Computation of a probabilistic statistical shape model in a maximum-a-posteriori framework.
نویسندگان
چکیده
OBJECTIVES When analyzing shapes and shape variabilities, the first step is bringing those shapes into correspondence. This is a fundamental problem even when solved by manually determining exact correspondences such as landmarks. We developed a method to represent a mean shape and a variability model for a training data set based on probabilistic correspondence computed between the observations. METHODS First, the observations are matched on each other with an affine transformation found by the Expectation-Maximization Iterative-Closest-Points (EM-ICP) registration. We then propose a maximum-a-posteriori (MAP) framework in order to compute the statistical shape model (SSM) parameters which result in an optimal adaptation of the model to the observations. The optimization of the MAP explanation is realized with respect to the observation parameters and the generative model parameters in a global criterion and leads to very efficient and closed-form solutions for (almost) all parameters. RESULTS We compared our probabilistic SSM to a SSM based on one-to-one correspondences and the PCA (classical SSM). Experiments on synthetic data served to test the performances on non-convex shapes (15 training shapes) which have proved difficult in terms of proper correspondence determination. We then computed the SSMs for real putamen data (21 training shapes). The evaluation was done by measuring the generalization ability as well as the specificity of both SSMs and showed that especially shape detail differences are better modeled by the probabilistic SSM (Hausdorff distance in generalization ability Re approximately 25% smaller). CONCLUSIONS The experimental outcome shows the efficiency and advantages of the new approach as the probabilistic SSM performs better in modeling shape details and differences.
منابع مشابه
A Maximum-A-Posteriori Framework for Statistical Appearance Models with Probabilistic Correspondences
The identification of one-to-one correspondences in a training set is a key aspect of building statistical models. But the determination of these corresponding landmarks is the most challenging part of such methods. Hufnagel et al. [1] developed an alternative method using correspondence probabilities for statistical shape models. We propose the use of probabilistic correspondences for statisti...
متن کاملDisparity Estimation Based on Bayesian Maximum A Posteriori (MAP) Algorithm∗
In this paper, a general formula of disparity estimation based on Bayesian Maximum A Posteriori (MAP) algorithm is derived and implemented with simplified probabilistic models. The formula is the generalized probabilistic diffusion equation based on Bayesian model, and can be implemented into some different forms corresponding to the probabilistic models in the disparity neighborhood system or ...
متن کاملAn Introduction to Inference and Learning in Bayesian Networks
Bayesian networks (BNs) are modern tools for modeling phenomena in dynamic and static systems and are used in different subjects such as disease diagnosis, weather forecasting, decision making and clustering. A BN is a graphical-probabilistic model which represents causal relations among random variables and consists of a directed acyclic graph and a set of conditional probabilities. Structure...
متن کاملCoupled level set segmentation using a point-based statistical shape model relying on correspondence probabilities
In order to successfully perform automatic segmentation in medical images containing noise and intensity inhomogeneities, modern algorithms often rely on a priori knowledge about the respective anatomy. This is often introduced by statistical shape models (SSMs) which are typically based on one-to-one point correspondences. In this work, we propose a unified statistical framework for image segm...
متن کاملA Probabilistic Model for Recovering Camera Translation
This paper describes the mathematical basis and application of a probabilistic model for recovering the direction of camera translation (heading) from optical flow. According to the theorem that heading cannot lie between two converging points in a stationary environment, one can compute the posterior probability distribution of heading across the image and choose the heading with maximum a pos...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Methods of information in medicine
دوره 48 4 شماره
صفحات -
تاریخ انتشار 2009