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Tutorial  MICCAI 2013 Nagoya, Japan, Sept. 2226, 2013 

Stochastic Modeling for Medical Image Analysis 
Outline
Stochastic modeling facilitates understanding of natural phenomena depicted in medical anatomical and functional (dynamic) MRI and CT images. Computerassisted diagnostics calls for fast and accurate unsupervised learning of models from images. The tutorial details efficient stochastic modeling techniques, including (i) shape models of objectsofinterest; (ii) shape and visual appearance models based on analytic learning of 2^{nd} or higherorder nonparametric MarkovGibbs random fields, and (iii) appearance models based on precise unsupervised learning of a mixture of pseudodistributions approximating an empirical marginal probability distribution of pixel/voxel intensities. The pseudodistribution, one per object associated with a prominent mode of the empirical distribution, is a linear combination of unimodal distributions, e.g. discrete Gaussians, with a dominant positive and several signalternate subordinate components. Integration of the models and learning techniques will be illustrated in application to early detection of lung and prostate cancer, kidney transplant rejection, and autism, as well as to cardiac functionality assessment. 

Tutorial organizers
Ayman ElBaz, 
Georgy Gimel'farb,
Department of Computer Science, University of Auckland, Auckland 1142, New Zealand. Email: g.gimelfarb@auckland.ac.nz 
Tutorial presenters – contributors
Ayman ElBaz, BioImaging Laboratory, Bioengineering Department, University of Louisville, Louisville, KY 40292, USA. Email: aselba01@exchange.louisville.edu

Georgy Gimel'farb,
Department of Computer Science, University of Auckland, Auckland 1142, New Zealand. Email: g.gimelfarb@auckland.ac.nz 
Ahmed Elnakib, BioImaging Laboratory, Bioengineering Department, University of Louisville, Louisville, KY 40292, USA. 
Fahmi Khalifa, BioImaging Laboratory, Bioengineering Department, University of Louisville, Louisville, KY 40292, USA. 
Mathew Nitzken, BioImaging Laboratory, Bioengineering Department, University of Louisville, Louisville, KY 40292, USA. 
Ahmed Soliman, BioImaging Laboratory, Bioengineering Department, University of Louisville, Louisville, KY 40292, USA. 
Amir Alansary, BioImaging Laboratory, Bioengineering Department, University of Louisville, Louisville, KY 40292, USA. 
Mahmoud Mostapha, BioImaging Laboratory, Bioengineering Department, University of Louisville, Louisville, KY 40292, USA. 
Detailed Program 
Stochastic Modeling for Medical Image Analysis 
The objective of this tutorial is to find an accurate mathematical model that describes all possible information in the image. So, the question is: what is the possible information that can be modeled in an image? The answer to this question depends on the applications that these mathematical models will be utilized to analyze. The focus of this tutorial is to find the mathematical model which could improve the performance of the existing registration and segmentation approaches. The most important models that could capture the visual characteristics of an image are (See Fig. 1):
a) Modeling the distribution of the intensity in each object in a particular image, b Modeling the interaction between the pixels in each object in the given image, and c) Modeling the shape of the objects in the given image. 
Fig. 1. Illustration of the proposed joint MarkovGibbs model of T1weighted MR brain images 
a) Modeling the distribution of the intensity in each object in a particular image 
In this tutorial we present a new approach for density estimation. The introduced approach is based on modifying ExpectationMaximization (EM) algorithm to approximate an empirical probability density function of scalar data with a Linear Combination of Discrete Gaussians (LCDG). We also propose a novel EMbased sequential technique to get a close initial LCDG approximation the modified EM algorithm should start with. Due to both positive and negative components, the LCDG approximates interclass transitions more accurately than a conventional mixture of only positive Gaussians. 
Example 1: Density Estimation Using LCDG Probabilistic Model 
b) Modeling the interaction between the pixels in each object in the given image 
b1)Neighborhood System for Higherorder Potts MGRF Model 
b2) 3D Neighborhood System for Potts MGRF Model 
b3) 3D Rotation Invariant MGRF Model 
c) Modeling the shape of the objects in the given image. 
c1) Probabilistic Shape Model 
Applications 
1. Lung Segmenation 
2. 2D/3D Kidney Segmenation 
3. Segmentation of 3D Magnetic Resonance Angiography 
4. Brain Segemnation from T1MR images 
5. LV Wall Segmentation from 4D Cine MR Images 
5. Dynamic ContrastEnhanced MRIBased Early Detection of Acute Renal Transplant Rejection 
In this tutorial, we present a new framework for early detection of acute renal transplant rejection from dynamic contrastenhanced MRI. Our framework consists of four steps. First, kidney objects are segmented from adjacent abdominal structures with a geometric (level setbased) deformable model guided by a stochastic speed function, which accounts for a fourthorder MarkovGibbs random field (MGRF) model of the kidney/background shape and appearance. Second, local kidney deformations caused by physiological effects are compensated for by a Laplacebased nonrigid registration approach that deforms target kidney objects over a set of closed, equispaced contours (isocontours) to closely match the reference object. Next, the cortex is segmented as it is the functional kidney unit that is at is primarily affected by the perfusion deficits that underlie the pathophysiology of acute rejection. To characterize rejection, perfusion is estimated from contrast agent kinetics using transient phase empirical indexes,(peak signal intensity, timetopeak, and initial upslope), and a steadyphase index defined as the average signal change during the slowly varying tissue distribution phase of agent transit. We used a k_{n} nearest neighbor classifier to distinguish between rejection and nonrejection. In a cohort of 50 participants, our framework correctly classified 92% of training subjects, 100% of the test subjects as rejection or nonrejection transplant candidates. Thus, our framework holds promise as a reliable diagnostic tool, which is comparable to the biopsy gold standard but without the associated deleterious side effects. 
6. Improving fullcardiac cycle strain estimation from tagged CMR by accurate modeling of 3D image appearance characteristics 
This tutorial will focus on the uses of such a a 3dimensional Markov Gibbs Random Field (MGRF) for use in improving tagged CMR images, along with a detailed explanation and discussion of how to implement the model in programming, and its application to cardiac CMR images. The 3D MGRF model can be used as a selective and highly configurable and controllable method of filtering on a wide variety of data, and can be implemented as an extremely useful filter to achieve many types of results. The usage of such a filter can serve to improve many other applications. Finally, it will be discussed how combining the previously discussed mixture of distributions can be implemented alongside the MGRF to improve its application to cardiac imaging. Discussions involving implementation of the MGRF in a uniform 3dimensional way, along with weighted and selective MGRF applications will be explored. For all of these discussions general programming guidance and code/pseudocode will be used to provide a meaningful understanding of the procedures. It is the goal of this tutorial that participants learn not only the uses and benefits of a 3D MGRF for image improvement purposes, but also gain an understanding of how to implement such an approach for their own uses. Specifically, the application of the technique on tagged CMR images will be used to illustrate the effects of the 3D MGRF on real world data. 
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