GRID-ENABLED AUTOMATIC CONSTRUCTION OF A TWO-CHAMBER CARDIAC PDM FROM A LARGE DATABASE OF DYNAMIC 3D SHAPES S. Ordas 1 , L. Boisrobert 1 , M. Bossa 1 , M. Huguet 2 , M. Laucelli 3 , S. Olmos 1 , AF. Frangi 1 1 Computer Vision Group, Aragon Institute of Engineering Research, University of Zaragoza, Spain. 2 Centre Cardiovascular, CETIR Sant Jordi, Barcelona, Spain. 3 GridSystems S.A., Palma de Mallorca, Spain. ABSTRACT Point Distribution Modelling (PDM) is an efficient generative technique that can be used to incorporate statistical shape priors into image analysis methods like Active Shape Models (ASMs) or Active Appearance Models (AAMs). They are described by a set of landmarks usually manually pinpointed in a training set. Frangi et al. [1] have proposed an automatic auto-landmarking technique capable of dealing with multi-object arrangements. In this paper, we present an experimental extension of this previous work, validating the method provided. Our contributions can be summarized as follows: A two-chamber shape model of the heart is constructed from a large data-set comprising 90 subjects and considering 5 phases of the cardiac cycle. The computational demand of our technique is addressed using Grid computing. The results of our experiments suggest that the method presented in [1] as a proof-of-concept, can truly cope with the large inter-subject and inter-phase deformations present in clinical cardiac data sets including pathologies. The achieved accuracy in our validation is comparable to the former tests. 1. INTRODUCTION Magnetic Resonance Imaging (MRI) is a promising modality for one-stop-shop cardiac examination thanks to its increased spatial and temporal resolution and its ability to provide quantitative morphological and functional information of the heart. An inevitable step before pursuing any kind of quantitative and/or functional analysis, is the segmentation of the cardiac chambers. As the amount of data in dynamic 3D cardiac scans is very large, manual segmentation is not viable, and thus automatic methods are required. During the last few years, model-driven methods and, in particular, statistical 3D models, are being developed for 3D cardiac image segmentation [2], [3]. In a cardiac 3D Point Distribution Model (PDM), a set of landmarks is positioned in the endo and epi boundaries of the ventricles. These landmarks have to be placed in a consistent way over a large database of training shapes to ensure that the final model gathers representative statistics of the shape population. Manual landmarking of dynamic 3D structures like the heart is basically unfeasible due to the large number of landmarks and training shapes that are required This work is funded by MAPFRE Medicina Foundation, and partially supported by TIC2002-04495-C02, ISCIII G03/185, and FIT-070000- 2003-585 grants. SeO and LB hold a MEC-FPU grant AP2002-3955 and AP2002-3946 respectively. AFF holds a MCyT Ramon Y Cajal Fellowship. The authors acknowledge the technical support team of GridSystems, for their help with the InnerGrid Nitya Middleware. for the construction of detailed spatio-temporal models. The purpose of this paper is thus to further validate the approach in [1] and to investigate the properties of a 3D+t bi-ventricular model constructed from a large population of healthy and diseased hearts, at different instants of the cardiac cycle. 2. THEORY 2.1. Statistical Shape Models Consider a set X = {x i ; i =1 ··· n} of n shapes. Each shape is described by the concatenation of m 3–D landmarks p j = (p 1j ,p 2j ,p 3j ); j =1 ··· m, obtained from a surface triangulation. X is thus a distribution in a 3m-dimensional space. The goal is to obtain a general and reasonably compact representation of the population, learnt from the training set. This representation allows to approximate any shape using the following linear model x = ˆ x + Φb (1) where ˆ x = 1 n ∑ n i=1 x i is the average landmark vector, b is the shape parameter vector of the model, and Φ is a matrix whose columns are the principal components of the covariance matrix S = 1 n-1 ∑ n i=1 (x i - ˆ x)(x i - ˆ x) T . The principal components of S are calculated as its eigenvectors, φ i , with corresponding eigenvalues, λ i (sorted so that λ i ≥ λ i+1 ). If Φ contains only the first t< min{m, n} eigenvectors corresponding to the largest non-zero eigenvalues, we can approximate any shape of the training set, x, using Eq. (1) where Φ =(φ 1 |φ2 |···|φt ) and b is a t dimensional vector given by b = Φ T (x - ˆ x). Assuming that the cloud of landmark vectors follows a multi-dimensional Gaussian distribution, the variance of the i-th parameter, b i , across the training set is given by λi . By varying these parameters, different instances of the shape class under analysis can be generated using Eq. (1). By applying limits to the variation of b i , usually |b i |≤ ±3 √ λ i , it can be enforced that a generated shape is similar to the shapes contained in the training class. 2.2. Automatic Landmarking Method The general layout of the method is to align all the shapes of the training set to an atlas that can be interpreted as a mean shape. Once all the necessary transformations are obtained, they are inverted and used to propagate any number of arbitrarily sampled landmarks on the atlas, to the coordinate system of each subject. In this way, while it is still necessary to manually draw the contours in each training image, our technique reliefs from manual landmark