Statistical models of partial volume effect

Statistical models of partial volume effect for systems with various types of noise or pixel value distributions are developed and probability density functions are derived. The models assume either Gaussian system sampling noise or intrinsic material variances with Gaussian or Poisson statistics. In particular, a material can be viewed as having a distinct value that has been corrupted by additive noise either before or after partial volume mixing, or the material could have nondistinct values with a Poisson distribution as might be the case in nuclear medicine images. General forms of the probability density functions are presented for the N material cases and particular forms for two- and three-material cases are derived. These models are incorporated into finite mixture densities in order to more accurately model the distribution of image pixel values. Examples are presented using simulated histograms to demonstrate the efficacy of the models for quantification. Modeling of partial volume effect is shown to be useful when one of the materials is present in images mainly as a pixel component.

[1]  Kanti V. Mardia,et al.  Spatial Classification Using Fuzzy Membership Models , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Wesley E. Snyder,et al.  Optimization of functions with many minima , 1991, IEEE Trans. Syst. Man Cybern..

[3]  T Lei,et al.  Statistical approach to X-ray CT imaging and its applications in image analysis. II. A new stochastic model-based image segmentation technique for X-ray CT image , 1992, IEEE Trans. Medical Imaging.

[4]  R F McLoughlin,et al.  Quantitative analysis of CT brain images: a statistical model incorporating partial volume and beam hardening effects. , 1992, The British journal of radiology.

[5]  D R Haynor,et al.  Partial volume tissue classification of multichannel magnetic resonance images-a mixel model. , 1991, IEEE transactions on medical imaging.

[6]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[7]  P. Santago,et al.  Quantification of MR brain images by mixture density and partial volume modeling , 1993, IEEE Trans. Medical Imaging.

[8]  David A. Rottenberg,et al.  A statistical method for determining the proportions of gray matter, white matter, and CSF using computed tomography , 2004, Neuroradiology.

[9]  Hamid Soltanian-Zadeh,et al.  A comparative analysis of several transformations for enhancement and segmentation of magnetic resonance image scene sequences , 1992, IEEE Trans. Medical Imaging.

[10]  Wesley E. Snyder,et al.  Quantification of brain tissue through incorporation of partial volume effects , 1992, Medical Imaging.

[11]  B. Everitt,et al.  Finite Mixture Distributions , 1981 .

[12]  Stanley L. Sclove,et al.  Application of the Conditional Population-Mixture Model to Image Segmentation , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  S. Strother,et al.  Graphical Analysis of MR Feature Space for Measurement of CSF, Gray‐Matter, and White‐Matter Volumes , 1993, Journal of computer assisted tomography.

[14]  L M Fletcher,et al.  A multispectral analysis of brain tissues , 1993, Magnetic resonance in medicine.

[15]  J P Windham,et al.  Eigenimage Filtering in MR Imaging , 1988, Journal of computer assisted tomography.

[16]  B. Horwitz,et al.  Method for quantification of brain, ventricular, and subarachnoid CSF volumes from MR images. , 1992, Journal of computer assisted tomography.

[17]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .