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.

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: Clutter invariant ATR
abstract: 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.

title: Information-Theoretic Bounds on Target Recognition Performance Based on Degraded Image Data
abstract: This paper derives bounds on the performance of statistical object recognition systems, wherein an image of a target is observed by a remote sensor. Detection and recognition problems are modeled as composite hypothesis testing problems involving nuisance parameters. We develop information-theoretic performance bounds on target recognition based on statistical models for sensors and data, and examine conditions under which these bounds are tight. In particular, we examine the validity of asymptotic approximations to probability of error in such imaging problems. Problems involving Gaussian, Poisson, and multiplicative noise, and random pixel deletions are considered, as well as least-favorable Gaussian clutter. A sixth application involving compressed sensor image data is considered in some detail. This study provides a systematic and computationally attractive framework for analytically characterizing target recognition performance under complicated, non-Gaussian models and optimizing system parameters.

title: On the existence of positive-definite maximum-likelihood estimates of structured covariance matrices
abstract: It is shown that a sufficient condition for the likelihood function of a zero-mean Gaussian random vector with covariance R from some class of covariances R to be unbounded above over the set of positive-definite matrices in R is that some singular R/sub o/ exists in R whose range space contains the data. The results obtained imply that, for the spectrum estimation problem in which R is the class of Toeplitz covariances and only one long observation vector is available, by constraining the maximum-likelihood estimation problem to the class of Toeplitz matrices with nonnegative definite circulant extensions, a positive-definite solution is guaranteed to exist.

title: A MAC protocol to reduce sensor network energy consumption using a wakeup radio
abstract: For increasing the life of sensor networks, each node must conserve energy as much as possible. In this paper, we propose a protocol in which energy is conserved by amortizing the energy cost of communication over multiple packets. In addition, we allow sensors to control the amount of buffered packets since storage space is limited. To achieve this, a two-radio architecture is used which allows a sensor to "wakeup" a neighbor with a busy tone and send its packets for that destination. However, this process is expensive because all neighbors must awake and listen to the primary channel to determine who is the intended destination. Therefore, triggered wakeups on the primary channel are proposed to avoid using the more costly wakeup procedure. We present a protocol for efficiently determining how large the period for these wakeups should be such that energy consumption is reduced.

title: Leveraging Channel Diversity for Key Establishment in Wireless Sensor Networks
abstract: As the use of sensor networks increases, security in this domain becomes a very real concern. One fundamental aspect of providing confidentiality and authentication is key distribution. While public-key encryption has provided these properties historically, sensors are resource constrained and benefit from symmetric key approaches. In this work, we propose a novel protocol for symmetric key distribution that uses the multiple channels available on sensor hardware. This channel diversity, along with spatial diversity of device locations, allows neighboring sensors to establish secure link keys from plaintext keys that are broadcast by sensors in their neighborhood. In particular, we show that using even one extra channel during the initialization procedure significantly improves the security of key establishment. Via analysis and simulation, we show that our protocol performs well in terms of network connectivity and resilience to colluding malicious devices, when compared to previous work. We show that our protocol can achieve over 90% connectivity among neighboring sensors with link keys that are uncompromised even when 80% of the devices in the network are malicious and collude. Finally, we present a thorough discussion of the comparative advantages and disadvantages of our approach compared to previous techniques.

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: Complete characterization of almost Moore digraphs of degree three
abstract: It is well known that Moore digraphs do not exist except for trivial cases (degree 1 or diameter 1), but there are digraphs of diameter two and arbitrary degree which miss the Moore bound by one. No 2004 Wiley Periodicals, Inc.

title: Minimum Diameter of Diregular Digraphs of Degree 2
abstract: 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