Registering 3D Lung Surfaces Using the Shape Context Approach * Martin Urschler and Horst Bischof † Institute for Computer Graphics and Vision, Graz University of Technology Abstract.Studying the complex thorax breathing motion is an important research topic for medical (e.g. fusion of function and anatomy, radiotherapy planning) and engineering (reduction of motion artifacts) questions. In this paper we present first results on studying the 4D motion of segmented lung surfaces from CT scans at several different breathing states. For this registration task we extend the shape context approach for shape matching by Belongie et al. [1] from 2D shapes to 3D surfaces and apply it to segmented lung surfaces. Result- ing point correspondences are used for a non-rigid thin-plate-spline registration. We describe our experiments on synthetic and real thorax data and show our quantitative and qualitative results. 1 Introduction According to the European Respiratory Society, lung diseases rank second behind cardiac diseases in terms of mortality and cost of treatment. Computerized methods for objective, accurate and reproducible analysis of lung structure and function can provide important insights into these problems. However, due to the complexity of the breathing motion, investigations are often very complicated. In this paper we present first results on studying the 4D motion of segmented lung surfaces from several different breathing states scanned between Functional Residual Capacity (FRC) and Total Lung Capacity (TLC). We especially regard the problem of matching surfaces from consecutive breathing states and non-rigidly registering them by using a thin-plate-spline transformation model [2] for the deformation of the corresponding points. In general it is not possible to robustly derive corresponding features from the lung surfaces since the diaphragm-induced motion component and the movement of the rib cage tend to deform the elastic lung tissue, such that e.g. ridges might become valleys after deformation. The shape context approach introduced by Belongie et al. [1] was reported as a reasonable and promising method for matching 2D shapes (especially hand-written digits and letters) and 2D object recognition without relying on extracted features. We extend this approach to match 3D shapes and we are up to our knowledge the first ones to apply it to 4D medical image data, i.e. the segmented lung surfaces at several breathing states. Our image data stems from high-speed multi-detector spiral CT sheep studies. The sheep CT data was provided by Prof. Eric Hoffman, University of Iowa. The data is acquired at several (two, four or five) breathing states between TLC and FRC by a protocol where breath is held at fixed inspiration levels during the 30 sec scan time. This leads to a static breathing scheme, which has to be considered for the interpretation of derived motion models from matched and registered shapes. However, a protocol to scan thorax anatomy at different breathing states with high spatial resolution during dynamic (normal) breathing is currently not feasible. The image dimensions per breathing state are 512x512x550 with voxel dimensions of 0.52mm x 0.52mm x 0.6mm. 2 Method 2.1 Related Work An older survey on the state of the art in 2D shape matching can be found in Veltkamp et al. [3]. Audette et al. give an algorithmic overview of surface registration techniques for medical imaging in [4], while Zitova et al. recently published an overview of image registration techniques [5]. Some examples for closely related methods for shape matching/registration are the modal matching approach proposed by Sclaroff et al. [6] or the TPS-RPM (Thin-Plate-Spline - Robust Point Matching) method developed by Chui et al. [7]. The main contribution of the work from Belongie et al. [1] is to present a robust and simple algorithm for finding shape correspondences by using shape context as a very discriminative representation that incorporates global shape information into a local descriptor. 2.2 The Shape Context Approach The shape context approach [1] treats objects as (possibly infinite) point sets and assumes that the shape of an object is captured by a finite subset of its points, giving us a set P = {p 1 , ..., p n }. The points can be obtained as * We gratefully acknowledge the support of Prof. Eric Hoffman, Department of Physiologic Imaging, University of Iowa, Iowa City for providing the CT image data. † EMail: {urschler,bischof}@icg.tu-graz.ac.at