Multispectral Tissue Characterization In Magnetic Resonance Imaging Using Bayesian Estimation And Markov Random Fields

Abstract

A stochastic model b s been developed to provide visualization and classification of 3 dimensional mullispecld nugnetic m n n n c e images. A set of manually drawn regiona comprirt the ramplc space on which a statistical model is built for each tiwe. The stack of imagw is then analyzed using parametric Maximum A Posteriori @LAP) classification with the a priori probability modeled as a Markov random field. The result i s either a stack of claasificd inuges or a stack of imager whicb epresents the probability of finding a particular tissue at each location in space. Either of t h e image stacks can be used as direct input to 3V object reconstructionpackages like that found in ISG Allegro. INTRODIJCTIONMagnetic Rcaonence (MR) inuging has introduced lo d i o l o g y the potential to pmduce multispectral images like those con~ionly used in remote sensing. The flexibility afForded by MR brings with it a complexity. This complexity is twofold being not only in the number of acquisition niethods nnd paranleten. but also in the adequate coniniunication. or visualization. of niultidimensionnl data. The ability to generate and display 3D ohjects on the computer greatly enhanced the effective communication of MR and CAT SCM data by synthesizing the information on numerous inlagea and producing consolidated ohjects. These objects are more intuitively understandableand do not require that the person kcep track of multiple images simultaneously. The problem is even niore acute in multispectral data where there is an added diniension. METHODThe input to the system is a set of M stacks of images. This 4V volume V is comprised of Mdimensional voxel vectors vW. V is transformed into a probability volume P which is conlprised of Tdiniensional probability vectors P ,~. These elements indicate the likelihood of finding each of the T tissues of intenst at each point (x,y,z) in the originnl volume U. Using vector notation for the position index pi is a vector of mnrginal probabilities.Pi, =p(q = 0,The ptubabilitiesare b a d on parametric Bayesian estinution [ I , 21 using a multivariate gaussiae niodel for the probability density function (pdf). 6, is the a priori marginal probability for tissue t at i. p(vJ is left as a normalizing constant. The a priori probability volume @ is comprised of a priori vectors the elements of which are marginnl prohabilitiesassociated with the state of node oj in a Markov random field R 131. Each node uj can he in one of T possible staten. Therefore (3)Because 0 is a Markov random field the state probability 9 is defined as (4) 131 where U(R). is the energy function associated with the stale of R in the neighhourlidof q. The energy function is the weighted suni of the local potentials. The potential is calculacad on the probability that a node is at one of T stntes rather than on the field node values themselves. The energy function is then defined as (5) ucn, =G' pc09 B P(n) = G ' + ' B + where ci = Lgo, 8 , . .., gi, .., gN.J is a weight matrix which defines the neiglihourhoodsai, and B is an interact...

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