Thoracic non-rigid registration combining self-organizing maps and radial basis functions George K. Matsopoulos a, * , Nikolaos A. Mouravliansky a , Pantelis A. Asvestas a , Konstantinos K. Delibasis a , Vassilis Kouloulias b a Institute of Communications and Computer Systems, National Technical University of Athens, 9, Iroon Polytechniou Street, Zografos, Athens 157 80, Greece b Department of Radiology, Areteion Hospital, Medical School, University of Athens, Greece Received 2 September 2003; received in revised form 21 April 2004; accepted 21 September 2004 Available online 30 December 2004 Abstract An automatic three-dimensional non-rigid registration scheme is proposed in this paper and applied to thoracic computed tomography (CT) data of patients with stage III non-small cell lung cancer (NSCLC). According to the registration scheme, initially anatomical set of points such as the vertebral spine, the ribs, and shoulder blades are automatically segmented slice by slice from the two CT scans of the same patient in order to serve as interpolant points. Based on these extracted features, a rigid-body transfor- mation is then applied to provide a pre-registration of the data. To establish correspondence between the feature points, the novel application of the self-organizing maps (SOMs) is adopted. In particular, the automatic correspondence of the interpolant points is based on the initialization of the Kohonen neural network model capable to identify 500 corresponding pairs of points approxi- mately in the two CT sets. Then, radial basis functions (RBFs) using the shifted log function is subsequently employed for elastic warping of the image volume, using the correspondence between the interpolant points, as obtained in the previous phase. Quan- titative and qualitative results are also presented to validate the performance of the proposed elastic registration scheme resulting in an alignment error of 6 mm, on average, over 15 CT paired datasets. Finally, changes of the tumor volume in respect to each ref- erence dataset are estimated for all patients, which indicate inspiration and/or movement of the patient during acquisition of the data. Thus, the practical implementation of this scheme could provide estimations of lung tumor volumes during radiotherapy treat- ment planning. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Computed tomography; Stage III non-small cell lung cancer; Non-rigid registration; Self-organizing maps; Kohonen neural network; Radial basis functions 1. Introduction Lung cancer, the most preventable of all human can- cers, remains the leading cause of cancer death for both sexes in 2003 (Jemal et al., 2003). Almost one-third of the cancer deaths in men, and almost one-quarter of the cancer deaths in women, are due to lung cancer alone (National Cancer Institute, 1994). The four major types of lung cancer described by the World Health Organization classification are small cell lung cancer (25% of lung cancer), adenocarcinoma (30%), squamous cell carcinoma (25%), and large cell carcinoma (15%) (The World Health Organization, 1982). The last three types are grouped as non-small cell lung cancers (NSCLC) and they have been further categorized in dif- ferent stages (from Stage 0 to Stage IV), depending on 1361-8415/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.media.2004.09.002 * Corresponding author. Tel.: +30 210 7722288/1 7722285; fax: +30 210 7223557/1 7723557. E-mail address: gmatso@esd.ece.ntua.gr (G.K. Matsopoulos). www.elsevier.com/locate/media Medical Image Analysis 9 (2005) 237–254