Information-Theoretic Bounds on Target Recognition Performance Based on Degraded Image Data
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: 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: 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: 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: A stochastic model for studying the laminar structure of cortex from MRI
abstract: The human cerebral cortex is a laminar structure about 3 mm thick, and is easily visualized with current magnetic resonance (MR) technology. The thickness of the cortex varies locally by region, and is likely to be influenced by such factors as development, disease and aging. Thus, accurate measurements of local cortical thickness are likely to be of interest to other researchers. We develop a parametric stochastic model relating the laminar structure of local regions of the cerebral cortex to MR image data. Parameters of the model include local thickness, and statistics describing white, gray and cerebrospinal fluid (CSF) image intensity values as a function of the normal distance from the center of a voxel to a local coordinate system anchored at the gray/white matter interface. Our fundamental data object, the intensity-distance histogram (IDH), is a two-dimensional (2-D) generalization of the conventional 1-D image intensity histogram, which indexes voxels not only by their intensity value, but also by their normal distance to the gray/white interface. We model the IDH empirically as a marked Poisson process with marking process a Gaussian random field model of image intensity indexed against normal distance. In this paper, we relate the parameters of the IDH model to the local geometry of the cortex. A maximum-likelihood framework estimates the parameters of the model from the data. Here, we show estimates of these parameters for 10 volumes in the posterior cingulate, and 6 volumes in the anterior and posterior banks of the central sulcus. The accuracy of the estimates is quantified via Cramer-Rao bounds. We believe that this relatively crude model can be extended in a straightforward fashion to other biologically and theoretically interesting problems such as segmentation, surface area estimation, and estimating the thickness distribution in a variety of biologically relevant contexts.

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: Mod sum number of wheels

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: Further results on almost Moore digraphs
abstract: 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

title: Bounds on the number of isolates in sum graph labeling
abstract: A simple undirected graph H is called a sum graph if there is a labeling L of the vertices of H into distinct positive integers such that any two vertices u and v of H are adjacent if and only if there is a vertex w with label L(w )= L(u )+ L(v). The sum number � (G) of a graph G =( V; E) is the least integer r such that the graph H consisting of G and r isolated vertices is a sum graph. It is clear that � (G)6|E|. In this paper, we discuss general upper and lower bounds on the sum number. In particular, we prove that, over all graphs G =( V; E) with 5xed |V |?3 and |E|, the average of � (G) is at least |E |− 3|V |(log|V |)=[log(( |V | 2 )=|E|)] −| V |− 1. In other words, for most graphs, � (G) ∈ (|E|).

title: Almost Moore digraphs are diregular
abstract: An almost Moore digraph is a digraph of diameter k⩾2 , maximum out-degree d⩾2 and order n=d+d 2 +⋯+d k , that is, one less than the Moore bound. It is easy to show that the out-degree of an almost Moore digraph is constant (=d) . In this note we prove that also the in-degree of an almost Moore digraph is constant (=d) , that is, every almost Moore digraph is diregular of degree d .