Asymptotic performance analysis of Bayesian target recognition
This article investigates the asymptotic performance of Bayesian target recognition algorithms using deformable-template representations. Rigid computer-aided design (CAD) models represent the underlying targets; low-dimensional matrix Lie-groups (rotation and translation) extend them to particular instances. Remote sensors observing the targets are modeled as projective transformations, converting three-dimensional scenes into random images. Bayesian target recognition corresponds to hypothesis selection in the presence of nuisance parameters; its performance is quantified as the Bayes' error. Analytical expressions for this error probability in small noise situations are derived, yielding asymptotic error rates for exponential error probability decay.

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: Volumetric transformation of brain anatomy
abstract: 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.

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: 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: Exploring the Energy-Latency Trade-Off for Broadcasts in Energy-Saving Sensor Networks
abstract: Networking protocols for multi-hop wireless sensor networks (WSNs) are required to simultaneously minimize resource usage as well as optimize performance metrics such as latency and reliability. This paper explores the energy-latency-reliability trade-off for broadcast in multi-hop WSNs, by presenting a new protocol called PBBF (probability-based broadcast forwarding). PBBF works at the MAC layer and can be integrated into any sleep scheduling protocol. For a given application-defined level of reliability for broadcasts, the energy required and latency obtained are found to be inversely related to each other. Our analysis and simulation study quantify this relationship at the reliability boundary, as well as performance numbers to be expected from a deployment. PBBF essentially offers a WSN application designer considerable flexibility in choice of desired operation points

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: Digraphs of degree two which miss the Moore bound by two
abstract: It is well known that Moore digraphs do not exist except for trivial cases (degree one or diameter one). Consequently, for a given maximum out-degree d and a given diameter, we wish to find a digraph whose order misses the Moore bound by the smallest possible ‘defect’. For diameter two and arbitrary degree there are digraphs which miss the Moore bound by one. No examples of such digraphs of diameter at least three are known, although several necessary conditions for their existence have been obtained. In the case of degree two, it has been shown that there are no digraphs of diameter greater than two and defect one. There are five nonisomorphic digraphs of degree two, diameter two and defect two. In this paper we prove that digraphs of degree two and diameter k ⩾3 which miss the Moore bound by two do not exist.

title: Proving Facts about "|"
abstract: We study the Knights and Knaves problem, and find that for a proper treatment via theorem-proving, an interaction with natural language processing research is helpful. In particular, we discuss Ohlbach's claim that first-order logic is not well suited to handling this problem. Then we provide another interpretation of the problem using indexicals, and axiomatize it so that the desired result follows. We conclude by suggesting a broader context for dealing with "self-utterances" in automatic theorem-proving. Fuller details of automated proofs are given in a longer paper.

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.