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18
CORTICAL CORRESPONDENCE USING ENTROPYBASED PARTICLE SYSTEMS AND LOCAL FEATURES
"... This paper presents a new method of constructing compact statistical pointbased models of populations of human cortical surfaces with functions of spatial locations driving the correspondence optimization. The proposed method is to establish a tradeoff between an even sampling of the surfaces (a lo ..."
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This paper presents a new method of constructing compact statistical pointbased models of populations of human cortical surfaces with functions of spatial locations driving the correspondence optimization. The proposed method is to establish a tradeoff between an even sampling of the surfaces (a low surface entropy) and the similarity of corresponding points across the population (a low ensemble entropy). The similarity metric, however, isn’t constrained to be just spatial proximity, but can be any function of spatial location, thus allowing the integration of local cortical geometry as well as DTI connectivity maps and vasculature information from MRA images. This method does not require a spherical parameterization or fine tuning of parameters. Experimental results are also presented, showing lower local variability for both sulcal depth and cortical thickness measurements, compared to other commonly used methods such as FreeSurfer.
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
Cortical correspondence with probabilistic fiber connectivity
 In Information Processing in Medical Imaging (IPMI 2009), LNCS 5636
, 2009
"... Abstract. This paper presents a novel method of optimizing pointbased correspondence among populations of human cortical surfaces by combining structural cues with probabilistic connectivity maps. The proposed method establishes a tradeoff between an even sampling of the cortical surfaces (a low sur ..."
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Abstract. This paper presents a novel method of optimizing pointbased correspondence among populations of human cortical surfaces by combining structural cues with probabilistic connectivity maps. The proposed method establishes a tradeoff between an even sampling of the cortical surfaces (a low surface entropy) and the similarity of corresponding points across the population (a low ensemble entropy). The similarity metric, however, isn’t constrained to be just spatial proximity, but uses local sulcal depth measurements as well as probabilistic connectivity maps, computed from DWI scans via a stochastic tractography algorithm, to enhance the correspondence definition. We propose a novel method for projecting this fiber connectivity information on the cortical surface, using a surface evolution technique. Our cortical correspondence method does not require a spherical parameterization. Experimental results are presented, showing improved correspondence quality demonstrated by a cortical thickness analysis, as compared to correspondence methods using spatial metrics as the sole correspondence criterion. 1
Populationbased fitting of medial shape models with correspondence optimization. Inf Process Med Imaging 20
, 2007
"... Abstract. A crucial problem in statistical shape analysis is establishing the correspondence of shape features across a population. While many solutions are easy to express using boundary representations, this has been a considerable challenge for medial representations. This paper uses a new 3D me ..."
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Abstract. A crucial problem in statistical shape analysis is establishing the correspondence of shape features across a population. While many solutions are easy to express using boundary representations, this has been a considerable challenge for medial representations. This paper uses a new 3D medial model that allows continuous interpolation of the medial manifold and provides a map back and forth between it and the boundary. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial coordinates, enabling the expression of important object properties in an objectrelative coordinate system. We use these integrals to optimize correspondence during model construction, reducing variability due to the model parameterization that could potentially mask true shape change effects. Discrimination and hypothesis testing of populations of shapes are expected to benefit, potentially resulting in improved significance of shape differences between populations even with a smaller sample size. 1
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
Segmentation by Posterior Optimization of Mreps: Strategy and Results
"... Abstract. For many years we have been developing a variety of methods that together would allow segmentation of 3D objects from medical images in a way reflecting knowledge of both the population of anatomic geometries sought and the population of images consistent with that geometry. To support the ..."
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Abstract. For many years we have been developing a variety of methods that together would allow segmentation of 3D objects from medical images in a way reflecting knowledge of both the population of anatomic geometries sought and the population of images consistent with that geometry. To support the probability estimation methods we use to reflect this knowledge, the methods use a medial description, the mrep, as the object representation and regional intensity quantile functions as the representation of image information in regions relative to the mrep. Using manually segmented images to which mreps have been fit and which contain information to allow alignment, our methods use principal geodesic analysis to estimate prior probability density, on the anatomic geometry, and they use principal component analysis to estimate a likelihood density, on the regional intensity quantile functions. They then segment automatically via posterior optimization over principal geodesic coefficients, after initialization via bones or a few contours. Each component of this methodology is briefly reviewed. Pelvic organs from multiday populations from individual patients were segmented from CT by training a prior and a likelihood density by the methods indicated. The results are compared to human segmentations. The resulting measurements indicate that in a significant majority of cases, maximizing the log posterior objective function provides segmentations in as good or better agreement with experts than they agree with each other. Similar results are reported for other organs, other image types, and betweenpatient variation. 1
Elastic shape matching of parameterized surfaces using square root normal fields
 In Proceedings of the 12th European conference on Computer Vision  Volume Part V, ECCV’12
, 2012
"... Abstract. In this paper we define a new methodology for shape analysis of parameterized surfaces, where the main issues are: (1) choice of metric for shape comparisons and (2) invariance to reparameterization. We begin by defining a general elastic metric on the space of parameterized surfaces. Th ..."
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Abstract. In this paper we define a new methodology for shape analysis of parameterized surfaces, where the main issues are: (1) choice of metric for shape comparisons and (2) invariance to reparameterization. We begin by defining a general elastic metric on the space of parameterized surfaces. The main advantages of this metric are twofold. First, it provides a natural interpretation of elastic shape deformations that are being quantified. Second, this metric is invariant under the action of the reparameterization group. We also introduce a novel representation of surfaces termed square root normal fields or SRNFs. This representation is convenient for shape analysis because, under this representation, a reduced version of the general elastic metric becomes the simple L2 metric. Thus, this transformation greatly simplifies the implementation of our framework. We validate our approach using multiple shape analysis examples for quadrilateral and spherical surfaces. We also compare the current results with those of Kurtek et al. [1]. We show that the proposed method results in more natural shape matchings, and furthermore, has some theoretical advantages over previous methods. 1
ParameterizationInvariant Shape Statistics and Probabilistic Classification of Anatomical Surfaces
"... Abstract. We consider the task of computing shape statistics and classification of 3D anatomical structures (as continuous, parameterized surfaces) under a Riemannian framework. This task requires a Riemannian metric that allows: (1) reparameterizations of surfaces by isometries, and (2) efficient ..."
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Abstract. We consider the task of computing shape statistics and classification of 3D anatomical structures (as continuous, parameterized surfaces) under a Riemannian framework. This task requires a Riemannian metric that allows: (1) reparameterizations of surfaces by isometries, and (2) efficient computations of geodesic paths between surfaces. These tools allow for computing Karcher means and covariances (using tangent PCA) for shape classes, and a probabilistic classification of surfaces into disease and control classes. In a separate paper [13], we introduced a mathematical representation of surfaces, called qmaps, and we used the L2 metric on the space of qmaps to induce a Riemannian metric on the space of parameterized surfaces. We also developed a pathstraightening algorithm for computing geodesic paths [14]. This process requires optimal reparameterizations (deformations of grids) of surfaces and achieves a superior alignment of geometric features across surfaces. The resulting means and covariances are better representatives of the original data and lead to parsimonious shape models. These two moments specify a normal probability model on shape classes, which are then used for classifying test shapes. Through improved random sampling and a higher classification performance, we demonstrate the success of this model over some past methods. In addition to toy objects, we use the Detroit Fetal Alcohol and Drug Exposure Cohort data to study brain structures and present classification results for the Attention Deficit Hyperactivity Disorder cases and controls in this study. We find that using the mean and covariance structure of the given data, we are able to attain a 88 % classification rate, which is an improvement over a previously reported result of 82 % on the same data.
COMPACT PARTBASED SHAPE SPACES FOR DENSE CORRESPONDENCES OLIVER BURGHARD, UNIVERSITY
"... Abstract. We consider the problem of establishing dense correspondences within a set of related shapes of strongly varying geometry. For such input, traditional shape matching approaches often produce unsatisfactory results. We propose an ensemble optimization method that improves given coarse corr ..."
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Abstract. We consider the problem of establishing dense correspondences within a set of related shapes of strongly varying geometry. For such input, traditional shape matching approaches often produce unsatisfactory results. We propose an ensemble optimization method that improves given coarse correspondences to obtain dense correspondences. Following ideas from minimum description length approaches, it maximizes the compactness of the induced shape space to obtain highquality correspondences. We make a number of improvements that are important for computer graphics applications: Our approach handles meshes of general topology and handles partial matching between input of varying topology. To this end we introduce a novel partbased generative statistical shape model. We develop a novel analysis algorithm that learns such models from training shapes of varying topology. We also provide a novel synthesis method that can generate new instances with varying part layouts and subject to generic variational constraints. In practical experiments, we obtain a substantial improvement in correspondence quality over stateoftheart methods. As example application, we demonstrate a system that learns shape families as assemblies of deformable parts and permits realtime editing with continuous and discrete variability. (a) shape collection (b) coarse segmentation (c) dense correspondences 1.
Statistics of Shape.
, 2006
"... (Under the direction of Guido Gerig.) In questions of statistical shape analysis, the foremost is how such shapes should be represented. The number of parameters required for a given accuracy and the types of deformation they can express directly influence the quality and type of statistical inferen ..."
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(Under the direction of Guido Gerig.) In questions of statistical shape analysis, the foremost is how such shapes should be represented. The number of parameters required for a given accuracy and the types of deformation they can express directly influence the quality and type of statistical inferences one can make. One example is a medial model, which represents a solid object using a skeleton of a lower dimension and naturally expresses intuitive changes such as “bending”, “twisting”, and “thickening”. In this dissertation I develop a new threedimensional medial model that allows continuous interpolation of the medial surface and provides a map back and forth between the boundary and its medial axis. It is the first such model to support branching, allowing the representation of a much wider class of objects than previously possible using continuous medial methods. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial coordinates, enabling the expression of