IPMI 2013 - LNCS 7917

Geometric Tree Kernels: Classification of COPD from Airway Tree Geometry

Aasa Feragen^{1, 2}, Jens Petersen¹, Dominik Grimm², Asger Dirksen⁴, Jesper Holst Pedersen⁵, Karsten Borgwardt^{2, 3}, and Marleen de Bruijne^{1, 6}

¹Department of Computer Science, University of Copenhagen, Denmark
aasa@diku.dk
phup@diku.dk
marleen@diku.dk
http://www.image.diku.dk/aasa

²Max Planck Institute for Intelligent Systems and Max Planck Institute for Developmental Biology, Tübingen, Germany
aasa.feragen@tuebingen.mpg.de
dominik.grimm@tuebingen.mpg.de
karsten.borgwardt@tuebingen.mpg.de

³Zentrum für Bioinformatik, Eberhard Karls Universität Tübingen, Germany

⁴Lungemedicinsk Afdeling, Gentofte Hospital, Denmark

⁵Department of Cardiothoracic Surgery, Rigshospitalet, Denmark

⁶Erasmus MC - University Medical Center Rotterdam, The Netherlands

Abstract. Methodological contributions: This paper introduces a family of kernels for analyzing (anatomical) trees endowed with vector valued measurements made along the tree. While state-of-the-art graph and tree kernels use combinatorial tree/graph structure with discrete node and edge labels, the kernels presented in this paper can include geometric information such as branch shape, branch radius or other vector valued properties. In addition to being flexible in their ability to model different types of attributes, the presented kernels are computationally efficient and some of them can easily be computed for large datasets (N ~10.000) of trees with 30 – 600 branches. Combining the kernels with standard machine learning tools enables us to analyze the relation between disease and anatomical tree structure and geometry. Experimental results: The kernels are used to compare airway trees segmented from low-dose CT, endowed with branch shape descriptors and airway wall area percentage measurements made along the tree. Using kernelized hypothesis testing we show that the geometric airway trees are significantly differently distributed in patients with Chronic Obstructive Pulmonary Disease (COPD) than in healthy individuals. The geometric tree kernels also give a significant increase in the classification accuracy of COPD from geometric tree structure endowed with airway wall thickness measurements in comparison with state-of-the-art methods, giving further insight into the relationship between airway wall thickness and COPD. Software: Software for computing kernels and statistical tests is available at http://image.diku.dk/aasa/software.php.

LNCS 7917, p. 171 ff.

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