Mark Oxley is a Professor of Mathematics in the Department of Mathematics and Statistics, Graduate School of Engineering and Management, Air Force Institute of Technology located on Wright-Patterson Air Force Base, Ohio. Dr. Oxley earned the B.S. degree in mathematics from Cumberland College in 1978 (renamed to the University of the Cumberlands in 2005), the M.S. degree in applied mathematics from Purdue University in 1980, and the Ph.D. degree in mathematics from North Carolina State University in 1987. He joined the faculty at AFIT in July 1987. He has advised several M.S. and Ph.D. student research in artificial neural network theory, applied mathematics and information fusion. He has received research funding from AFOSR, AFRL, ACC, DARPA and NASIC. He has published over 70 research journal articles in mathematics, applied mathematics, and engineering. His research began in nonlinear partial differential equations, and has developed other areas of expertise in pattern recognition, signal and image processing, category theory, information fusion, and Receiver Operating Characteristics (ROC) curve and manifold analysis.

**Publications**(65)

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^{2}. Fourier transforms are used to extract the phase scattering properties of the material from the intensity measurements. We investigate the effectiveness this method for constructing the reflection matrix (RM) of a diffuse reflecting medium where the propagation distances and observation plane are almost 1,000 times greater than the previous work based on transmissive scatter. The RM performance is based on its ability to refocus reflectively scattered light to a single focused spot or multiple foci in the observation plane. Diffraction-based simulations are used to corroborate experimental results.

*N*possible output labels (or decisions) will have

*N*(

*N*− 1) possible errors. The Receiver Operating Characteristic (ROC) manifold was created to quantify all of these errors. When multiple ATR systems are fused, the assumption of independence is usually made in order to mathematically combine the individual ROC manifolds for each system into one ROC manifold. This paper will investigate the label fusion (also called decision fusion) of multiple classification systems that have the same number of output labels. Boolean rules do not exist for multiple symbols, thus, we will derive possible Boolean-like rules as well as other rules that will yield label fusion rules. The formula for the resultant ROC manifold of the fused classification systems which incorporates the individual classification systems will be derived. Specifically, given a fusion rule and two classification systems, the ROC manifold for the fused system is produced. We generate formulas for the Boolean-like OR rule, Boolean-like AND rule, and other rules and give the resultant ROC manifold for the fused system. Examples will be given that demonstrate how each formula is used.

*a priori*information. Building on existing knowledge that calculates the degree of linear polarization (DOLP) and the angle of polarization (AOP) for a given surface normal in a forward model (from an object's characteristics to calculation of the DOLP and AOP), this research quantifies the impact of

*a priori*information with the development of an inverse algorithm to estimate surface normals from thermal polarimetric emissions in long-wave infrared (LWIR). The inverse algorithm assumes a polarized infrared focal plane array capturing LWIR intensity images which are then converted to Stokes vectors. Next, the DOLP and AOP are calculated from the Stokes vectors. Last, the viewing angles,

*θ*, to the surface normals are estimated assuming perfect material information about the imaged scene. A sensitivity analysis is presented to quantitatively describe the

_{v}*a priori*information's impact on the amount of error in the estimation of surface normals, and a bound is determined given perfect information about an object. Simulations explored the impact of surface roughness (

*σ*) and the real component (

*n*) of a dielectric's complex index of refraction across a range of viewing angles (

*θ*) for a given wavelength of observation.

_{v}
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