determined by finitely supported, stationary, linear difference operators, adjusted to be nonstationary at the boundaries. It is shown that as the scale of the underlying shape increases, the log-normalizer converges to the integral of the log-spectrum of the operator inducing the random field. Fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator-induced random field model. Matrix analysis techniques are proposed for handling textures with variable orientation. Examples of texture parameters estimated from training data via asymptotic maximum-likelihood are shown. Isotropic models involving powers of the Laplacian and directional models involving partial derivative mixtures are explored. Parameters are estimated for mitochondria and actin-myocin complexes in electron micrographs and clutter in forward-looking infrared images. Deformable template models are used to infer the shape of mitochondria in electron micrographs, with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds.
7980241
Segmenting magnetic resonance images via hierarchical mixture modelling
We present a statistically innovative as well as scientifically and practically relevant method for automatically segmenting magnetic resonance images using hierarchical mixture models. Our method is a general tool for automated cortical analysis which promises to contribute substantially to the science of neuropsychiatry. We demonstrate that our method has advantages over competing approaches on a magnetic resonance brain imagery segmentation task.
6192829
Clutter invariant ATR
One of the central problems in automated target recognition is to accommodate the infinite variety of clutter in real military environments. The principle focus of our paper is on the construction of metric spaces where the metric measures the distance between objects of interest invariant to the infinite variety of clutter. Such metrics are formulated using second-order random field models. Our results indicate that this approach significantly improves detection/classification rates of targets in clutter.
14209020
Volumetric transformation of brain anatomy
Presents diffeomorphic transformations of three-dimensional (3-D) anatomical image data of the macaque occipital lobe and whole brain cryosection imagery and of deep brain structures in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner, accommodating both global and local anatomical detail. The initial low-dimensional registration is accomplished by constraining the transformation to be in a low-dimensional basis. The basis is defined by the Green's function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The high-dimensional large deformations are vector fields generated via the mismatch between the template and target-image volumes constrained to be the solution of a Navier-Stokes fluid model. As part of this procedure, the Jacobian of the transformation is tracked, insuring the generation of diffeomorphisms. It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration.
5537969
Individualizing Anatomical Atlases of the Head
This paper presents diffeomorphic transformations of 3D anatomical image data in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner accommodating both global and local anatomical detail. The initial low-dimensional registration is accomplished by constraining the transformation to be in a low-dimensional basis. The basis is defined by the Green's function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The high-dimensional, large-deformation registration is accomplished by minimizing the mismatch between the template (atlas) and target image volumes constrained by solving the Navier Stokes fluid model on a vector field.
28891049
Connected graphs which are not mod sum graphs
Abstract In this paper we prove that no wheel with the exception of W 4 can be a mod sum graph. We also give the unique (up to multiplication by positive integers) mod sum labelling of W 4 . We also prove that the symmetric complete bipartite graph K n . n is not a mod sum graph.
35339559
Two new families of large compound graphs
A question of special interest in graph theory is the design of large graphs. Specifically, we want to find constructions of graphs with order as large as possible for a given degree and diameter D . Two generalizations of two large compound graphs are proposed in this article. Three particular cases of these families of graphs presented here allow us to improve the order for the entries (15, 7), (13, 10), and (15, 10) in the table of the largest known ( , D)-graphs. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(3), 140–146 2006
40582600
Concurrency Among Strangers
Programmers write programs, expressing plans for machines to execute. When composed so that they may cooperate, plans may instead interfere with each other in unanticipated ways. Plan coordination is the art of simultaneously enabling plans to cooperate, while avoiding hazards of destructive plan interference. For sequential computation within a single machine, object programming supports plan coordination well. For concurrent computation, this paper shows how hard it is to use locking to prevent plans from interfering without also destroying their ability to cooperate.
35322596
On the degrees of a strongly vertex-magic graph
Let G=(V,E) be a finite graph, where |V|=n>=2 and |E|=e>=1. A vertex-magic total labeling is a bijection @l from V@?E to the set of consecutive integers {1,2,...,n+e} with the property that for every v@?V, @l(v)+@?"w"@?"N"("v")@l(vw)=h for some constant h. Such a labeling is strong if @l(V)={1,2,...,n}. In this paper, we prove first that the minimum degree of a strongly vertex-magic graph is at least two. Next, we show that if 2e>=10n^2-6n+1, then the minimum degree of a strongly vertex-magic graph is at least three. Further, we obtain upper and lower bounds of any vertex degree in terms of n and e. As a consequence we show that a strongly vertex-magic graph is maximally edge-connected and hamiltonian if the number of edges is large enough. Finally, we prove that semi-regular bipartite graphs are not strongly vertex-magic graphs, and we provide strongly vertex-magic total labeling of certain families of circulant graphs.
24203387
Characterization of eccentric digraphs
The eccentric digraphED(G) of a digraph G represents the binary relation, defined on the vertex set of G, of being 'eccentric'; that is, there is an arc from u to v in ED(G) if and only if v is at maximum distance from u in G. A digraph G is said to be eccentric if there exists a digraph H such that G=ED(H). This paper is devoted to the study of the following two questions: what digraphs are eccentric and when the relation of being eccentric is symmetric. We present a characterization of eccentric digraphs, which in the undirected case says that a graph G is eccentric iff its complement graph G@? is either self-centered of radius two or it is the union of complete graphs. As a consequence, we obtain that all trees except those with diameter 3 are eccentric digraphs. We also determine when ED(G) is symmetric in the cases when G is a graph or a digraph that is not strongly connected.