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Radiation therapy for lung cancer using heavy ion particles is going on at the National Institute of Radiological Sciences of Japan. In such a field, image registration between different modalities or different images is very effective for overall and more precious diagnosis and treatment and its realization is strongly desired. In the radiation therapy, three kinds of medical images, namely, CT, SPECT and dose map are used. There are two kinds of CT image, one is CT for treatment planning and the other is CT for diagnosis. For image registration, we use CT images to relate all images. At first, two kinds of CT images are registered by a nonlinear transformation method newly developed. Next, CT image for diagnosis and SPECT images are registered by a linear transformation or a rigid body transformation. The dose map has already a good agreement with the CT for treatment planning. Then, the dose map is nonlinearly transformed using the transformation parameters obtained through the CT-CT matching and a SPECT image is linearly transformed using parameters obtained through the CT-SPECT matching. Finally those images are superposed on the CT for diagnosis and evaluation of lung function is performed. The framework of image registration is presented with detail description on nonlinear transformation of CT images and the application to the evaluation of lung function is shown.