title: A theory of fine structure image models with an application to detection and classification of dementia.
abstract: BACKGROUND
  Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations.
  
  
  METHODS
  In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters.
  
  
  RESULTS
  We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one.
  
  
  CONCLUSIONS
  Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible.
authors.affiliation: 1 Bioengineering Department, University of Illinois at Chicago, Chicago, Illinois 60607, USA ; 2 Department of Neurosurgery, Rush University and Hospital, Chicago, Illinois 60607, USA ; 3 Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, Illinois 60607, USA.
authors.forename: William
authors.initials: W
authors.lastname: O'Neill
authors.affiliation: 1 Bioengineering Department, University of Illinois at Chicago, Chicago, Illinois 60607, USA ; 2 Department of Neurosurgery, Rush University and Hospital, Chicago, Illinois 60607, USA ; 3 Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, Illinois 60607, USA.
authors.forename: Richard
authors.initials: R
authors.lastname: Penn
authors.affiliation: 1 Bioengineering Department, University of Illinois at Chicago, Chicago, Illinois 60607, USA ; 2 Department of Neurosurgery, Rush University and Hospital, Chicago, Illinois 60607, USA ; 3 Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, Illinois 60607, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Werner
authors.affiliation: 1 Bioengineering Department, University of Illinois at Chicago, Chicago, Illinois 60607, USA ; 2 Department of Neurosurgery, Rush University and Hospital, Chicago, Illinois 60607, USA ; 3 Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, Illinois 60607, USA.
authors.forename: Justin
authors.initials: J
authors.lastname: Thomas
keywords: Image regression models; MRI classification information; dementia classification; parameter classification information