Stephen B. Robinson

Computational imaging systems for iris recognition

Computational imaging systems are modern systems that consist of generalized aspheric optics and image processing capability. These systems can be optimized to greatly increase the performance above systems consisting solely of traditional optics. Computational imaging technology can be used to advantage in iris recognition applications. A major difficulty in current iris recognition systems is a very shallow depth-of-field that limits system usability and increases system complexity. We first review some current iris recognition algorithms, and then describe computational imaging approaches to iris recognition using cubic phase wavefront encoding. These new approaches can greatly increase the depth-of-field over that possible with traditional optics, while keeping sufficient recognition accuracy. In these approaches the combination of optics, detectors, and image processing all contribute to the iris recognition accuracy and efficiency. We describe different optimization methods for designing the optics and the image processing algorithms, and provide laboratory and simulation results from applying these systems and results on restoring the intermediate phase encoded images using both direct Wiener filter and iterative conjugate gradient methods.

Public avoidance and epidemics: insights from an economic model.

In this paper, we present a mathematical model of infectious disease transmission in which people can engage in public avoidance behavior to minimize the likelihood of acquiring an infection. The framework employs the economists theory of utility maximization to model peoples decision regarding their level of public avoidance. We derive the reproductive number of a disease which determines whether an endemic equilibrium exists or not. We show that when the contact function exhibits saturation, an endemic equilibrium must be unique. Otherwise, multiple endemic equilibria that differ in disease prevalence can coexist, and which one the population gets to depends on initial conditions. Even when a unique endemic equilibrium exists, peoples preferences and the initial conditions may determine whether the disease will eventually die out or become endemic. Public health policies that increase the recovery rate or encourage self-quarantine by infected people can be beneficial to the community by lowering disease prevalence. However, it is also possible for these policies to worsen the situation and cause prevalence to rise since these measures give people less incentive to engage in public avoidance behavior. We also show that implementing policies that result in a higher level of public avoidance behavior in equilibrium does not necessarily lower prevalence and can result in more infections.

Nonlinear boundary value problems for shallow membrane caps, II

Abstract Suppose a shallow membrane cap, with an undeformed shape described in cylindrical coordinates by z = C(1−rγ) (where 0⩽r⩽1 and γ>1), is subjected to a uniform vertical pressure P. If the resulting deformed shape is radially symmetric, then under certain assumptions, the radial stress Sr satisfies the ordinary differential equation r 2 S r ″ + 3rS r ′ = λ 2 r 2y−2 2 + βvr 2 S r − r 2 8S r 2 , for 0 0 (if the boundary stress S is specified) or S r ′ (1)+(1 − v)S r (1) = ⌜ (if the boundary displacement ⌜ is specified). Here v(0⩽v 1, a radially symmetric solution Sr(r), positive for 0 S⩽ 1 (4βv) or ⌜ (1−v) ⩽ 1 (4βv) , the solution is unique. In the case γ⩽ 4 3 , if λ is fairly large, it may happen that Sr(r) → 0 as r → 0. In all other cases, Sr(r) has a positive limit as r → 0. Rather detailed information on the behavior of solutions Sr(r) is provided. Conditions are obtained which guarantee monotonicity of Sr. In any case, Sr has at most one critical point and is monotone in some neighborhood of r = 0. A computational algorithm, making use of the qualitative behavior of Sr, is discussed and some numerical results are included.

Resonance problems for the one-dimensional -Laplacian

We consider resonance problems for the one dimensional p-Laplacian, and prove the existence of solutions assuming a standard LandesmanLazer condition. Our proofs use variational techniques to characterize the eigenvalues, and then to establish the solvability of the given boundary value problem.

Geometric problem in medical imaging

In this paper we provide a rigorous mathematical foundation for Tuned- Aperture Computed Tomography, a generalization of standard tomosynthesis that provides a significantly more flexible diagnostic tool. We also describe how the general TACT algorithm simplifies in important special cases, and we investigate the possibility of optimizing the algorithm by reducing the number of fiducial reference points. The key theoretical problem is how to sue information within an x-ray image to discover, after the fact, what the relative positions of the x-ray source, the patient, and the x-ray detector were when the x-ray image was created.

On the Fredholm Alternative for the Fučík Spectrum

We consider resonance problems for the one-dimensional p-Laplacian assuming Dirichlet boundary conditions. In particular, we consider resonance problems associated with the first three curves of the Fucik Spectrum. Using variational arguments based on linking theorems, we prove sufficient conditions for the existence of at least one solution. Our results are related to the classical Fredholm Alternative for linear operators. We also provide a new variational characterization for points on the third Fucik curve.

Improved 3D reconstructions for generalized tomosynthesis

This paper describes a unique system for constructing a three-dimensional volume from a set of two-dimensional (2D) x-ray projection images based on optical aperture theory. This proprietary system known as Tuned-Aperture Computed Tomography (TACT) is novel in that only a small number of projections acquired from arbitrary or task-specific projection angles is required for the reconstruction process. We used TACT to reconstruct a simulated phantom from seven 2D projections made with the x-ray source positioned within 30 degrees of perpendicular to a detector array. The distance from the x-ray source was also varied to change the amount of perspective distortion in each projection. Finally, we determined the reconstruction accuracy of TACT and compared it to that of a conventional tomosynthesis system. We found the reconstructed volumetric data sets computed with TACT to be geometrically accurate and contain significantly less visible blurring than a similar data set computed with the control technique.

On the existence of multiple positive solutions to some superlinear systems

We use the method of upper and lower solutions combined with degree-theoretic techniques to prove the existence of multiple positive solutions to some superlinear elliptic systems of the form on a smooth, bounded domain Ω⊂ℝ n with Dirichlet boundary conditions, under suitable conditions on g 1 and g 2 . Our techniques apply generally to subcritical, superlinear problems with a certain concave–convex shape to their nonlinearity.