TY - GEN

T1 - Tree-space statistics and approximations for large-scale analysis of anatomical trees

AU - Feragen, Aasa

AU - Owen, Megan

AU - Petersen, Jens

AU - Wille, Mathilde M.W.

AU - Thomsen, Laura H.

AU - Dirksen, Asger

AU - De Bruijne, Marleen

PY - 2013

Y1 - 2013

N2 - Statistical analysis of anatomical trees is hard to perform due to differences in the topological structure of the trees. In this paper we define statistical properties of leaf-labeled anatomical trees with geometric edge attributes by considering the anatomical trees as points in the geometric space of leaf-labeled trees. This tree-space is a geodesic metric space where any two trees are connected by a unique shortest path, which corresponds to a tree deformation. However, tree-space is not a manifold, and the usual strategy of performing statistical analysis in a tangent space and projecting onto tree-space is not available. Using tree-space and its shortest paths, a variety of statistical properties, such as mean, principal component, hypothesis testing and linear discriminant analysis can be defined. For some of these properties it is still an open problem how to compute them; others (like the mean) can be computed, but efficient alternatives are helpful in speeding up algorithms that use means iteratively, like hypothesis testing. In this paper, we take advantage of a very large dataset (N = 8016) to obtain computable approximations, under the assumption that the data trees parametrize the relevant parts of tree-space well. Using the developed approximate statistics, we illustrate how the structure and geometry of airway trees vary across a population and show that airway trees with Chronic Obstructive Pulmonary Disease come from a different distribution in tree-space than healthy ones. Software is available from http://image.diku.dk/aasa/software.php.

AB - Statistical analysis of anatomical trees is hard to perform due to differences in the topological structure of the trees. In this paper we define statistical properties of leaf-labeled anatomical trees with geometric edge attributes by considering the anatomical trees as points in the geometric space of leaf-labeled trees. This tree-space is a geodesic metric space where any two trees are connected by a unique shortest path, which corresponds to a tree deformation. However, tree-space is not a manifold, and the usual strategy of performing statistical analysis in a tangent space and projecting onto tree-space is not available. Using tree-space and its shortest paths, a variety of statistical properties, such as mean, principal component, hypothesis testing and linear discriminant analysis can be defined. For some of these properties it is still an open problem how to compute them; others (like the mean) can be computed, but efficient alternatives are helpful in speeding up algorithms that use means iteratively, like hypothesis testing. In this paper, we take advantage of a very large dataset (N = 8016) to obtain computable approximations, under the assumption that the data trees parametrize the relevant parts of tree-space well. Using the developed approximate statistics, we illustrate how the structure and geometry of airway trees vary across a population and show that airway trees with Chronic Obstructive Pulmonary Disease come from a different distribution in tree-space than healthy ones. Software is available from http://image.diku.dk/aasa/software.php.

UR - http://www.scopus.com/inward/record.url?scp=84901258938&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-38868-2_7

DO - 10.1007/978-3-642-38868-2_7

M3 - Conference proceeding

C2 - 24683959

AN - SCOPUS:84901258938

SN - 9783642388675

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 74

EP - 85

BT - Information Processing in Medical Imaging - 23rd International Conference, IPMI 2013, Proceedings

T2 - 23rd International Conference on Information Processing in Medical Imaging, IPMI 2013

Y2 - 28 June 2013 through 3 July 2013

ER -