7046743
Large deformation diffeomorphic metric mapping of vector fields
This paper proposes a method to match diffusion tensor magnetic resonance images (DT-MRIs) 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 geodesics on the space of diffeomorphisms connecting two images. 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 images.
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
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.
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.
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.
14414468
Information measures for object recognition accommodating signature variability
This paper presents measures characterizing the information content of remote observations of ground scenes imaged via optical and infrared sensors. Object recognition is posed in the context of deformable templates; the special Euclidean group is used to accommodate geometric variation of object pose. Principal component analysis of object signatures is used to represent and efficiently accommodate variation in object signature due to changes in the thermal state of the object surface. Mutual information measures, which are independent of the recognition system, are calculated quantifying both the information gain due to remote observations of the scene and the information loss due to signature variability. Signature model mismatch is quantitatively examined using the Kullback-Leibler divergence. Expressions are derived quadratically approximating the posterior conditional entropy on the orthogonal group for high signal-to-noise ratio. It is demonstrated that quadratic modules accurately characterize the posterior entropy for broad ranges of signal-to-mise ratio. Information gain in multiple-sensor scenarios is quantified, and it is demonstrated that the cost of signature uncertainty for the Comanche series of FLIR images collected by the US Army Night Vision Electronic Sensors Directorate is approximately 0.8 bits with an associated near doubling of mean-squared error uncertainty in pose.
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
5303657
Consecutive magic graphs
Let G be a graph of order n and size e. A vertex-magic total labeling is an assignment of the integers 1,2,...,n+e to the vertices and the edges of G, so that at each vertex, the vertex label and the labels on the edges incident at that vertex, add to a fixed constant, called the magic number of G. Such a labeling is a-vertex consecutive magic if the set of the labels of the vertices is {a+1,a+2,...,a+n}, and is b-edge consecutive magic if the set of labels of the edges is {b+1,b+2,...,b+e}. In this paper we prove that if an a-vertex consecutive magic graph has isolated vertices then the order and the size satisfy (n-1)^2+n^2=(2e+1)^2. Moreover, we show that every tree with even order is not a-vertex consecutive magic and, if a tree of odd order is a-vertex consecutive then a=n-1. Furthermore, we show that every a-vertex consecutive magic graph has minimum degree at least two if a=0, or both 2e>=6n^2-2n+1 and 2a==10n^2-6n+1+4a and 2a=
10536355
Further results on almost Moore digraphs
The nonexistence of digraphs with order equal to the Moore bound Md k d d k for d k has lead to the study of the problem of the existence of almost Moore digraphs namely digraphs with order close to the Moore bound In it was shown that almost Moore digraphs of order Md k degree d diameter k d k contain either no cycle of length k or exactly one such cycle In this paper we shall derive some further necessary conditions for the existence of almost Moore digraphs for degree and diameter greater than As a consequence for diameter and degree d d we show that there are no almost Moore digraphs of order Md with one vertex in a C except the digraphs with every vertex in C
14631873
Paradigm Regained: Abstraction Mechanisms for Access Control
Access control systems must be evaluated in part on how well they enable one to distribute the access rights needed for cooperation, while simultaneously limiting the propagation of rights which would create vulnerabilities. Analysis to date implicitly assumes access is controlled only by manipulating a system’s protection state – the arrangement of the access graph. Because of the limitations of this analysis, capability systems have been ”proven” unable to enforce some basic policies: revocation, confinement, and the *-properties (explained in the text).
28355264
Minimum Diameter of Diregular Digraphs of Degree 2
Etude de certaines relations entre le nombre de sommets, degre et diametre de graphes finis diregulaires. Les trois problemes consideres sont N(d,k), K(u,d) et D(u, k) ou, autrement dit, trouver le nombre maximum possible de sommets etant donnes le degre d et le diametre k; trouver le diametre minimum possible etant donnes le nombre de sommets n et le degre d et trouver le degre minimum possible etant donnes le nombre de sommets n et le diametre k respectivement