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Shape Analysis Using a PointBased Statistical Shape Model Built on Correspondence Probabilities
"... Abstract. A fundamental problem when computing statistical shape models is the determination of correspondences between the instances of the associated data set. Often, homologies between points that represent the surfaces are assumed which might lead to imprecise mean shape and variability results. ..."
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Abstract. A fundamental problem when computing statistical shape models is the determination of correspondences between the instances of the associated data set. Often, homologies between points that represent the surfaces are assumed which might lead to imprecise mean shape and variability results. We propose an approach where exact correspondences are replaced by evolving correspondence probabilities. These are the basis for a novel algorithm that computes a generative statistical shape model. We developed an unified MAP framework to compute the model parameters (’mean shape ’ and ’modes of variation’) and the nuisance parameters which leads to an optimal adaption of the model to the set of observations. The registration of the model on the instances is solved using the Expectation Maximization Iterative Closest Point algorithm which is based on probabilistic correspondences and proved to be robust and fast. The alternated optimization of the MAP explanation with respect to the observation and the generative model parameters leads to very efficient and closedform solutions for (almost) all parameters. Experimental results on brain structure data sets demonstrate the efficiency and wellposedness of the approach. The algorithm is then extended to an automatic classification method using the kmeans clustering and applied to synthetic data as well as brain structure classification problems. 1
Generation of a Statistical Shape Model with Probabilistic Point Correspondences and EMICP
"... Abstract In this paper, we present a method to compute a statistical shape model based on shapes which are represented by unstructured point sets with arbitrary point numbers. A fundamental problem when computing statistical shape models is the determination of correspondences between the points of ..."
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Abstract In this paper, we present a method to compute a statistical shape model based on shapes which are represented by unstructured point sets with arbitrary point numbers. A fundamental problem when computing statistical shape models is the determination of correspondences between the points of the shape observations of the training data set. In the absence of landmarks, exact correspondences can only be determined between continuous surfaces, not between unstructured point sets. To overcome this problem, we introduce correspondence probabilities instead of exact correspondences. The correspondence probabilities are found by aligning the observation shapes with the affine Expectation Maximization Iterative Closest Points registration algorithm. In a second step, the correspondence probabilities are used as input to compute a mean shape (represented once again by an unstructured point set). Both steps are unified in a single optimization criterion which depends on the two parameters ’ registration transformation ’ and ’mean shape’. In a last step, a variability model which best represent the variability in the training data set is computed. Experiments on synthetic data sets and real brain structure data sets are then designed to evaluate the performance of our algorithm. The method is compared to a statistical shape model built on exact correspondences. Results regarding the established measures ”generalization ability ” and ”specificity ” show the relevance of our approach. 1
Comparison of Statistical Shape Models Built on Correspondence Probabilities and OnetoOne Correspondences
"... In this paper, we present a method to compute a statistical shape model based on shapes which are represented by unstructured point sets with arbitrary point numbers. A fundamental problem when computing statistical shape models is the determination of correspondences between the observations of the ..."
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In this paper, we present a method to compute a statistical shape model based on shapes which are represented by unstructured point sets with arbitrary point numbers. A fundamental problem when computing statistical shape models is the determination of correspondences between the observations of the associated data set. Often, homologies between points that represent the surfaces are assumed. When working merely with point clouds, this might lead to imprecise mean shape and variability results. To overcome this problem, we propose an approach where exact correspondences are replaced by evolving correspondence probabilities. These are the basis for a novel algorithm that computes a generative statistical shape model. We developed a unified Maximum A Posteriori (MAP) framework to compute the model parameters (’mean shape ’ and ’modes of variation’) and the nuisance parameters which leads to an optimal adaption of the model to the set of observations. The registration of the model on the observations is solved using the Expectation Maximization Iterative Closest Point algorithm which is based on probabilistic correspondences and proved to be robust and fast. The alternated optimization of the MAP explanation with respect to the observation and the generative model parameters leads to very efficient and closedform solutions for nearly all parameters. A comparison with a statistical shape model which is built using the Iterative Closest Point (ICP) registration algorithm and a Principal Component Analysis (PCA) shows that our approach leads to better SSM quality measures.