Deformable templates using large deformation kinematics
A general automatic approach is presented for accommodating local shape variation when mapping a two-dimensional (2-D) or three-dimensional (3-D) template image into alignment with a topologically similar target image. Local shape variability is accommodated by applying a vector-field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth (globally positive definite Jacobian). Smoothness is guaranteed without specifically penalizing large-magnitude deformations of small subvolumes by constraining the transformation on the basis of a Stokesian limit of the fluid-dynamical Navier-Stokes equations. This differs fundamentally from quadratic penalty methods, such as those based on linearized elasticity or thin-plate splines, in that stress restraining the motion relaxes over time allowing large-magnitude deformations. Kinematic nonlinearities are inherently necessary to maintain continuity of structures during large-magnitude deformations, and are included in all results. After initial global registration, final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem. Automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular. Application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability.

title: Individualizing Anatomical Atlases of the Head
abstract: 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.

title: Bayesian Segmentation via Asymptotic Partition Functions
abstract: 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.

title: Information measures for object recognition accommodating signature variability
abstract: 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.

title: Segmenting magnetic resonance images via hierarchical mixture modelling
abstract: 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.

title: Large deformation diffeomorphic metric mapping of fiber orientations
abstract: 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

title: Capability-Based Financial Instruments
abstract: Every novel cooperative arrangement of mutually suspicious parties interacting electronically -- every smart contract -- effectively requires a new cryptographic protocol. However, if every new contract requires new cryptographic protocol design, our dreams of cryptographically enabled electronic commerce would be unreachable. Cryptographic protocol design is too hard and expensive, given our unlimited need for new contracts.Just as the digital logic gate abstraction allows digital circuit designers to create large analog circuits without doing analog circuit design, we present cryptographic capabilities as an abstraction allowing a similar economy of engineering effort in creating smart contracts. We explain the E system, which embodies these principles, and show a covered-call-option as a smart contract written in a simple security formalism independent of cryptography, but automatically implemented as a cryptographic protocol coordinating five mutually suspicious parties.

title: Consecutive magic graphs
abstract: 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=

title: Group Actions, Homeomorphisms, and Matching: A General Framework
abstract: This paper constructs metrics on the space of images I defined as orbits under group actions G. The groups studied include the finite dimensional matrix groups and their products, as well as the infinite dimensional diffeomorphisms examined in Trouvé (1999, Quaterly of Applied Math.) and Dupuis et al. (1998). Quaterly of Applied Math. Left-invariant metrics are defined on the product G × I thus allowing the generation of transformations of the background geometry as well as the image values. Examples of the application of such metrics are presented for rigid object matching with and without signature variation, curves and volume matching, and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another.

title: On the sum number of wheels
abstract: A graph G=(V,E) is a sum graph if there exists a labelling of the vertices of G with distinct positive integers so that uv∈E if and only if the sum of the labels assigned to u and v is the label of a vertex of G. The sum number of a graph is the minimum number of isolated vertices that, together with the given graph, form a sum graph. Sum graph labellings of wheels have been examined previously by other investigators. The sum number of an n spoked wheel, σ(Wn),n⩾5, has been found to be n when n is odd and n2+2 when n is even; however the proofs of these results are incomplete. In this paper we provide a complete proof and affirm that these previous results are correct.

title: Antimagic Labelings of Generalized Petersen Graphs That Are Plane